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Publications de l'équipe Procédés et mécanique aux petites échelles
2017
Henri Gouin, Pierre Seppecher. Temperature profile in a liquid-vapor interface near the critical point. Proceedings of the Royal Society of London. Series A, Mathematical and physical sciences, Royal Society, The, 2017, 473 (20170229), pp.1-13. Plus de détails...
Thanks to an expansion with respect to densities of energy, mass and entropy, we discuss the concept of thermocapillary fluid for inhomogeneous fluids. The non-convex state law valid for homogeneous fluids is modified by adding terms taking account of the gradients of these densities. This seems more realistic than Cahn and Hilliard's model which uses a density expansion in mass-density gradient only. Indeed, through liquid-vapor interfaces, realistic potentials in molecular theories show that entropy density and temperature do not vary with the mass density as it would do in bulk phases. In this paper, we prove using a rescaling process near the critical point that liquid-vapor interfaces behave essentially in the same way as in Cahn and Hilliard's model.
Henri Gouin, Pierre Seppecher. Temperature profile in a liquid-vapor interface near the critical point. Proceedings of the Royal Society of London. Series A, Mathematical and physical sciences, Royal Society, The, 2017, 473 (20170229), pp.1-13. <10.1098/rspa.2017.0229>. <hal-01492802v2>
Journal: Proceedings of the Royal Society of London. Series A, Mathematical and physical sciences
Gwenn Boedec, Marc Leonetti, Marc Jaeger. Isogeometric FEM-BEM simulations of drop, capsule and vesicle dynamics in Stokes flow. Journal of Computational Physics, Elsevier, 2017, 342, pp.117 - 138. Plus de détails...
We develop an algorithm for the three dimensional simulation of the dynamics of soft objects (drops, capsules, vesicles) under creeping flow conditions. Loop elements are used to describe the shape of the soft objects. This surface representation is used both for membrane solver based on finite element method (FEM) and for the fluid solver based on the boundary element method (BEM). This isogeometric analysis of the low Reynolds fluid-structure interaction problem is then coupled to high-order explicit time stepping or second-order implicit time stepping algorithm. For vesicles simulation, a preconditioner is designed for the resolution of the surface velocity incompressibility constraint, which is treated by the use of a local Lagrange multiplier. A mesh quality preserving algorithm is introduced to improve the control mesh quality over long simulation times. We test the proposed algorithm on capsule and vesicle dynamics in various flows, and study its convergence properties, showing a second-order convergence O(N-2) with mesh number of elements.
Gwenn Boedec, Marc Leonetti, Marc Jaeger. Isogeometric FEM-BEM simulations of drop, capsule and vesicle dynamics in Stokes flow. Journal of Computational Physics, Elsevier, 2017, 342, pp.117 - 138. <10.1016/j.jcp.2017.04.024>. <hal-01590257>
Xue Chen, Xun Wang, Paul G. Chen, Qiusheng Liu. Thermal effects of substrate on Marangoni flow in droplet evaporation: Response surface and sensitivity analysis. International Journal of Heat and Mass Transfer, Elsevier, 2017, 113, pp.354 - 365. Plus de détails...
In this paper, the evaporation of sessile droplets resting on a substrate with different thermal properties is numerically investigated. Computations are based on a transient axisymmetric numerical model. Special attention is paid to evaluate thermal effects of substrate on the structure of bulk fluid flow in the course of evaporation. Numerical results reveal that Marangoni convection induced by non-uniform distribution of temperature along the interface exhibits three distinctly different behaviours: inward flow, multicellular flow and outward flow, consequently resulting in different particle depositions. It is highlighted that three factors (i.e. relative thermal conductivity, relative substrate thickness and relative substrate temperature) strongly affect the flow pattern. In order to further investigate the coupling effects of different influential factors, a Kriging-based response surface method is introduced. We model the flow behaviour as a function of continuous influential factors using a limited number of computations corresponding to discrete values of the inputs. The sensitivities of the Marangoni flow are also analysed using Sobol’ index to study the coupling mechanisms of influential factors. The proposed method can be used to forecast the flow patterns for any input parameter without additional sophisticated computer simulation, and allows to confidently estimate an unknown environmental parameter.
Xue Chen, Xun Wang, Paul G. Chen, Qiusheng Liu. Thermal effects of substrate on Marangoni flow in droplet evaporation: Response surface and sensitivity analysis. International Journal of Heat and Mass Transfer, Elsevier, 2017, 113, pp.354 - 365. <10.1016/j.ijheatmasstransfer.2017.05.076>. <hal-01532757>
Journal: International Journal of Heat and Mass Transfer
Xue Chen, Paul G. Chen, Jalil Ouazzani, Qiusheng Liu. Numerical simulations of sessile droplet evaporating on heated substrate. European Physical Journal - Special Topics, EDP Sciences, 2017, 226 (6), pp.1325-1335. Plus de détails...
Motivated by the space project EFILE, a 2D axisymmetric numerical model in the framework of ALE method is developed to investigate the coupled physical mechanism during the evaporation of a pinned drop that partially wets on a heated substrate. The model accounts for mass transport in surrounding air, Marangoni convection inside the drop and heat conduction in the substrate as well as moving interface. Numerical results predict simple scaling laws for the evaporation rate which scales linearly with drop radius but follows a power-law with substrate temperature. It is highlighted that thermal effect of the substrate has a great impact on the temperature profile at the drop surface, which leads to a multicellular thermocapillary flow pattern. In particular, the structure of the multicellular flow behavior induced within a heated drop is mainly controlled by a geometric parameter (aspect ratio). A relationship between the number of thermal cells and the aspect ratio is proposed。
Xue Chen, Paul G. Chen, Jalil Ouazzani, Qiusheng Liu. Numerical simulations of sessile droplet evaporating on heated substrate. European Physical Journal - Special Topics, EDP Sciences, 2017, 226 (6), pp.1325-1335. <10.1140/epjst/e2016-60203-y>. <hal-01509843>
Journal: European Physical Journal - Special Topics
B. Bernales, Pierre Haldenwang, Pierrette Guichardon, Nelson Ibaseta. Prandtl model for concentration polarization and osmotic counter-effects in a 2-D membrane channel. Desalination, Elsevier, 2017, 404, pp.341 - 359. Plus de détails...
B. Bernales, Pierre Haldenwang, Pierrette Guichardon, Nelson Ibaseta. Prandtl model for concentration polarization and osmotic counter-effects in a 2-D membrane channel. Desalination, Elsevier, 2017, 404, pp.341 - 359. <10.1016/j.desal.2016.09.026>. <hal-01405589>
E Alekseenko, B Roux, D Fougere, Paul G. Chen. The effect of wind induced bottom shear stress and salinity on Zostera noltii replanting in a Mediterranean coastal lagoon. Estuarine, Coastal and Shelf Science, Elsevier, 2017, 187, pp.293-305. Plus de détails...
The paper concerns the wind influence on bottom shear stress and salinity levels in a Mediterranean semi-enclosed coastal lagoon (Etang de Berre), with respect to a replanting program of Zostera noltii . The MARS3D numerical model is used to analyze the 3D current, salinity and temperature distribution induced by three meteorological, oceanic and anthropogenic forcings in this lagoon. The numerical model has been carefully validated by comparison with daily observations of the vertical salinity and temperature profiles at three mooring stations, for one year. Then, two modelling scenarios are considered. The first scenario (scen.## 1), starting with an homogeneous salinity of S = 20 PSU and without wind forcing, studies a stratification process under the influence of a periodic seawater inflow and a strong freshwater inflow from an hydropower plant (250 m3/s). Then, in the second scenario (scen.## 2), we study how a strong wind of 80 km/h can mix the haline stratification obtained at the end of scen.## 1. The most interesting results concern four nearshore replanting areas; two are situated on the eastern side of EB and two on the western side. The results of scen.## 2 show that all these areas are subject to a downwind coastal jet. Concerning bottom salinity, the destratification process is very beneficial; it always remains greater than 12 PSU for a N-NW wind of 80 km/h and an hydropower runoff of 250 m3/s. Special attention is devoted to the bottom shear stress (BSS) for different values of the bottom roughness parameter (for gravels, sands and silts), and to the bottom salinity. Concerning BSS, it presents a maximum near the shoreline and decreases along transects perpendicular to the shoreline. There exists a zone, parallel to the shoreline, where BSS presents a minimum (close to zero). When comparing the BSS value at the four replanting areas with the critical value, BSScr, at which the sediment mobility would occur, we see that for the smaller roughness values (ranging from z0 = 3.5 × 10-4 mm, to 3.5 × 10-2 mm) BSS largely surpasses this critical value. For a N-NW wind speed of 40 km/h (which is blowing for around 100 days per year), BSS still largely surpasses BSScr - at least for the silt sediments (ranging from z0 = 3.5 × 10-4 mm, to 3.5 × 10-3 mm). This confirms the possibility that the coastal jet could generate sediment mobility which could have a negative impact for SAV replanting.
E Alekseenko, B Roux, D Fougere, Paul G. Chen. The effect of wind induced bottom shear stress and salinity on Zostera noltii replanting in a Mediterranean coastal lagoon. Estuarine, Coastal and Shelf Science, Elsevier, 2017, 187, pp.293-305. <10.1016/j.ecss.2017.01.010>. <hal-01453377>
Henri Gouin, Tommaso Ruggeri. Symmetric form for the hyperbolic-parabolic system of fourth-gradient fluid model. Ricerche di matematica, Springer Verlag, 2017, 37, pp.1495 . Plus de détails...
The fourth-gradient model for fluids-associated with an extended molecular mean-field theory of capillarity-is considered. By producing fluctuations of density near the critical point like in computational molecular dynamics, the model is more realistic and richer than van der Waals' one and other models associated with a second order expansion. The aim of the paper is to prove-with a fourth-gradient internal energy already obtained by the mean field theory-that the quasi-linear system of conservation laws can be written in an Hermitian symmetric form implying the stability of constant solutions. The result extends the symmetric hyperbolicity property of governing-equations' systems when an equation of energy associated with high order deformation of a continuum medium is taken into account.
Henri Gouin, Tommaso Ruggeri. Symmetric form for the hyperbolic-parabolic system of fourth-gradient fluid model. Ricerche di matematica, Springer Verlag, 2017, 37, pp.1495 <10.1016/S0020-7225(98)00131-1>. <hal-01573721>
Henri Gouin. Continuum mechanics at nanoscale. A tool to study trees' watering and recovery.. Rendiconti Lincei - Matematica e Applicazioni, European Mathematical Society, 2017. Plus de détails...
The cohesion-tension theory expounds the crude sap ascent thanks to the negative pressure generated by evaporation of water from leaves. Nevertheless, trees pose multiple challenges and seem to live in unphysical conditions: the negative pressure increases cavitation; it is possible to obtain a water equilibrium between connected parts where one is at a positive pressure and the other one is at negative pressure; no theory is able to satisfactorily account for the refilling of vessels after embolism events. A theoretical form of our paper in the Journal of Theoretical Biology is proposed together with new results: a continuum mechanics model of the disjoining pressure concept refers to the Derjaguin School of physical chemistry. A comparison between liquid behaviour both in tight-filled microtubes and in liquid thin-films is offered when the pressure is negative in liquid bulks and is positive in liquid thin-films and vapour bulks. In embolized xylem microtubes, when the air-vapour pocket pressure is greater than the air-vapour bulk pressure, a refilling flow occurs between the air-vapour domains to empty the air-vapour pockets although the liquid-bulk pressure remains negative. The model has a limit of validity taking the maximal size of trees into account. These results drop inkling that the disjoining pressure is an efficient tool to study biological liquids in contact with substrates at a nanoscale range.
Henri Gouin. Continuum mechanics at nanoscale. A tool to study trees' watering and recovery.. Rendiconti Lincei - Matematica e Applicazioni, European Mathematical Society, 2017. <hal-01540964>
Journal: Rendiconti Lincei - Matematica e Applicazioni
Camille Maumet, Tibor Auer, Alexander Bowring, Gang Chen, Samir Das, et al.. Sharing brain mapping statistical results with the neuroimaging data model. Scientific Data , Nature Publishing Group, 2016, 3, . Plus de détails...
Only a tiny fraction of the data and metadata produced by an fMRI study is finally conveyed to the community. This lack of transparency not only hinders the reproducibility of neuroimaging results but also impairs future meta-analyses. In this work we introduce NIDM-Results, a format specification providing a machine-readable description of neuroimaging statistical results along with key image data summarising the experiment. NIDM-Results provides a unified representation of mass univariate analyses including a level of detail consistent with available best practices. This standardized representation allows authors to relay methods and results in a platform-independent regularized format that is not tied to a particular neuroimaging software package. Tools are available to export NIDM-Result graphs and associated files from the widely used SPM and FSL software packages, and the NeuroVault repository can import NIDM-Results archives. The specification is publically available at: http://nidm.nidash.org/specs/nidm-results.html.
Camille Maumet, Tibor Auer, Alexander Bowring, Gang Chen, Samir Das, et al.. Sharing brain mapping statistical results with the neuroimaging data model. Scientific Data , Nature Publishing Group, 2016, 3, <10.1038/sdata.2016.102>. <inserm-01411025>
Henri Gouin. Properties of thermocapillary fluids and symmetrization of motion equations. International Journal of Non-Linear Mechanics, Elsevier, 2016, 85, pp.152-160. Plus de détails...
The equations of fluid motions are considered in the case of internal energy depending on mass density, volume entropy and their spatial derivatives. The model corresponds to domains with large density gradients in which the temperature is not necessarily uniform. The new general representation is written in symmetric form with respect to the mass and entropy densities. For conservative motions of perfect thermocapillary fluids, Kelvin's circulation theorems are always valid. Dissipative cases are also considered; we obtain the balance of energy and we prove that equations are compatible with the second law of thermodynamics. The internal energy form allows to obtain a Legendre transformation inducing a quasi-linear system of conservation laws which can be written in a divergence form and the stability near equilibrium positions can be deduced. The result extends classical hyperbolicity theory for governing equations' systems in hydrodynamics, but symmetric matrices are replaced by Hermitian matrices. (C) 2016 Elsevier Ltd. All rights reserved.
Henri Gouin. Properties of thermocapillary fluids and symmetrization of motion equations. International Journal of Non-Linear Mechanics, Elsevier, 2016, 85, pp.152-160. <10.1016/j.ijnonlinmec.2016.06.003>. <hal-01461793>
Journal: International Journal of Non-Linear Mechanics
Henri Gouin. Properties of thermocapillary fluids and symmetrization of motion equations. International Journal of Non-Linear Mechanics, Elsevier, 2016, 85, pp.152 - 160. Plus de détails...
The equations of fluid motions are considered in the case of internal energy depending on mass density, volume entropy and their spatial derivatives. The model corresponds to domains with large density gradients in which the temperature is not necessary uniform. In this new general representation writes in symmetric form with respect to the mass and entropy densities. For conservative motions of perfect thermocapillary fluids, Kelvin's circulation theorems are always valid. Dissipative cases are also considered; we obtain the balance of energy and we prove that equations are compatible with the second law of thermodynamics. The internal energy form allows to obtain a Legendre transformation inducing a quasi-linear system of conservation laws which can be written in a divergence form and the stability near equilibrium positions can be deduced. The result extends classical hyperbolicity theory for governing-equations' systems in hydrodynamics, but symmetric matrices are replaced by Hermitian matrices.
Henri Gouin. Properties of thermocapillary fluids and symmetrization of motion equations. International Journal of Non-Linear Mechanics, Elsevier, 2016, 85, pp.152 - 160. <10.1016/j.ijnonlinmec.2016.06.003>. <hal-01541196>
Journal: International Journal of Non-Linear Mechanics
Gustavo H. Lopes, Nelson Ibaseta, Pierrette Guichardon. How can osmosis and solute diffusion be coupled for the simultaneous measurement of the solvent and solute permeabilities of membranes?. Desalination, Elsevier, 2016, 387, pp.61. . Plus de détails...
A novel experimental method and its associated model are proposed for the simultaneous determination of membrane solute and solvent permeabilities, which are essential transport parameters of reverse osmosis models used for process simulation. The method utilizes a single bench-scale batch apparatus consisting of two stirred half-cells containing solutions of different concentrations separated by a membrane across which coupled non-steady-state solute diffusion and solvent osmosis take place countercurrently in the absence of transmembrane pressure difference. Results are presented from days-long determinations of the water and sodium chloride permeabilities of Filmtec BW30 and NF270 membrane samples for initial transmembrane salt concentration differences ranging from 1 g L-1 to 35 g L-1. When used as input parameters for the simulation of pilot reverse osmosis desalination tests, the osmotic-diffusive salt permeabilities approximated the experimental rejection rates.
Gustavo H. Lopes, Nelson Ibaseta, Pierrette Guichardon. How can osmosis and solute diffusion be coupled for the simultaneous measurement of the solvent and solute permeabilities of membranes?. Desalination, Elsevier, 2016, 387, pp.61. <http://www.sciencedirect.com/science/article/pii/S0011916416301011>. <10.1016/j.desal.2016.03.006>. <hal-01290973>
J. Gounley, G. Boedec, Marc Jaeger, M. Leonetti. Influence of surface viscosity on droplets in shear flow. Journal of Fluid Mechanics, Cambridge University Press (CUP), 2016, 791, pp.464- 494. Plus de détails...
The behaviour of a single droplet in an immiscible external fluid, submitted to shear flow is investigated using numerical simulations. The surface of the droplet is modelled by a Boussinesq–Scriven constitutive law involving the interfacial viscosities and a constant surface tension. A numerical method using Loop subdivision surfaces to represent droplet interface is introduced. This method couples boundary element method for fluid flows and finite element method to take into account the stresses due to the surface dilational and shear viscosities and surface tension. Validation of the numerical scheme with respect to previous analytic and computational work is provided, with particular attention to the viscosity contrast and the shear and dilational viscosities characterized both by a Boussinesq number Bq. Then, influence of equal surface viscosities on steady-state characteristics of a droplet in shear flow are studied, considering both small and large deformations and for a large range of bulk viscosity contrast. We find that small deformation analysis is surprisingly predictive at moderate and high surface viscosities. Equal surface viscosities decrease the Taylor deformation parameter and tank-treading angle and also strongly modify the dynamics of the droplet: when the Boussinesq number (surface viscosity) is large relative to the capillary number (surface tension), the droplet displays damped oscillations prior to steady-state tank-treading, reminiscent from the behaviour at large viscosity contrast. In the limit of infinite capillary number Ca, such oscillations are permanent. The influence of surface viscosities on breakup is also investigated, and results show that the critical capillary number is increased. A diagram (Bq;Ca) of breakup is established with the same inner and outer bulk viscosities. Additionally, the separate roles of shear and dilational surface viscosity are also elucidated, extending results from small deformation analysis. Indeed, shear (dilational) surface viscosity increases (decreases) the stability of drops to breakup under shear flow. The steady-state deformation (Taylor parameter) varies nonlinearly with each Boussinesq number or a linear combination of both Boussinesq numbers. Finally, the study shows that for certain combinations of shear and dilational viscosities, drop deformation for a given capillary number is the same as in the case of a clean surface while the inclination angle varies.
J. Gounley, G. Boedec, Marc Jaeger, M. Leonetti. Influence of surface viscosity on droplets in shear flow. Journal of Fluid Mechanics, Cambridge University Press (CUP), 2016, 791, pp.464- 494. <10.1017/jfm.2016.39>. <hal-01281643>
Henri Gouin, Giuseppe Saccomandi. Travelling waves of density for a fourth-gradient model of fluids. Continuum Mechanics and Thermodynamics, Springer Verlag, 2016, 28 (5), pp.1511 - 1523. Plus de détails...
In mean-field theory, the non-local state of fluid molecules can be taken into account using a statistical method. The molecular model combined with a density expansion in Taylor series of the fourth order yields an internal energy value relevant to the fourth-gradient model, and the equation of isother-mal motions takes then density's spatial derivatives into account for waves travelling in both liquid and vapour phases. At equilibrium, the equation of the density profile across interfaces is more precise than the Cahn and Hilliard equation, and near the fluid's critical-point, the density profile verifies an Extended Fisher-Kolmogorov equation, allowing kinks, which converges towards the Cahn-Hillard equation when approaching the critical point. Nonetheless, we also get pulse waves oscillating and generating critical opalescence.
Henri Gouin, Giuseppe Saccomandi. Travelling waves of density for a fourth-gradient model of fluids. Continuum Mechanics and Thermodynamics, Springer Verlag, 2016, 28 (5), pp.1511 - 1523. <10.1007/s00161-016-0492-3>. <hal-01480940>
Achim Guckenberger, Marcel P. Schrame, Paul G. Chen, Marc Leonetti, Stephan Gekle. On the bending algorithms for soft objects in flows. Computer Physics Communications, Elsevier, 2016, 207, pp.1-23. Plus de détails...
One of the most challenging aspects in the accurate simulation of three-dimensional soft objects such as vesicles or biological cells is the computation of membrane bending forces. The origin of this difficulty stems from the need to numerically evaluate a fourth order derivative on the discretized surface geometry. Here we investigate six different algorithms to compute membrane bending forces, including regularly used methods as well as novel ones. All are based on the same physical model (due to Canham and Helfrich) and start from a surface discretization with flat triangles. At the same time, they differ substantially in their numerical approach. We start by comparing the numerically obtained mean curvature, the Laplace-Beltrami operator of the mean curvature and finally the surface force density to analytical results for the discocyte resting shape of a red blood cell. We find that none of the considered algorithms converges to zero error at all nodes and that for some algorithms the error even diverges. There is furthermore a pronounced influence of the mesh structure: Discretizations with more irregular triangles and node connectivity present serious difficulties for most investigated methods. To assess the behavior of the algorithms in a realistic physical application, we investigate the deformation of an initially spherical capsule in a linear shear flow at small Reynolds numbers. To exclude any influence of the flow solver, two conceptually very different solvers are employed: the Lattice-Boltzmann and the Boundary Integral Method. Despite the largely different quality of the bending algorithms when applied to the static red blood cell, we find that in the actual flow situation most algorithms give consistent results for both hydrodynamic solvers. Even so, a short review of earlier works reveals a wide scattering of reported results for, e.g., the Taylor deformation parameter. Besides the presented application to biofluidic systems, the investigated algorithms are also of high relevance to the computer graphics and numerical mathematics communities.
Achim Guckenberger, Marcel P. Schrame, Paul G. Chen, Marc Leonetti, Stephan Gekle. On the bending algorithms for soft objects in flows. Computer Physics Communications, Elsevier, 2016, 207, pp.1-23. <10.1016/j.cpc.2016.04.018>. <hal-01314722>
Umberto D'Ortona, Nathalie Thomas, Richard M. Lueptow. Influence of Rough and Smooth Walls on Macroscale Granular Segregation Patterns. Physical Review E , American Physical Society (APS), 2016, 93 (2), pp.022906. Plus de détails...
Size bidisperse granular materials in a spherical tumbler segregate into two different patterns of three bands with either small particles at the equator and large particles at the poles or vice versa, depending upon the fill level in the tumbler. Here we use discrete element method (DEM) simulations with supporting qualitative experiments to explore the effect of the tumbler wall roughness on the segregation pattern, modeling the tumbler walls as either a closely packed monolayer of fixed particles resulting in a rough wall, or as a geometrically smooth wall. Even though the tumbler wall is in contact with the flowing layer only at its periphery, the impact of wall roughness is profound. Smooth walls tend toward a small-large-small (SLS) band pattern at the pole-equator-pole at all but the highest fill fractions; rough walls tend toward a large-small-large (LSL) band pattern at all but the lowest fill fractions. This comes about because smooth walls induce poleward axial drift of small particles and an equator-directed drift for large particles, resulting in an SLS band pattern. On the other hand, rough walls result in both sizes of particles moving poleward at the surface of the flow, but due to radial segregation, small particles percolate lower in the flowing layer where there is a return drift toward the equator while large particles remain at the surface near the pole, resulting in an LSL band pattern. The tendency toward either of the two band patterns depends on the fill level in the tumbler and the roughness of the tumbler's bounding wall.
Umberto D'Ortona, Nathalie Thomas, Richard M. Lueptow. Influence of Rough and Smooth Walls on Macroscale Granular Segregation Patterns. Physical Review E , American Physical Society (APS), 2016, 93 (2), pp.022906. <10.1103/PhysRevE.93.022906>. <hal-01306600>
R. Trozzo, G. Boedec, M. Leonetti, M. Jaeger. Axisymmetric Boundary Element Method for vesicles in a capillary. Journal of Computational Physics, Elsevier, 2015, 289, pp.62-82. Plus de détails...
The problem of a vesicle transported by a fluid flow can present a large range of length scales. One example is the case of a vesicle producing a tether, and eventually pearls, in an elongational flow. Another case occurs when a lubrication film is formed, such as during the short range interaction between two vesicles. Such problems are still challenging for 3D simulations. On the other hand, a good understanding could be obtained by first considering the axisymmetric regime when such a regime exists. An axisymmetric model could then be used, without the criticisms that can be made of a 2D approach. We propose such a model, primarily interested in flows through narrow cylindrical capillaries. Two options are compared, with and without explicit representation of the capillary boundaries by a mesh. The numerical effort is characterized as a function of the vesicle’s initial shape, the flow magnitude and the confinement. The model is able to treat typical configurations of red blood cells flowing through very narrow pores with extremely thin lubrication films.
R. Trozzo, G. Boedec, M. Leonetti, M. Jaeger. Axisymmetric Boundary Element Method for vesicles in a capillary. Journal of Computational Physics, Elsevier, 2015, 289, pp.62-82. <10.1016/j.jcp.2015.02.022>. <hal-01281961>
Henri Gouin. The watering of tall trees - Embolization and recovery: Crude sap ascent and tree recovery. Journal of Theoretical Biology, Elsevier, 2015, 369, pp.42 - 50. Plus de détails...
We can propound a thermo-mechanical understanding of the ascent of sap to the top of tall trees thanks to a comparison between experiments associated with the cohesion-tension theory and the disjoining pressure concept for liquid thin-films. When a segment of xylem is tight-filled with crude sap, the liquid pressure can be negative although the pressure in embolized vessels remains positive. Examples are given that illustrate how embolized vessels can be refilled and why the ascent of sap is possible even in the tallest trees avoiding the problem due to cavitation. However, the maximum height of trees is limited by the stability domain of liquid thin-films.
Henri Gouin. The watering of tall trees - Embolization and recovery: Crude sap ascent and tree recovery. Journal of Theoretical Biology, Elsevier, 2015, 369, pp.42 - 50. <10.1016/j.jtbi.2015.01.009>. <hal-00979793v2>
Umberto D'Ortona, Nathalie Thomas, Zafir Zaman, Richard M. Lueptow. Influence of rough and smooth walls on macroscale flows in tumblers. Physical Review E : Statistical, Nonlinear, and Soft Matter Physics, American Physical Society, 2015, 92 (6), pp.062202. Plus de détails...
Walls in discrete element method simulations of granular flows are sometimes modeled as a closely packed monolayer of fixed particles, resulting in a rough wall rather than a geometrically smooth wall. An implicit assumption is that the resulting rough wall differs from a smooth wall only locally at the particle scale. Here we test this assumption by considering the impact of the wall roughness at the periphery of the flowing layer on the flow of monodisperse particles in a rotating spherical tumbler. We find that varying the wall roughness significantly alters average particle trajectories even far from the wall. Rough walls induce greater poleward axial drift of particles near the flowing layer surface but decrease the curvature of the trajectories. Increasing the volume fill level in the tumbler has little effect on the axial drift for rough walls but increases the drift while reducing curvature of the particle trajectories for smooth walls. The mechanism for these effects is related to the degree of local slip at the bounding wall, which alters the flowing layer thickness near the walls, affecting the particle trajectories even far from the walls near the equator of the tumbler. Thus, the proper choice of wall conditions is important in the accurate simulation of granular flows, even far from the bounding wall.
Umberto D'Ortona, Nathalie Thomas, Zafir Zaman, Richard M. Lueptow. Influence of rough and smooth walls on macroscale flows in tumblers. Physical Review E : Statistical, Nonlinear, and Soft Matter Physics, American Physical Society, 2015, 92 (6), pp.062202. <10.1103/PhysRevE.92.062202>. <hal-01306604>
Journal: Physical Review E : Statistical, Nonlinear, and Soft Matter Physics
G. Boedec, Marc Jaeger, Marc Leonetti. Pearling instability of a cylindrical vesicle. Journal of Fluid Mechanics, Cambridge University Press (CUP), 2014, 743, pp.262-279. Plus de détails...
A cylindrical vesicle under tension can undergo a pearling instability, characterized by the growth of a sinusoidal perturbation which evolves towards a collection of quasi-spherical bulbs connected by thin tethers, like pearls on a necklace. This is reminiscent of the well-known Rayleigh-Plateau instability, where surface tension drives the amplification of sinusoidal perturbations of a cylinder of fluid. We calculate the growth rate of perturbations for a cylindrical vesicle under tension, considering the effect of both inner and outer fluids, with different viscosities. We show that this situation differs strongly from the classical Rayleigh-Plateau case in the sense that, first, the tension must be above a critical value for the instability to develop and, second, even in the strong tension limit, the surface preservation constraint imposed by the presence of the membrane leads to a different asymptotic behaviour. The results differ from previous studies on pearling due to the consideration of variations of tension, which are shown to enhance the pearling instability growth rate, and lower the wavenumber of the fastest growing mode.
G. Boedec, Marc Jaeger, Marc Leonetti. Pearling instability of a cylindrical vesicle. Journal of Fluid Mechanics, Cambridge University Press (CUP), 2014, 743, pp.262-279. <10.1017/jfm.2014.34>. <hal-01050140>
The equations governing the conditions of mechanical equilibrium in fluid membranes subject to bending are revisited thanks to the principle of virtual work. The note proposes systematic tools to obtain the shape equation and the line condition instead of Christoffel symbols and the complex calculations they entail. The method seems adequate to investigate all problems involving surface energies.
Henri Gouin. Vesicle model with bending energy revisited. Acta Applicandae Mathematicae, Springer Verlag, 2014, <10.1007/s10440-014-9907-y>. <hal-01216424>
Joan Escandell, Isabelle Raspo, Evelyne Neau. Prediction of Solid Polycyclic Aromatic Hydrocarbons Solubility in Water with the NRTL-PR Model. Fluid Phase Equilibria, Elsevier, 2014, 362 (25), pp.87-95. Plus de détails...
The accurate prediction of high pressure phase equilibria is crucial for the development and the design of chemical engineering processes. Among them the modeling of complex systems, such as petroleum fluids with water, has become more and more important with the exploitation of reservoirs in extreme conditions. The aim of this work is to explore the capability of the NRTL-PR model to predict the solubility of solid polycyclic aromatic hydrocarbons in water. For this purpose, we first validate our methodology for fluid phase equilibria predictions of aromatic hydrocarbons and gas (CO2, C2H6) mixtures. Finally, we consider the prediction of the solid solubility of PAH in water, by fitting group parameters either only on SLE data or on both LLE and SLE data of aromatic hydrocarbon-water binary systems.
Joan Escandell, Isabelle Raspo, Evelyne Neau. Prediction of Solid Polycyclic Aromatic Hydrocarbons Solubility in Water with the NRTL-PR Model. Fluid Phase Equilibria, Elsevier, 2014, 362 (25), pp.87-95. <10.1016/j.fluid.2013.09.009>. <hal-00872639>
Henri Gouin. Interfaces endowed with nonconstant surface energies revisited with the d'Alembert–Lagrange principle. Mathematics and Mechanics of Complex Systems, mdp, 2014, 2 (1), pp.23-43. Plus de détails...
The equation of motion and the conditions on surfaces and edges between fluids and solids in the presence of nonconstant surface energies, as in the case of surfactants attached to fluid particles at the interfaces, are revisited under the principle of virtual work. We point out that adequate behaviors of surface concentrations may drastically modify the surface tension which naturally appears in the Laplace and the Young–Dupré equations. Thus, the principle of virtual work points out a strong difference between the two revisited concepts of surface energy and surface tension.
Henri Gouin. Interfaces endowed with nonconstant surface energies revisited with the d'Alembert–Lagrange principle. Mathematics and Mechanics of Complex Systems, mdp, 2014, 2 (1), pp.23-43. <hal-01152429>
Journal: Mathematics and Mechanics of Complex Systems
Mihail Garajeu, Henri Gouin, Giuseppe Saccomandi. Scaling Navier-Stokes Equation in Nanotubes. Physics of Fluids, American Institute of Physics, 2013, 25, pp.082003. Plus de détails...
On one hand, classical Monte Carlo and molecular dynamics (MD) simulations have been very useful in the study of liquids in nanotubes, enabling a wide variety of properties to be calculated in intuitive agreement with experiments. On the other hand, recent studies indicate that the theory of continuum breaks down only at the nanometer level; consequently flows through nanotubes still can be investigated with Navier-Stokes equations if we take suitable boundary conditions into account. The aim of this paper is to study the statics and dynamics of liquids in nanotubes by using methods of non-linear continuum mechanics. We assume that the nanotube is filled with only a liquid phase; by using a second gradient theory the static profile of the liquid density in the tube is analytically obtained and compared with the profile issued from molecular dynamics simulation. Inside the tube there are two domains: a thin layer near the solid wall where the liquid density is non-uniform and a central core where the liquid density is uniform. In the dynamic case a closed form analytic solution seems to be no more possible, but by a scaling argument it is shown that, in the tube, two distinct domains connected at their frontiers still exist. The thin inhomogeneous layer near the solid wall can be interpreted in relation with the Navier length when the liquid slips on the boundary as it is expected by experiments and molecular dynamics calculations.
Mihail Garajeu, Henri Gouin, Giuseppe Saccomandi. Scaling Navier-Stokes Equation in Nanotubes. Physics of Fluids, American Institute of Physics, 2013, 25, pp.082003. <10.1063/1.4818159>. <hal-00903295>
Henri Gouin. Motions in liquid-vapour interfaces by using a continuous mechanical model. AAPP | Physical, Mathematical, and Natural Sciences, Accademia Peloritana dei Pericolanti, 2013, 91 (Suppl. No. 1), pp.A10. Plus de détails...
By using a limit analysis for the motion equations of viscous fluid endowed with internal capillarity, we are able to propose a dynamical expression for the surface tension of moving liquid-vapour interfaces without any phenomenological assumption. The proposed relation extends the static case, yields the Laplace formula in cases of mass transfer across interfacial layers and allows to take the second coefficient of viscosity of compressible fluids into account. We generalize the Maxwell rule in dynamics and directly explain the Marangoni effect.
Henri Gouin. Motions in liquid-vapour interfaces by using a continuous mechanical model. AAPP | Physical, Mathematical, and Natural Sciences, Accademia Peloritana dei Pericolanti, 2013, 91 (Suppl. No. 1), pp.A10. <10.1478/AAPP.91S1A10>. <hal-00905148>
Journal: AAPP | Physical, Mathematical, and Natural Sciences
Zafir Zaman, Umberto D'Ortona, Paul B. Umbanhowar, Julio M. Ottino, Richard M. Lueptow. Slow axial drift in three-dimensional granular tumbler flow. Physical Review E : Statistical, Nonlinear, and Soft Matter Physics, American Physical Society, 2013, 88 (1), pp.012208. Plus de détails...
Models of monodisperse particle flow in partially filled three-dimensional tumblers often assume that flow along the axis of rotation is negligible. We test this assumption, for spherical and double cone tumblers, using experiments and discrete element method simulations. Cross sections through the particle bed of a spherical tumbler show that, after a few rotations, a colored band of particles initially perpendicular to the axis of rotation deforms: particles near the surface drift toward the pole, while particles deeper in the flowing layer drift toward the equator. Tracking of mm-sized surface particles in tumblers with diameters of 8-14 cm shows particle axial displacements of one to two particle diameters, corresponding to axial drift that is 1-3% of the tumbler diameter, per pass through the flowing layer. The surface axial drift in both double cone and spherical tumblers is zero at the equator, increases moving away from the equator, and then decreases near the poles. Comparing results for the two tumbler geometries shows that wall slope causes axial drift, while drift speed increases with equatorial diameter. The dependence of axial drift on axial position for each tumbler geometry is similar when both are normalized by their respective maximum values.
Zafir Zaman, Umberto D'Ortona, Paul B. Umbanhowar, Julio M. Ottino, Richard M. Lueptow. Slow axial drift in three-dimensional granular tumbler flow. Physical Review E : Statistical, Nonlinear, and Soft Matter Physics, American Physical Society, 2013, 88 (1), pp.012208. <10.1103/PhysRevE.88.012208>. <hal-00905562>
Journal: Physical Review E : Statistical, Nonlinear, and Soft Matter Physics
Marc Leonetti, Gwenn Boedec, Marc Jaeger. Breathing instability in biological cells, patterns of membrane proteins. Discontinuity, Nonlinearity, and Complexity, 2013, 2 (1), pp.75-84. Plus de détails...
The activity of biological cells involves often the electric activity of its membranes which exhibit various spatiotemporal dynamics, from pulse, oscillatory bifurcation to stationary spatial modulation. This last kind of patterns appears on a typical diffusive time. A model has been proposed implying a coupling between the current flowing through membrane proteins and their electrophoretic motions in the case of mobile proteins. Here, we study the stability of the pattern in a 2D circular model cell versus the appearance of standing waves, the so-called breathing secondary instability.
Marc Leonetti, Gwenn Boedec, Marc Jaeger. Breathing instability in biological cells, patterns of membrane proteins. Discontinuity, Nonlinearity, and Complexity, 2013, 2 (1), pp.75-84. <10.5890/DNC.2012.12.001>. <hal-00997680>
Journal: Discontinuity, Nonlinearity, and Complexity
Henri Gouin. Interfaces endowed with non-constant surface energies revisited with the d'Alembert-Lagrange principle. Mathematics and Mechanics of Complex Systems, mdp, 2013, 1 (3), pp.248-269. Plus de détails...
The equation of motions and the conditions on surfaces and edges between fluids and solids in presence of non-constant surface energies, as in the case of surfactants attached to the fluid particles at the interfaces, are revisited under the principle of virtual work. We point out that adequate behaviors of surface concentrations may drastically modify the surface tension which naturally appears in the Laplace and the Young-Dupré equations. Thus, the principle of virtual work points out a strong difference between the two revisited concepts of surface energy and surface tension.
Henri Gouin. Interfaces endowed with non-constant surface energies revisited with the d'Alembert-Lagrange principle. Mathematics and Mechanics of Complex Systems, mdp, 2013, 1 (3), pp.248-269. <10.2140/memocs2013>. <hal-00880256>
Journal: Mathematics and Mechanics of Complex Systems
H. Hchaichi, Hamza Elfil, Pierrette Guichardon, Ahmed Hannachi. Scaling tendency assessment in reverse osmosis modules. Desalination and Water Treatment, FHF, 2013, 51 (4-6), pp.892-898. Plus de détails...
A mathematical model was developed to predict super saturation along ă reverse osmosis modules (RO) for water desalination. This model is based on conservation principles and chemical equilibrium equations for concentrated solutions. Pitzer's model was used for the activity coefficient calculations. An average rejection rate for each ionic species was also considered. Supersaturations with respect to all calcium carbonate forms and to calcium sulfate are calculated. The model allows assessing when scale is likely to occur along the RO modules. The results for two brackish water qualities and seawater are shown.
H. Hchaichi, Hamza Elfil, Pierrette Guichardon, Ahmed Hannachi. Scaling tendency assessment in reverse osmosis modules. Desalination and Water Treatment, FHF, 2013, 51 (4-6), pp.892-898. <10.1080/19443994.2012.715410>. <hal-01464722>
T. Prusek, E. Moleiro, F. Oukacine, A. Adobes, Marc Jaeger, et al.. Deposit models for tube support plate flow blockage in Steam Generators. Nuclear Engineering and Design, Elsevier, 2013, 262, pp.418-428. Plus de détails...
Corrosion product deposits in the secondary side of nuclear power plant Steam Generators may result in Tube Support Plate flow blockage, and tube fouling. In order to simulate those two phenomena in the whole Steam Generator, a solid deposit growth model has been developed by the EDF R&D Division. This model is implemented in the frame of THYC, which is the EDF's reference code for the modeling of two-phase thermal-hydraulic phenomena at the subchannel scale. A new deposit process, based on Tube Support Plate flow blockage studies, has been developed and implemented in the model, and is presented in this work. It can be defined by two main steps: particle deposition, and strengthening process called "flashing" due to soluble species precipitation in the pores of the particle deposit. The relevance of this process is tested by comparing the simulation results to the actual levels of flow blockage observed in some nuclear plants. Two dominant trends are showed in this work: the flow blockage is more important on the hot leg than on the cold leg and at the top than at the bottom of the Steam Generators. Moreover the flow blockages at the upper Tube Support Plate have the special feature to be more important at the periphery than at the center. The "flashing" phenomenon allows one to underline the magnetite solubility dependence, so the pH dependence, of flow blockage phenomenon. A pH elevation of the secondary circuit seems to be a interesting remedy which is currently considered on EDF fleet.
T. Prusek, E. Moleiro, F. Oukacine, A. Adobes, Marc Jaeger, et al.. Deposit models for tube support plate flow blockage in Steam Generators. Nuclear Engineering and Design, Elsevier, 2013, 262, pp.418-428. <10.1016/j.nucengdes.2013.05.017>. <hal-00997704>
Gwenn Boedec, Marc Jaeger, Marc Leonetti. Sedimentation-induced tether on a settling vesicle. Physical Review E : Statistical, Nonlinear, and Soft Matter Physics, American Physical Society, 2013, 88, pp.010702. Plus de détails...
Destabilization of soft interfaces into thin cylindrical filaments under external stresses is ubiquitous and is generally the first step toward breakup. We show that such filaments, called tethers, emerge from a vesicle subjected to gravity. Contrary to the pendant drop experiment, we demonstrate that the bending rigidity, a specific membrane property of vesicles, ensures the tethers reach a stationary state. Moreover, unlike point-like force experiments, we show that the family of shapes is continuous.
Gwenn Boedec, Marc Jaeger, Marc Leonetti. Sedimentation-induced tether on a settling vesicle. Physical Review E : Statistical, Nonlinear, and Soft Matter Physics, American Physical Society, 2013, 88, pp.010702. <10.1103/PhysRevE.88.010702>. <hal-00997686>
Journal: Physical Review E : Statistical, Nonlinear, and Soft Matter Physics
The purpose of this article is to study the statics and dynamics of nanotubes by using the methods of continuum mechanics. The nanotube can be filled with only a liquid or a vapour phase according to the physicochemical characteristics of the wall and to the disjoining pressure associated with the liquid and vapour mother bulks of the fluid, regardless of the nature of the external mother bulk. In dynamics, flows through nanotubes can be much more important than classical Poiseuille flows. When the external mother bulk is of vapour, the flow can be a million times larger than the classical flows when slippage on wall does not exist.
Henri Gouin. Statics and dynamics of fluids in nanotubes. Note di Matematica, 2012, 32 (1), pp.105-124. <10.1285/i15900932v32n1p105>. <hal-00903254>
Henri Gouin, Tommaso Ruggeri. A consistent thermodynamical model of incompressible media as limit case of quasi-thermal-incompressible materials. International Journal of Non-Linear Mechanics, Elsevier, 2012, 47, pp.688-693. Plus de détails...
In this paper we consider the conditions on quasi-thermal-incompressible so that they satisfy all the principles of thermodynamics, including the stability condition associated with the concavity of the chemical potential. We analyze the approximations under which a quasi-thermal-incompressible medium can be considered as incompressible. We find that the pressure cannot exceed a very large critical value and that the compressibility factor must be greater than a lower limit that is very small. The analysis is first done for the case of fluids and then extended to the case of thermoelastic solids.
Henri Gouin, Tommaso Ruggeri. A consistent thermodynamical model of incompressible media as limit case of quasi-thermal-incompressible materials. International Journal of Non-Linear Mechanics, Elsevier, 2012, 47, pp.688-693. <10.1016/j.ijnonlinmec.2011.11.005>. <hal-00700797>
Journal: International Journal of Non-Linear Mechanics
Gwenn Boedec, Marc Jaeger, Marc Leonetti. Settling of a vesicle in the limit of quasi-spherical shapes. Journal of Fluid Mechanics, Cambridge University Press (CUP), 2012, 690, pp.227-261. Plus de détails...
Vesicles are drops of radius of a few tens of micrometres bounded by an impermeable lipid membrane of approximately 4 nm thickness in a viscous fluid. The salient characteristics of such a deformable object are a membrane rigidity governed by flexion due to curvature energy and a two-dimensional membrane fluidity characterized by a local membrane incompressibility. This provides unique properties with strong constraints on the internal volume and membrane area. Yet, when subjected to external stresses, vesicles exhibit a large deformability. The deformation of a settling vesicle in an infinite flow is studied theoretically, assuming a quasispherical shape and expanding all variables of the problem onto spherical harmonics. The contribution of thermal fluctuations is neglected in this analysis. A system of equations describing the temporal evolution of the shape is derived with this formalism. The final shape and the settling velocity are then determined and depend on two dimensionless parameters: the Bond number and the excess area. This simultaneous study leads to three stationary shapes, an egg-like shape already observed in an analogous experimental configuration in the limit of weak flow magnitude (Chatkaew, Georgelin, Jaeger & Leonetti, Phys. Rev. Lett, 2009, vol. 103(24), 248103), a parachute-like shape and a non-trivial non-axisymmetrical shape. The final shape depends on the initial conditions: prolate or oblate vesicle and orientation compared with gravity. The analytical solution in the small deformation regime is compared with numerical results obtained with a three-dimensional code. A very good agreement between numerical and theoretical results is found.
Gwenn Boedec, Marc Jaeger, Marc Leonetti. Settling of a vesicle in the limit of quasi-spherical shapes. Journal of Fluid Mechanics, Cambridge University Press (CUP), 2012, 690, pp.227-261. <10.1017/jfm.2011.427>. <hal-00997678>
Sergey Gavrilyuk, Henri Gouin. Geometric evolution of the Reynolds stress tensor. International Journal of Engineering Science, Elsevier, 2012, 59, pp.65-73. Plus de détails...
The dynamics of the Reynolds stress tensor for turbulent flows is described with an evolution equation coupling both geometric effects and turbulent source terms. The effects of the mean flow geometry are shown up when the source terms are neglected: the Reynolds stress tensor is then expressed as the sum of three tensor products of vector fields which are governed by a distorted gyroscopic equation. Along the mean flow trajectories, the fluctuations of velocity are described by differential equations whose coefficients depend only on the mean flow deformation. If the mean flow vorticity is small enough, an approximate turbulence model is derived, and its application to shear shallow water flows is proposed. Moreover, the approximate turbulence model admits a variational formulation which is similar to the one of capillary fluids.
Sergey Gavrilyuk, Henri Gouin. Geometric evolution of the Reynolds stress tensor. International Journal of Engineering Science, Elsevier, 2012, 59, pp.65-73. <10.1016/j.ijengsci.2012.03.008>. <hal-00371444v3>
Journal: International Journal of Engineering Science
S. Moussiere, A. Roubaud, Olivier Boutin, Pierrette Guichardon, B. Fournel, et al.. 2D and 3D CFD modelling of a reactive turbulent flow in a double shell supercritical water oxidation reactor. Journal of Supercritical Fluids, Elsevier, 2012, 65, pp.25-31. Plus de détails...
In order to design and define appropriate dimensions for a supercritical oxidation reactor, a comparative 2D and 3D simulation of the fluid dynamics and heat transfer during an oxidation process has been performed. The solver used is a commercial code, Fluent 6.2®. The turbulent flow field in the reactor, created by the stirrer, is taken into account with a k-ω model and a swirl imposed to the fluid. In the 3D case the rotation of the stirrer can be modelled using the sliding mesh model and the moving reference frame model. This work allows comparing 2D and 3D velocity and heat transfer calculations. The predicted values (mainly species concentrations and temperature profiles) are of the same order in both cases. The reactivity of the system is taken into account with a classical Eddy Dissipation Concept combustion model. Comparisons with experimental temperature measurements validate the ability of the CFD modelling to simulate the supercritical water oxidation reactive medium. Results indicate that the flow can be considered as plug flow-like and that heat transfer is strongly enhanced by the stirring.
S. Moussiere, A. Roubaud, Olivier Boutin, Pierrette Guichardon, B. Fournel, et al.. 2D and 3D CFD modelling of a reactive turbulent flow in a double shell supercritical water oxidation reactor. Journal of Supercritical Fluids, Elsevier, 2012, 65, pp.25-31. <10.1016/j.supflu.2012.02.019>. <hal-00992976>
Henri Gouin, Augusto Muracchini, Tommaso Ruggeri. On the Müller paradox for thermal-incompressible media. Continuum Mechanics and Thermodynamics, Springer Verlag, 2012, 24, pp.505-513. Plus de détails...
In his monograph Thermodynamics, I. Müller proves that for incompressible media the volume does not change with the temperature. This Müller paradox yields an incompatibility between experimental evidence and the entropy principle. This result has generated much debate within the mathematical and thermodynamical communities as to the basis of Boussinesq approximation in fluid dynamics. The aim of this paper is to prove that for an appropriate definition of incompressibility, as a limiting case of quasi thermal-incompressible body, the entropy principle holds for pressures smaller than a critical pressure value. The main consequence of our result is the physically obvious one, that for very large pressures, no body can be perfectly incompressible. The result is first established in the fluid case. In the case of hyperelastic media subject to large deformations the approach is similar, but with a suitable definition of the pressure associated with convenient stress tensor decomposition.
Henri Gouin, Augusto Muracchini, Tommaso Ruggeri. On the Müller paradox for thermal-incompressible media. Continuum Mechanics and Thermodynamics, Springer Verlag, 2012, 24, pp.505-513. <10.1007/s00161-011-0201-1>. <hal-00748817>
Henri Gouin, Augusto Muracchini, Tommaso Ruggeri. Travelling waves near a critical point of a binary fluid mixture. International Journal of Non-Linear Mechanics, Elsevier, 2011, 47, pp.77-84. Plus de détails...
Travelling waves of densities of binary fluid mixtures are investigated near a critical point. The free energy is considered in a non-local form taking account of the density gradients. The equations of motions are applied to a universal form of the free energy near critical conditions and can be integrated by a rescaling process where the binary mixture is similar to a single fluid. Nevertheless, density solution profiles obtained are not necessarily monotonic. As indicated in Appendix, the results might be extended to other topics like finance or biology.
Henri Gouin, Augusto Muracchini, Tommaso Ruggeri. Travelling waves near a critical point of a binary fluid mixture. International Journal of Non-Linear Mechanics, Elsevier, 2011, 47, pp.77-84. <10.1016/j.ijnonlinmec.2011.09.016>. <hal-00634703>
Journal: International Journal of Non-Linear Mechanics
Henri Gouin. Liquid-solid interaction at nanoscale and its application in vegetal biology. Colloids and Surfaces A: Physicochemical and Engineering Aspects, Elsevier, 2011, 383 (1-3), pp.17-22. Plus de détails...
The water ascent in tall trees is subject to controversy: the vegetal biologists debate on the validity of the cohesion-tension theory which considers strong negative pressures in microtubes of xylem carrying the crude sap. This article aims to point out that liquids are submitted at the walls to intermolecular forces inferring density gradients making heterogeneous liquid layers and therefore disqualifying the Navier-Stokes equations for nanofilms. The crude sap motion takes the disjoining pressure gradient into account and the sap flow dramatically increases such that the watering of nanolayers may be analogous to a microscopic flow. Application to microtubes of xylem avoids the problem of cavitation and enables us to understand why the ascent of sap is possible for very high trees.
Henri Gouin. Liquid-solid interaction at nanoscale and its application in vegetal biology. Colloids and Surfaces A: Physicochemical and Engineering Aspects, Elsevier, 2011, 383 (1-3), pp.17-22. <10.1016/j.colsurfa.2011.01.004>. <hal-00598246>
Journal: Colloids and Surfaces A: Physicochemical and Engineering Aspects
Gwen Boedec, Marc Leonetti, Marc Jaeger. 3D vesicle dynamics simulations with a linearly triangulated surface. Journal of Computational Physics, Elsevier, 2011, 230 (4), pp.1020-1034. Plus de détails...
Simulations of biomembranes have gained an increasing interest in the past years. specificities of these membranes propose new challenges for the numerics. In particular, vesicle dynamics are governed by bending forces as well as a surface incompressibility constraint. A method to compute the bending force density resultant onto piecewise linearly triangulated surface meshes is described. This method is coupled with a boundary element method solver for inner and outer fluids, to compute vesicle dynamics under external flows. The surface incompressibility constraint is satisfied by the construction of a projection operator.
Gwen Boedec, Marc Leonetti, Marc Jaeger. 3D vesicle dynamics simulations with a linearly triangulated surface. Journal of Computational Physics, Elsevier, 2011, 230 (4), pp.1020-1034. <10.1016/j.jcp.2010.10.021>. <hal-00717365>
Joan Escandell, Evelyne Neau, Christophe Nicolas. A new formulation of the predictive NRTL-PR model in terms of k(ij) ă mixing rules. Extension of the group contributions for the modeling of ă hydrocarbons in the presence of associating compounds. Fluid Phase Equilibria, Elsevier, 2011, 301 (1), pp.80-97. Plus de détails...
A generalized NRTL model was previously proposed for the modeling of non ă ideal systems and was extended to the prediction of phase equilibria ă under pressure according to the cubic NRTL-PR EoS. In this work, the ă model is reformulated with a predictive k(ij) temperature and ă composition dependent mixing rule and new interaction parameters are ă proposed between permanent gases, ethane and nitrogen with hydrocarbons, ă ethane with water and ethylene glycol. Results obtained for excess ă enthalpies, liquid-vapor and liquid-liquid equilibria are compared with ă those provided by the literature models, such as VTPR, PPR78, CPA and ă SRKm. A wide variety of mixtures formed by very asymmetric compounds, ă such as hydrocarbons, water and ethylene glycols are considered and ă special attention is paid to the evolution of k(ij) with respect to mole ă fractions and temperature. (C) 2010 Elsevier B.V. All rights reserved.
Joan Escandell, Evelyne Neau, Christophe Nicolas. A new formulation of the predictive NRTL-PR model in terms of k(ij) ă mixing rules. Extension of the group contributions for the modeling of ă hydrocarbons in the presence of associating compounds. Fluid Phase Equilibria, Elsevier, 2011, 301 (1), pp.80-97. <10.1016/j.fluid.2010.11.009>. <hal-01464747>
Pierre Haldenwang, Pierrette Guichardon. Pressure runaway in a 2D plane channel with permeable walls submitted to pressure-dependent suction. European Journal of Mechanics - B/Fluids, Elsevier, 2011, 30 (2), pp.177-183. Plus de détails...
A leaking duct carries a flow that is a characteristic of several applications. Devices for cross-flow microfiltration are composed of a duct, the walls of which are semi-permeable membranes. In subsurface irrigation, the walls of watering pipes can be of porous clay, whereas the watering hoses are riddled with holes or made of porous material, in surface drip irrigation. In these applications, the first approach consists of assuming that the flow concerns a pure fluid (as in a microfiltration system operating at a very low species concentration), and that the wall's leakage depends only on the local pressure difference between both inner and outer sides of the wall.
Pierre Haldenwang, Pierrette Guichardon. Pressure runaway in a 2D plane channel with permeable walls submitted to pressure-dependent suction. European Journal of Mechanics - B/Fluids, Elsevier, 2011, 30 (2), pp.177-183. <10.1016/j.euromechflu.2010.09.007>. <hal-00905831>
Evelyne Neau, Joan Escandell, Christophe Nicolas. Modeling of highly nonideal systems: 2. Prediction of high pressure phase equilibria with the group contribution NRTL-PR EoS. Industrial and engineering chemistry research, American Chemical Society, 2010, 49 (16), pp.7589-7596. Plus de détails...
The purpose of this study is to propose a simple cubic equation of state for the prediction of phase equilibria in highly non ideal systems. The NRTL-PR equation of state is based on the association of the Peng−Robinson EoS and the generalized NRTL model developed in the first part of this work. This model, which derives from the lattice two-fluid theory, was specially developed to take account for the differences in size and shape between mixture components. The main advantage of the resulting NRTL-PR equation of state is to yield a simple and predictive model, depending on very few interaction parameters. In addition, it also allows satisfactory predictions of excess enthalpies, liquid−vapor and liquid−liquid equilibria occurring in mixtures formed by very asymmetric compounds, such as hydrocarbons, water, and ethylene glycols.
Evelyne Neau, Joan Escandell, Christophe Nicolas. Modeling of highly nonideal systems: 2. Prediction of high pressure phase equilibria with the group contribution NRTL-PR EoS. Industrial and engineering chemistry research, American Chemical Society, 2010, 49 (16), pp.7589-7596. <10.1021/ie101266x>. <hal-01025263>
Journal: Industrial and engineering chemistry research
Evelyne Neau, Joan Escandell, Christophe Nicolas. Modeling of highly nonideal systems: 1. A generalized version of the NRTL equation for the description of low-pressure equilibria. Industrial and engineering chemistry research, American Chemical Society, 2010, 49 (16), pp.7580-7588. Plus de détails...
The topic of the present work is the development of a simple model for the description of phase equilibria occurring in nonideal systems, such as those containing size-asymmetric components or mixtures made of polar or associating compounds with hydrocarbons, that are capable of strong demixing. The generalized NRTL model presented in this first part derives from the lattice two-fluid theory and differs from the original model by considering the size asymmetry of mixture components; results obtained for the modeling of phase equilibria in hydrocarbon, polar, and highly immiscible systems are compared with other literature models, such as the van Laar, NRTL, and UNIQUAC models. In the second part of this work, this model is associated with the Peng−Robinson EoS using the EoS/GE approach based on a generalized reference state, and a new group contribution is proposed for the prediction of the binary interaction parameters.
Evelyne Neau, Joan Escandell, Christophe Nicolas. Modeling of highly nonideal systems: 1. A generalized version of the NRTL equation for the description of low-pressure equilibria. Industrial and engineering chemistry research, American Chemical Society, 2010, 49 (16), pp.7580-7588. <10.1021/ie100121c>. <hal-01025255>
Journal: Industrial and engineering chemistry research
Pierre Haldenwang, Pierrette Guichardon, Guillaume Chiavassa, N. Ibaseta. Exact solution to mass transfer in Berman flow: application to concentration polarization combined with osmosis in crossflow membrane filtration. International Journal of Heat and Mass Transfer, Elsevier, 2010, 53 (19-20), pp.3898-3904. Plus de détails...
Concentration polarization affects numerous systems of membrane separation, and combined with osmosis, it can cause substantial reductions in permeation. We establish an exact solution to the conservation law of a solute advected by Berman flow. This flow is characteristic of reverse osmosis or nanofiltration. The resulting concentration polarization is then combined with the osmosis (counter-) effect. For large Péclet number of permeation, it yields a rigorous support to the semi-empirical "film" model, and accounts for the limit flux phenomenon. The main results are summarized in a simple diagram that relates three different Péclet numbers, and show that polarization combined with osmosis can withstand operating pressure almost totally.
Pierre Haldenwang, Pierrette Guichardon, Guillaume Chiavassa, N. Ibaseta. Exact solution to mass transfer in Berman flow: application to concentration polarization combined with osmosis in crossflow membrane filtration. International Journal of Heat and Mass Transfer, Elsevier, 2010, 53 (19-20), pp.3898-3904. <10.1016/j.ijheatmasstransfer.2010.05.008>. <hal-00907275>
Journal: International Journal of Heat and Mass Transfer
Henri Gouin, Tommaso Ruggeri. The Hamilton principle for fluid binary mixtures with two temperatures. Bollettino dell'Unione Matematica Italiana, 2009, Serie IX, vol. II (2), pp.403-422. Plus de détails...
For binary mixtures of fluids without chemical reactions, but with components having different temperatures, the Hamilton principle of least action is able to produce the equation of motion for each component and a balance equation of the total heat exchange between components. In this nonconservative case, a Gibbs dynamical identity connecting the equations of momenta, masses, energy and heat exchange allows to deduce the balance equation of energy of the mixture. Due to the unknown exchange of heat between components, the number of obtained equations is less than the number of field variables. The second law of thermodynamics constrains the possible expression of a supplementary constitutive equation closing the system of equations. The exchange of energy between components produces an increasing rate of entropy and creates a dynamical pressure term associated with the difference of temperature between components. This new dynamical pressure term fits with the results obtained by classical thermodynamical arguments and confirms that the Hamilton principle can afford to obtain the equations of motions for multi-temperature mixtures of fluids.
Henri Gouin, Tommaso Ruggeri. The Hamilton principle for fluid binary mixtures with two temperatures. Bollettino dell'Unione Matematica Italiana, 2009, Serie IX, vol. II (2), pp.403-422. <hal-00380525>
Journal: Bollettino dell'Unione Matematica Italiana
Henri Gouin. Elastic effects of liquids on surface physics. Comptes Rendus Mécanique, Elsevier Masson, 2009, 337, vol. 337 (in publication). Plus de détails...
The contact between a liquid and an elastic solid generates a stress vector depending on the curvature tensor in each point of the separating surface. For nanometer values of the mean curvature and for suitable materials, the stress vector takes significant amplitude on the surface. Although the surface average action of the liquid on the solid is the hydrostatic pressure, the local strain generates torques tending to regularize the surface undulations and asperities.
Henri Gouin. Elastic effects of liquids on surface physics. Comptes Rendus Mécanique, Elsevier Masson, 2009, 337, vol. 337 (in publication). <10.1016/j.crme.2009.04.005>. <hal-00380495>
Henri Gouin. Liquid nanofilms. A mechanical model for the disjoining pressure. International Journal of Engineering Science, Elsevier, 2009, 47 (5-6), pp.691-699. Plus de détails...
Liquids in contact with solids are submitted to intermolecular forces making liquids heterogeneous and, in a mechanical model, the stress tensor is not any more spherical as in homogeneous bulks. The aim of this article is to show that a square-gradient functional taking into account the volume liquid free energy corrected with two surface liquid density functionals is a mean field approximation allowing to study structures of very thin liquid nanofilms near plane solid walls. The model determines analytically the concept of disjoining pressure for liquid films of thicknesses of a very few number of nanometers and yields a behavior in good agreement with the shapes of experimental curves carried out by Derjaguin and his successors.
Henri Gouin. Liquid nanofilms. A mechanical model for the disjoining pressure. International Journal of Engineering Science, Elsevier, 2009, 47 (5-6), pp.691-699. <10.1016/j.ijengsci.2009.01.006>. <hal-00375026>
Journal: International Journal of Engineering Science
Henri Gouin, Tommaso Ruggeri. Dynamical pressure for fluid mixtures with several temperatures. Mécanique and Industries / Mécanique et Industries, EDP Sciences, 2009, 10, pp.239-243. Plus de détails...
We consider binary mixtures of fluids with components having different temperatures. A new dynamical pressure term is associated with the difference of temperatures between components even if fluid viscosities are null. The non-equilibrium dynamical pressure can be measured and may be convenient in several physical situations as for example in cosmological circumstances where a dynamical pressure played a major role in the evolution of the early universe.
Henri Gouin, Tommaso Ruggeri. Dynamical pressure for fluid mixtures with several temperatures. Mécanique and Industries / Mécanique et Industries, EDP Sciences, 2009, 10, pp.239-243. <10.1051/meca/2009052>. <hal-01216798>
Journal: Mécanique and Industries / Mécanique et Industries
Sunita Chatkaew, Marc Georgelin, Marc Jaeger, Marc Leonetti. Dynamics of Vesicle Unbinding under axisymmetric flow. Physical Review Letters, American Physical Society, 2009, 103 (24), pp.248103. Plus de détails...
Sunita Chatkaew, Marc Georgelin, Marc Jaeger, Marc Leonetti. Dynamics of Vesicle Unbinding under axisymmetric flow. Physical Review Letters, American Physical Society, 2009, 103 (24), pp.248103. <10.1103/PhysRevLett.103.248103>. <hal-00440220>
Bo Xun, Kai Li, Paul G. Chen, Wen-Rui Hu. Effect of interfacial heat transfer on the onset of oscillatory convection in liquid bridge. International Journal of Heat and Mass Transfer, Elsevier, 2009, 52 (19-20), pp.4211-4220. Plus de détails...
In present study, effect of interfacial heat transfer with ambient gas on the onset of oscillatory convection in a liquid bridge of large Prandtl number on the ground is systematically investigated by the method of linear stability analyses. With both the constant and linear ambient air temperature distributions, the numerical results show that the interfacial heat transfer modifies the free-surface temperature distribution directly and then induces a steeper temperature gradient on the middle part of the free surface, which may destabilize the convection. On the other hand, the interfacial heat transfer restrains the temperature disturbances on the free surface, which may stabilize the convection. The two coupling effects result in a complex dependence of the stability property on the Biot number. Effects of melt free-surface deformation on the critical conditions of the oscillatory convection were also investigated. Moreover, to better understand the mechanism of the instabilities, rates of kinetic energy change and ''thermal " energy change of the critical disturbances were investigated
Bo Xun, Kai Li, Paul G. Chen, Wen-Rui Hu. Effect of interfacial heat transfer on the onset of oscillatory convection in liquid bridge. International Journal of Heat and Mass Transfer, Elsevier, 2009, 52 (19-20), pp.4211-4220. <10.1016/j.ijheatmasstransfer.2009.04.008>. <hal-01307193>
Journal: International Journal of Heat and Mass Transfer
Jian-Kang Zhang, Bo Xun, Paul G. Chen. A Continuation Method Applied to the Study of Thermocapillary Instabilities in Liquid Bridges. Microgravity Science & Technology, 2009, 21 (Suppl 1), pp.111-117. Plus de détails...
A continuation method is applied to investigate the linear stability of the steady, axisymmetric thermocapillary flows in liquid bridges. The method is based upon an appropriate extended system of perturbation equations depending on the nature of transition of the basic flow. The dependence of the critical Reynolds number and corresponding azimuthal wavenumber on serval parameters is presented for both cylindrical and non-cylindrical liquid bridges.
Jian-Kang Zhang, Bo Xun, Paul G. Chen. A Continuation Method Applied to the Study of Thermocapillary Instabilities in Liquid Bridges. Microgravity Science & Technology, 2009, 21 (Suppl 1), pp.111-117. <10.1007/s12217-009-9111-2>. <hal-01307220>
Henri Gouin. A new approach for the limit to tree height using a liquid nanolayer model. Continuum Mechanics and Thermodynamics, Springer Verlag, 2008, 20 (5), pp.317-329. Plus de détails...
Liquids in contact with solids are submitted to intermolecular forces inferring density gradients at the walls. The van der Waals forces make liquid heterogeneous, the stress tensor is not any more spherical as in homogeneous bulks and it is possible to obtain stable thin liquid films wetting vertical walls up to altitudes that incompressible fluid models are not forecasting. Application to micro tubes of xylem enables to understand why the ascent of sap is possible for very high trees like sequoias or giant eucalyptus.
Henri Gouin. A new approach for the limit to tree height using a liquid nanolayer model. Continuum Mechanics and Thermodynamics, Springer Verlag, 2008, 20 (5), pp.317-329. <10.1007/s00161-008-0084-y>. <hal-00323328>
Henri Gouin, Tommaso Ruggeri. Identification of an average temperature and a dynamical pressure in a multitemperature mixture of fluids. Physical Review E : Statistical, Nonlinear, and Soft Matter Physics, American Physical Society, 2008, 78 (1), pp.016303. Plus de détails...
We present a classical approach of a mixture of compressible fluids when each constituent has its own temperature. The introduction of an average temperature together with the entropy principle dictates the classical Fick law for diffusion and also novel constitutive equations associated with the difference of temperatures between the components. The constitutive equations fit with results recently obtained through Maxwellian iteration procedure in extended thermodynamics theory of multitemperature mixtures. The differences of temperatures between the constituents imply the existence of a new dynamical pressure even if the fluids have a zero bulk viscosity. The nonequilibrium dynamical pressure can be measured and may be convenient in several physical situations as for example in cosmological circumstances where - as many authors assert - a dynamical pressure played a major role in the evolution of the early universe.
Henri Gouin, Tommaso Ruggeri. Identification of an average temperature and a dynamical pressure in a multitemperature mixture of fluids. Physical Review E : Statistical, Nonlinear, and Soft Matter Physics, American Physical Society, 2008, 78 (1), pp.016303. <10.1103/PhysRevE.78.016303>. <hal-00299294>
Journal: Physical Review E : Statistical, Nonlinear, and Soft Matter Physics
Henri Gouin, Sergey Gavrilyuk. Dynamics of liquid nanofilms. International Journal of Engineering Science, Elsevier, 2008, 46, pp.1195-1202. Plus de détails...
The van der Waals forces across a very thin liquid layer (nanofilm) in contact with a plane solid wall make the liquid nonhomogeneous. The dynamics of such flat liquid nanofilms is studied in isothermal case. The Navier-Stokes equations are unable to describe fluid motions in very thin films. The notion of surface free energy of a sharp interface separating gas and liquid layer is disqualified. The concept of disjoining pressure replaces the model of surface energy. In the nanofilm a supplementary free energy must be considered as a functional of the density. The equation of fluid motions along the nanofilm is obtained through the Hamilton variational principle by adding, to the conservative forces, the forces of viscosity in lubrication approximation. The evolution equation of the film thickness is deduced and takes into account the variation of the disjoining pressure along the layer.
Henri Gouin, Sergey Gavrilyuk. Dynamics of liquid nanofilms. International Journal of Engineering Science, Elsevier, 2008, 46, pp.1195-1202. <10.1016/j.ijengsci.2008.05.002>. <hal-00323322>
Journal: International Journal of Engineering Science
Juan-David Llamas, Cédric Pérat, François Lesage, Mathieu Weber, Umberto D'Ortona, et al.. Wire mesh tomography applied to trickle beds : a new way to study liquid maldistribution. Chemical Engineering and Processing : Process Intensification, 2008, 47, pp.1765-1770. Plus de détails...
Two sets of wire mesh tomography sensors have been developed for the study of liquid maldistribution in trickle bed reactors. The technique, based on the one used by Prasser et al. [H.M. Prasser, A. Böttger, J. Zschau, A new electrode-mesh tomograph for gas-liquid flows, Flow Meas. Instrum. 9 (1998), 111-119] in bubble columns, uses two horizontal planes of wires placed at fixed bed depths to measure the presence of a conductive liquid between them. Being only slightly invasive, the conceived wire mesh tomography device allows estimation of liquid concentration over a cross-sectional area of the column with a spatial resolution of 313 pixels. Examples of wire mesh tomography measurements inside a trickle bed reactor using different liquid distributors are presented here. Results are satisfying and wire mesh tomography appears to be a promising technique for the study of liquid maldistribution in trickle beds of non-porous particles.
Juan-David Llamas, Cédric Pérat, François Lesage, Mathieu Weber, Umberto D'Ortona, et al.. Wire mesh tomography applied to trickle beds : a new way to study liquid maldistribution. Chemical Engineering and Processing : Process Intensification, 2008, 47, pp.1765-1770. <10.1016/j.cep.2007.09.017>. <hal-00189354>
Journal: Chemical Engineering and Processing : Process Intensification
B Xun, Paul G. Chen, K Li, Z Yin, W.R. Hu. A linear stability analysis of large-Prandtl-number thermocapillary liquid bridges. Advances in Space Research, Elsevier, 2008, 41 (12), pp.2094-2100. Plus de détails...
A linear stability analysis is applied to determine the onset of oscillatory thermocapillary convection in cylindrical liquid bridges of large Prandtl numbers (4 ⩽ Pr ⩽ 50). We focus on the relationships between the critical Reynolds number Re c , the azimuthal wave number m, the aspect ratio C and the Prandtl number Pr. A detailed Re c–Pr stability diagram is given for liquid bridges with various C. In the region of Pr > 1, which has been less studied previously and where Re c has been usually believed to decrease with the increase of Pr, we found Re c exhibits an early increase for liquid bridges with C around one. From the computed surface temperature gradient, it is concluded that the boundary layers developed at both solid ends of liquid bridges strengthen the stability of basic axisymmetric thermocap-illary convection at large Prandtl number, and that the stability property of the basic flow is determined by the ''effective'' part of liquid bridge.
B Xun, Paul G. Chen, K Li, Z Yin, W.R. Hu. A linear stability analysis of large-Prandtl-number thermocapillary liquid bridges. Advances in Space Research, Elsevier, 2008, 41 (12), pp.2094-2100. <10.1016/j.asr.2007.07.016>. <hal-01307161>
Most of the models proposed in literature for binary diffusion coefficients of solids in supercritical fluids are restricted to infinite dilution; this can be explained by the fact that most of experimental data are performed in the dilute range. However some industrial processes, such as supercritical fluid separation, operate at finite concentration for complex mixtures. In this case, the concentration dependence of diffusion coefficients must be considered, especially near the upper critical endpoint (UCEP) where a strong decrease of diffusion coefficients was experimentally observed. In order to represent this slowing down, a modified version of the Darken equation was proposed in literature for naphthalene in supercritical carbon dioxide. In this paper, the conditions of application of such a modelling are investigated. In particular, we focus on the order of magnitude of the solubility of the solid and on the vicinity of the critical endpoint. Various equations proposed in literature for the modelling of the infinite dilution diffusion coefficients of the solutes are also compared. Ten binary mixtures of solids with supercritical carbon dioxide were considered for this purpose.
Isabelle Raspo, Christophe Nicolas, Evelyne Neau, Sofiane Meradji. Diffusion coefficients of solids in supercritical carbon dioxide: Modelling of near critical behaviour. Fluid Phase Equilibria, Elsevier, 2008, 263 (2), pp.214-222. <10.1016/j.fluid.2007.09.025>. <hal-01139192>
Henri Gouin. The d'Alembert-lagrange principle for gradient theories and boundary conditions. T. Ruggeri and M. Sammartino. Asymptotic Methods in Nonlinear Wave Phenomena, World Scientific, pp.79-95, 2007, . Plus de détails...
Motions of continuous media presenting singularities are associated with phenomena involving shocks, interfaces or material surfaces. The equations representing evolutions of these media are irregular through geometrical manifolds. A unique continuous medium is conceptually simpler than several media with surfaces of singularity. To avoid the surfaces of discontinuity in the theory, we transform the model by considering a continuous medium taking intoaccount more complete internal energies expressed in gradient developments associated with the variables of state. Nevertheless, resulting equations of motion are of an higher order than those of the classical models: they lead to non-linear models associated with more complex integration processes on the mathematical level as well as on the numerical point of view. In fact, such models allow a precise study of singular zones when they have a non negligible physical thickness. This is typically the case for capillarity phenomena in fluids or mixtures of fluids in which interfacial zones are transition layers between phases or layers between fluids and solid walls. Within the framework of mechanics for continuous media, we propose to deal with the functional point of view considering globally the equations of the media as well as the boundary conditions associated with these equations. For this aim, we revisit the d'Alembert-Lagrange principle of virtual works which is able to consider the expressions of the works of forces applied to a continuous medium as a linear functional value on a space of test functions in the form of virtual displacements. At the end, we analyze examples corresponding to capillary fluids. This analysis brings us to numerical or asymptotic methods avoiding the difficulties due to singularities in simpler -but with singularities- models.
Henri Gouin. The d'Alembert-lagrange principle for gradient theories and boundary conditions. T. Ruggeri and M. Sammartino. Asymptotic Methods in Nonlinear Wave Phenomena, World Scientific, pp.79-95, 2007, <10.981-270-782-4>. <hal-00204346>
G. Félix, V. Falk, Umberto D'Ortona. Granular flows in a rotating drum : the scaling law between velocity and thickness of the flow. European Physical Journal E: Soft matter and biological physics, EDP Sciences: EPJ, 2007, 22 (1), pp.25-31. Plus de détails...
The flow of dry granular material in a half-filled rotating drum is studied. The thickness of the flowing zone is measured for several rotation speeds, drum sizes and beads sizes (size ratio between drum and beads ranging from 47 to 7400). Varying the rotation speed, a scaling law linking mean velocity vs. thickness of the flow, v ∼hm, is deduced for each couple (beads, drum). The obtained exponent m is not always equal to 1, the value previously reported for a drum in litterature, but varies with the geometry of the system. For small size ratios, exponents higher than 1 are obtained due to a saturation of the flowing zone thickness. The exponent of the power law decreases with the size ratio, leading to exponents lower than 1 for high size ratios. These exponents imply that the velocity gradient of a dry granular flow in a rotating drum is not constant. More fundamentally, these results show that the flow of a granular material in a rotating drum is very sensible to the geometry, and that. the deduction of the "rheology" of a granular medium flowing in such a geometry is not obvious.
G. Félix, V. Falk, Umberto D'Ortona. Granular flows in a rotating drum : the scaling law between velocity and thickness of the flow. European Physical Journal E: Soft matter and biological physics, EDP Sciences: EPJ, 2007, 22 (1), pp.25-31. <10.1140/epje/e2007-00002-5>. <hal-00275307>
Journal: European Physical Journal E: Soft matter and biological physics
Vadim Nikolayev, Sergey Gavrilyuk, Henri Gouin. Modelling of the moving deformed triple contact line: influence of the fluid inertia. Journal of Colloid and Interface Science, Elsevier, 2006, 302 (2), pp.605-612. Plus de détails...
For partial wetting, motion of the triple liquid-gas-solid contact line is influenced by heterogeneities of the solid surface. This influence can be strong in the case of inertial (e.g. oscillation) flows where the line can be pinned or move intermittently. A model that takes into account both surface defects and fluid inertia is proposed. The viscous dissipation in the bulk of the fluid is assumed to be negligible as compared to the dissipation in the vicinity of the contact line. The equations of motion and the boundary condition at the contact line are derived from Hamilton's principle. The rapid capillary rise along a vertical inhomogeneous wall is treated as an example.
Vadim Nikolayev, Sergey Gavrilyuk, Henri Gouin. Modelling of the moving deformed triple contact line: influence of the fluid inertia. Journal of Colloid and Interface Science, Elsevier, 2006, 302 (2), pp.605-612. <10.1016/j.jcis.2006.06.046>. <hal-00256903>
Henri Gouin, Sergey Gavrilyuk. Dissipative Two-Fluid Models. Rendiconti del Circolo Matematico di Palermo, 2006, suppl. 78 (Serie II), pp.133-145. Plus de détails...
From Hamilton's principle of stationary action, we derive governing equations of two-fluid mixtures and extend the model to the dissipative case without chemical reactions. For both conservative and dissipative cases, an algebraic identity connecting equations of momentum, mass, energy and entropy is obtained by extending the Gibbs identity in dynamics. The obtained system is hyperbolic for small relative velocity of the phases.
Henri Gouin, Sergey Gavrilyuk. Dissipative Two-Fluid Models. Rendiconti del Circolo Matematico di Palermo, 2006, suppl. 78 (Serie II), pp.133-145. <hal-00204894>
Journal: Rendiconti del Circolo Matematico di Palermo
Henri Gouin. Non-linear waves in fluids near the critical point. Waves and Stability in Continuous Media: Proceedings Wascom 2005. World Scientific, pp.12, 2006, R. Monaco, G. Mulone, S. Rionero, T. Ruggeri. Plus de détails...
A non-linear model associated with a Landau-Ginzburg-like behavior in mean field approximation forecasts phase transition waves and solitary kinks near the critical point. The behavior of isothermal waves is different of the one of isentropic waves as well in conservative cases as in dissipative cases.
Henri Gouin. Non-linear waves in fluids near the critical point. Waves and Stability in Continuous Media: Proceedings Wascom 2005. World Scientific, pp.12, 2006, R. Monaco, G. Mulone, S. Rionero, T. Ruggeri. <hal-00204935>
Henri Gouin, Tommaso Ruggeri. Mixture of Fluids involving Entropy Gradients and Acceleration Waves in Interfacial Layers. European Journal of Mechanics - B/Fluids, Elsevier, 2005, 24 (5), pp.596-613. Plus de détails...
Through an Hamiltonian action we write down the system of equations of motions for a mixture of thermocapillary fluids under the assumption that the internal energy is a function not only of the gradient of the densities but also of the gradient of the entropies of each component. A Lagrangian associated with the kinetic energy and the internal energy allows to obtain the equations of momentum for each component and for the barycentric motion of the mixture. We obtain also the balance of energy and we prove that the equations are compatible with the second law of thermodynamics. Though the system is of parabolic type, we prove that there exist two tangential acceleration waves that characterize the interfacial motion. The dependence of the internal energy of the entropy gradients is mandatory for the existence of this kind of waves. The differential system is non-linear but the waves propagate without distortion due to the fact that they are linearly degenerate (exceptional waves).
Henri Gouin, Tommaso Ruggeri. Mixture of Fluids involving Entropy Gradients and Acceleration Waves in Interfacial Layers. European Journal of Mechanics - B/Fluids, Elsevier, 2005, 24 (5), pp.596-613. <10.1016/j.euromechflu.2005.01.001>. <hal-00204143>
Henri Gouin. Thermocapillary fluid and adiabatic waves near the critical point. Proceedings “Wascom 2003” 12th Conference on Waves and Stability in Continuous Media. World Scientific, p.p. 254-268, 2004, R. Monaco, S. Pennisi, S. Rionero, T. Ruggeri. Plus de détails...
Isothermal interfacial zones are investigated starting from a local energy which can be considered as the sum of two terms: one corresponding to a medium with a uniform composition equal to the local one and a second one associated with the non-uniformity of the fluid. In an extended van der Waals theory, the volume internal energy is proposed with a gradient expansion depending not only on the gradient of density but also on the gradient of entropy. We obtain the equation of conservative motions for non-homogeneous fluids near its critical point. For such a medium, it is not possible to obtain shock waves. The waves are tangential to the interface and the wave celerity is expressed depending on thermodynamic conditions at the critical point.
Henri Gouin. Thermocapillary fluid and adiabatic waves near the critical point. Proceedings “Wascom 2003” 12th Conference on Waves and Stability in Continuous Media. World Scientific, p.p. 254-268, 2004, R. Monaco, S. Pennisi, S. Rionero, T. Ruggeri. <hal-00261497>
Henri Gouin. Adiabatic waves along interfacial layers near the critical point. Comptes Rendus Mécanique, Elsevier Masson, 2004, 332 (4), pp.285-292. Plus de détails...
Near the critical point, isothermal interfacial zones are investigated starting from a non-local density of energy. From the equations of motion of thermocapillary fluids, we point out a new kind of adiabatic waves propagating along the interfacial layers. The waves are associated with the second derivatives of densities and propagate with a celerity depending on the proximity of the critical point.
Henri Gouin. Adiabatic waves along interfacial layers near the critical point. Comptes Rendus Mécanique, Elsevier Masson, 2004, 332 (4), pp.285-292. <10.1016/j.crme.2004.01.007>. <hal-00204792>
Sergey Gavrilyuk, Henri Gouin, Vladimir Teshukov. Bubble effect on Kelvin-Helmholtz' instability. Continuum Mechanics and Thermodynamics, Springer Verlag, 2004, 16 (1-2), pp.31-42. Plus de détails...
We derive boundary conditions at interfaces (contact discontinuities) for a class of Lagrangian models describing, in particular, bubbly flows. We use these conditions to study Kelvin-Helmholtz' instability which develops in the flow of two superposed layers of a pure incompressible fluid and a fluid containing gas bubbles, co-flowing with different velocities. We show that the presence of bubbles in one layer stabilizes the flow in some intervals of wave lengths.
Sergey Gavrilyuk, Henri Gouin, Vladimir Teshukov. Bubble effect on Kelvin-Helmholtz' instability. Continuum Mechanics and Thermodynamics, Springer Verlag, 2004, 16 (1-2), pp.31-42. <10.1007/s00161-003-0139-z>. <hal-00204936>
Henri Gouin, Françoise Cubisol. On the number of droplets in aerosols. Mechanics Research Communications, Elsevier, 2003, 30 (5), pp.403-409. Plus de détails...
The number of droplets which may be formed with a supersaturated vapor in presence of a gas cannot exceed a number proportional to (pv-pvo)4 where pv and pvo denote at the same temperature the pressure of the supersaturated vapor-gas mixture and the pressure of the saturated vapor-gas mixture. The energy necessary to the droplet formation is also bounded by a number proportional to (pv-pvo)2 .
Henri Gouin, Françoise Cubisol. On the number of droplets in aerosols. Mechanics Research Communications, Elsevier, 2003, 30 (5), pp.403-409. <10.1016/S0093-6413(03)00043-0>. <hal-00205429>
Henri Gouin. The wetting problem of fluids on solid surfaces. Part 1: the dynamics of contact lines. Continuum Mechanics and Thermodynamics, Springer Verlag, 2003, 15 (6), pp.581-596. Plus de détails...
The understanding of the spreading of liquids on solid surfaces is an important challenge for contemporary physics. Today, the motion of the contact line formed at the intersection of two immiscible fluids and a solid is still subject to dispute. In this paper, a new picture of the dynamics of wetting is offered through an example of non-Newtonian slow liquid movements. The kinematics of liquids at the contact line and equations of motion are revisited. Adherence conditions are required except at the contact line. Consequently, for each fluid, the velocity field is multivalued at the contact line and generates an equivalent concept of line friction but stresses and viscous dissipation remain bounded. A Young-Dupré equation for the apparent dynamic contact angle between the interface and solid surface depending on the movements of the fluid near the contact line is proposed.
Henri Gouin. The wetting problem of fluids on solid surfaces. Part 1: the dynamics of contact lines. Continuum Mechanics and Thermodynamics, Springer Verlag, 2003, 15 (6), pp.581-596. <hal-00203362>
Henri Gouin. The wetting problem of fluids on solid surfaces. Part 2: the contact angle hysteresis. Continuum Mechanics and Thermodynamics, Springer Verlag, 2003, 15 (6), pp.597-611. Plus de détails...
In part 1, we proposed a model of dynamics of wetting for slow movements near a contact line formed at the interface of two immiscible fluids and a solid when viscous dissipation remains bounded. The contact line is not a material line and a Young-Dupré equation for the apparent dynamic contact angle taking into account the line celerity was proposed. In this paper we consider a form of the interfacial energy of a solid surface in which many small oscillations are superposed on a slowly varying function. For a capillary tube, a scaling analysis of the microscopic law associated with the Young-Dupré dynamic equation yields a macroscopic equation for the motion of the contact line. The value of the deduced apparent dynamic contact angle yields for the average response of the line motion a phenomenon akin to the stick-slip motion of the contact line on the solid wall. The contact angle hysteresis phenomenon and the modelling of experimentally well-known results expressing the dependence of the apparent dynamic contact angle on the celerity of the line are obtained. Furthermore, a qualitative explanation of the maximum speed of wetting (and dewetting) can be given.
Henri Gouin. The wetting problem of fluids on solid surfaces. Part 2: the contact angle hysteresis. Continuum Mechanics and Thermodynamics, Springer Verlag, 2003, 15 (6), pp.597-611. <10.1007/s00161-003-0137-1>. <hal-00203368>
Henri Gouin, Tommaso Ruggeri. Hamiltonian Principle in Binary Mixtures of Euler Fluids with Applications to the Second Sound Phenomena. Rendiconti Lincei - Matematica E Applicationi, 2003, 14 (s 9), pp.69-83. Plus de détails...
In the present paper we compare the theory of mixtures based on Rational Thermomechanics with the one obtained by Hamilton principle. We prove that the two theories coincide in the adiabatic case when the action is constructed with the intrinsic Lagrangian. In the complete thermodynamical case we show that we have also coincidence in the case of low temperature when the second sound phenomena arises for superfluid Helium and crystals.
Henri Gouin, Tommaso Ruggeri. Hamiltonian Principle in Binary Mixtures of Euler Fluids with Applications to the Second Sound Phenomena. Rendiconti Lincei - Matematica E Applicationi, 2003, 14 (s 9), pp.69-83. <hal-00283148>
Journal: Rendiconti Lincei - Matematica E Applicationi
M. Jaeger, M. Carin. The Front-Tracking ALE Method: Application to a Model of the Freezing of Cell Suspensions. Journal of Computational Physics, Elsevier, 2002, 179 (2), . Plus de détails...
A new front-tracking method to compute discontinuous solutions on unstructured finite element meshes is presented. Using an arbitrary Lagrangian–Eulerian formula- tion, the mesh is continuously adapted by moving the nearest nodes to the interface. Thus, the solution is completely sharp at the interface and no smearing takes place. The dynamic node adjustment is confined to global nodes near the front, rendering remeshing unnecessary. The method has been applied to the osmotic motion of a two-dimensional cell arising from a concentration gradient generated by a moving solidification front. The engulfment of one cell by an advancing solidification front, which rejects the solutes in a binary salt solution, is then computed. The results indicate that the ice increases the solute gradient around the cell. Furthermore, the presence of the cell, which prevents diffusion of the solute, leads to large changes in the morphology of the ice front.
M. Jaeger, M. Carin. The Front-Tracking ALE Method: Application to a Model of the Freezing of Cell Suspensions. Journal of Computational Physics, Elsevier, 2002, 179 (2), <10.1006/jcph.2002.7084>. <hal-01282007>
M. Carin, M. Jaeger. Numerical simulation of the interaction of biological cells with an ice front during freezing. European Physical Journal: Applied Physics, EDP Sciences, 2001, 16 (3), . Plus de détails...
The goal of this study is a better understanding of the interaction between cells and a solidi- fication front during a cryopreservation process. This technique of freezing is commonly used to conserve biological material for long periods at low temperatures. However the biophysical mechanisms of cell in- juries during freezing are difficult to understand because a cell is a very sophisticated microstructure interacting with its environment. We have developed a finite element model to simulate the response of cells to an advancing solidification front. A special front-tracking technique is used to compute the motion of the cell membrane and the ice front during freezing. The model solves the conductive heat transfer equation and the diffusion equation of a solute on a domain containing three phases: one or more cells, the extra-cellular solution and the growing ice. This solid phase growing from a binary salt solution rejects the solute in the liquid phase and increases the solute gradient around the cell. This induces the shrinkage of the cell. The model is used to simulate the engulfment of one cell modelling a red blood cell by an advancing solidification front initially planar or not is computed. We compare the incorporation of a cell with that of a solid particle.
M. Carin, M. Jaeger. Numerical simulation of the interaction of biological cells with an ice front during freezing. European Physical Journal: Applied Physics, EDP Sciences, 2001, 16 (3), <10.1051/epjap:2001205>. <hal-01282025>
Journal: European Physical Journal: Applied Physics
Iain Shepherd, Tim Haste, Naouma Kourti, Francesco Oriolo, Mario Leonardi, et al.. Investigation of core degradation (COBE). Nuclear Engineering and Design, Elsevier, 2001, 209 (1-3), . Plus de détails...
The COBE project started in February 1996 and finished at the end of January 1999. The main objective was to improve understanding of core degradation behaviour during severe accidents through the development of computer codes, the carrying out of experiments and the assessment of the computer codes’ ability to reproduce experimental behaviour. A major effort was devoted to quenching behaviour and a substantial achievement of the project was the design and commissioning of a new facility for the simulation of quenching of intact fuel rods. Two tests, carefully scaled to represent realistic reactor conditions, were carried out in this facility and the hydrogen generated during the quenching process was measured using two independent measuring systems. The codes were able to reproduce the results in the first test, where little hydrogen was generated but not the second test, where the extra steam produced during quenching caused an invigorated Zircaloy oxidation and a substantial hydrogen generation. A number of smaller parametric experiments allowed detailed models to be developed for the absorption of hydrogen and the cracking of cladding during quenching. COBE also investigated other areas concerned with late-phase phenomena.
Iain Shepherd, Tim Haste, Naouma Kourti, Francesco Oriolo, Mario Leonardi, et al.. Investigation of core degradation (COBE). Nuclear Engineering and Design, Elsevier, 2001, 209 (1-3), <10.1016/S0029-5493(01)00393-4>. <hal-01282019>
Henri Gouin. The wetting problem of fluids on solid surfaces: Dynamics of lines and contact angle hysteresis. Journal de Physique IV Colloque, 2001, 11 (PR6), pp.261-269. Plus de détails...
In 1805, Young was the first who introduced an expression for contact angle in static, but today, the motion of the contact-line formed at the intersection of two immiscible fluids and a solid is still subject to dispute. By means of the new physical concept of line viscosity, the equations of motions and boundary conditions for fluids in contact on a solid surface together with interface and contact-line are revisited. A new Young-Dupré equation for the dynamic contact angle is deduced. The interfacial energies between fluids and solid take into account the chemical heterogeneities and the solid surface roughness. A scaling analysis of the microscopic law associated with the Young-Dupré dynamic equation allows us to obtain a new macroscopic equation for the motion of the contact-line. Here we show that our theoretical predictions fit perfectly together with the contact angle hysteresis phenomenon and the experimentally well-known results expressing the dependence of the dynamic contact angle on the celerity of the contact-line. We additively get a quantitative explanation for the maximum speed of wetting (and dewetting).
Henri Gouin. The wetting problem of fluids on solid surfaces: Dynamics of lines and contact angle hysteresis. Journal de Physique IV Colloque, 2001, 11 (PR6), pp.261-269. <hal-00211166>
A. Boukamel, Stéphane Méo, Olivier Débordes, Marc Jaeger. A thermo-viscoelastic model for elastomeric behaviour and its numerical application. Archive of Applied Mechanics, Springer Verlag, 2001, 71, pp.785-801. Plus de détails...
This paper presents a model of thermo-mechanical behaviour of viscoelastic elastomers under large strain. A formulation is proposed with a generalisation to large strain of the Poynting–Thomson rheological model. A finite element formulation is then exposed taking the incompressibility constraint for mechanical equilibrium into account. On the thermomechanical coupling aspect, an algorithm of time discretisation is proposed with two time scales corresponding respectively to mechanical and thermal behaviours. Finally, an application for the simulation of a double-shearing test is presented with an analysis of parameters' influence and a comparison between numerical and experimental results.
A. Boukamel, Stéphane Méo, Olivier Débordes, Marc Jaeger. A thermo-viscoelastic model for elastomeric behaviour and its numerical application. Archive of Applied Mechanics, Springer Verlag, 2001, 71, pp.785-801. <10.1007/s004190100191>. <hal-01236417>
A Decarlis, Marc Jaeger. Effective thermal conductivity of heterogeneous two-phase material using the self-consistent finite element method. Scripta Materialia, Elsevier, 2001, 44 (8-9), . Plus de détails...
Advanced materials often involve the mixture of a second phase material (the inclusions) in a host phase (the matrix). Indeed, materials with very specific properties can be synthesized by controlling the nature of each phase as well as the shape and spatial distribution of the inclusions. Therefore, homogenization tools yielding accurate effective transport properties are needed. We present a numerical extension of a pure analytical treatment of the problem, namely the self-consistent method.
A Decarlis, Marc Jaeger. Effective thermal conductivity of heterogeneous two-phase material using the self-consistent finite element method. Scripta Materialia, Elsevier, 2001, 44 (8-9), <10.1016/S1359-6462(01)00830-2>. <hal-01282039>
Eric Serre, Patrick Bontoux, Richard Kotarba. Numerical simulation of the transition in three-dimensional rotating flows with walls : boundary layers instabilities. International Journal of Computational Fluid Dynamics, Taylor & Francis, 2001, 5, pp.2. Plus de détails...
The purpose of this article is the direct numerical simulation (DNS) of the complex phenomena that precede the transition to turbulence inside a cavity subjected to rotation. The configurations of cylindrical cavities subjected to a radial throughflow or to a differential rotation of the walls are relevant to rotating machinery devices. At a high rotation rate, the DNS exhibits instability patterns arising inside the thin layers close to the disks. The efficient spectral solver is based on a Chebyshev-Fourier approximation. For large aspect ratio and at high Reynolds number, an instability occurs inside the Ekman and Bödewadt layers in the form of annular and spiral vortices that are characteristic of type I and type II instabilities.
Eric Serre, Patrick Bontoux, Richard Kotarba. Numerical simulation of the transition in three-dimensional rotating flows with walls : boundary layers instabilities. International Journal of Computational Fluid Dynamics, Taylor & Francis, 2001, 5, pp.2. <hal-00835770>
Journal: International Journal of Computational Fluid Dynamics
Eric Serre, Patrick Bontoux, Richard Kotarba. Numerical Simulation of the transition in three-dimensional rotating flows with walls. Boundary layer instabilities. International Journal of Computational Fluid Dynamics, Taylor & Francis, 2001, 5 (2), pp.873-879. Plus de détails...
Eric Serre, Patrick Bontoux, Richard Kotarba. Numerical Simulation of the transition in three-dimensional rotating flows with walls. Boundary layer instabilities. International Journal of Computational Fluid Dynamics, Taylor & Francis, 2001, 5 (2), pp.873-879. <hal-01023068>
Journal: International Journal of Computational Fluid Dynamics
Henri Gouin, Laurent Espanet. Bubble number in a caviting flow. Comptes rendus de l’Académie des sciences. Série IIb, Mécanique, Elsevier, 2000, 328 (2), pp.151-157. Plus de détails...
Cavitation is a general phenomenon of the fluid flows with obstacles. It appears in the cooling conduits of the fast nuclear engines. A model of this phenomenon using the theory of Laplace and a common non-convex energy for the liquid and vapour bulks is proposed. This model makes it possible to determine a higher limit of the density of bubbles (a number of bubbles per unit of volume in the flow). The maximum intensity of cavitation is associated with the mechanical and thermal characteristics of the fluid flow.
Henri Gouin, Laurent Espanet. Bubble number in a caviting flow. Comptes rendus de l’Académie des sciences. Série IIb, Mécanique, Elsevier, 2000, 328 (2), pp.151-157. <10.1016/S1287-4620(00)00105-8>. <hal-00308594>
Journal: Comptes rendus de l’Académie des sciences. Série IIb, Mécanique
Gang Chen, Stephan E. Belcher. Effects of Long Waves on Wind-Generated Waves. Journal of Physical Oceanography, American Meteorological Society, 2000, 30 (9), pp.2246-2256. Plus de détails...
A model is developed to explain the observation made in several laboratory experiments that short wind-generated waves are suppressed by a train of long, mechanically generated waves. A sheltering mechanism is responsible for generation of the short wind waves, by which wave growth is proportional to the local turbulent wind stress. Hence, if the turbulent wind stress near the surface is reduced by the long wave, then the short wind wave amplitude, and hence also the energy in the short waves at a given fetch, is lower than in the absence of long wave. A quantitative model of this process is formulated to examine the ratios of the growth rate and the total energy density of wind waves with and without a long wave, which is shown to agree reasonably well with the laboratory experiments. The model also explains why this suppression of wind waves by a very long swell is not observed in the ocean where the effects of swell on wind waves are extremely difficult to detect. In the model, the reduction in the turbulent wind stress by the long wave is largest for small values of C L /u * (where C L is the phase speed of the long wave and u * is the friction velocity of the wind). When this ratio is larger than about 25 (typical of ocean swell), both the reduction of the turbulent wind stress by the long wave and, consequently, the reduction in the total energy density of the wind waves are very small, which explains why this phenomenon has not yet been observed on the ocean.
Gang Chen, Stephan E. Belcher. Effects of Long Waves on Wind-Generated Waves. Journal of Physical Oceanography, American Meteorological Society, 2000, 30 (9), pp.2246-2256. <10.1175/1520-0485(2000)0302.0.CO;2>. <hal-01307127>
Marc Jaeger, Muriel Carin, Marc Medale, Gretar Tryggvason. The Osmotic Migration of Cells in a Solute Gradient. Biophysical Journal, Biophysical Society, 1999, 77 (3), . Plus de détails...
The effect of a nonuniform solute concentration on the osmotic transport of water through the boundaries of a simple model cell is investigated. A system of two ordinary differential equations is derived for the motion of a single cell in the limit of a fast solute diffusion, and an analytic solution is obtained for one special case. A two-dimensional finite element model has been developed to simulate the more general case (finite diffusion rates, solute gradient induced by a solidification front). It is shown that the cell moves to regions of lower solute concentration due to the uneven flux of water through the cell boundaries. This mechanism has apparently not been discussed previously. The magnitude of this effect is small for red blood cells, the case in which all of the relevant parameters are known. We show, however, that it increases with cell size and membrane permeability, so this effect could be important for larger cells. The finite element model presented should also have other applications in the study of the response of cells to an osmotic stress and for the interaction of cells and solidification fronts. Such investigations are of major relevance for the optimization of cryopreservation processes.
Marc Jaeger, Muriel Carin, Marc Medale, Gretar Tryggvason. The Osmotic Migration of Cells in a Solute Gradient. Biophysical Journal, Biophysical Society, 1999, 77 (3), <10.1016/S0006-3495(99)76977-8>. <hal-01282080>
Sergey Gavrilyuk, Henri Gouin. A new form of governing equations of fluids arising from Hamilton's principle. International Journal of Engineering Science, Elsevier, 1999, 37 (12), pp.1495-1520. Plus de détails...
A new form of governing equations is derived from Hamilton's principle of least action for a constrained Lagrangian, depending on conserved quantities and their derivatives with respect to the time-space. This form yields conservation laws both for non-dispersive case (Lagrangian depends only on conserved quantities) and dispersive case (Lagrangian depends also on their derivatives). For non-dispersive case the set of conservation laws allows to rewrite the governing equations in the symmetric form of Godunov-Friedrichs-Lax. The linear stability of equilibrium states for potential motions is also studied. In particular, the dispersion relation is obtained in terms of Hermitian matrices both for non-dispersive and dispersive case. Some new results are extended to the two-fluid non-dispersive case.
Sergey Gavrilyuk, Henri Gouin. A new form of governing equations of fluids arising from Hamilton's principle. International Journal of Engineering Science, Elsevier, 1999, 37 (12), pp.1495-1520. <10.1016/S0020-7225(98)00131-1>. <hal-00204738>
Journal: International Journal of Engineering Science
Henri Gouin, Sergey Gavrilyuk. Wetting problem for multi-component fluid mixtures. Physica A, Elsevier, 1999, 268 (3-4), pp.291-308. Plus de détails...
In this paper we propose an extension of the Cahn method to binary mixtures and study the problem of wetting near a two-phase critical point without any assumption on the form of intermolecular potentials. A comparison between Cahn's method and later works by Sullivan, Evans et al is made. By using an expression of the energy of interaction between solid surface and liquids proposed recently by Gouin, we obtain the equations of density profiles and the boundary conditions on a solid surface. In the case of a convex free energy, a one-dimensional solution of a linear problem is proposed for the density profiles between a bulk and on a solid wall. A non-linear model of binary mixtures extending Cahn's results for simple fluids is also studied. For the case of a purely attractive wall we have established a criterion of a first order transition in terms of the structure of the level set of the homogeneous part of the free energy. Additively, explicit expressions of density profiles near the wall are proposed. They allow one to consider the adsorption of mixture components by a solid wall.
Henri Gouin, Sergey Gavrilyuk. Wetting problem for multi-component fluid mixtures. Physica A, Elsevier, 1999, 268 (3-4), pp.291-308. <10.1016/S0378-4371(99)00069-2>. <hal-00260114>
Henri Gouin, Sergey Gavrilyuk. Hamilton's Principle and Rankine-Hugoniot Conditions for General Motions of Mixtures. Meccanica, Springer Verlag, 1999, 34 (1), pp.39-47. Plus de détails...
In previous papers, we have presented hyperbolic governing equations and jump conditions for barotropic fluid mixtures. Now we extend our results to the most general case of two-fluid conservative mixtures taking into account the entropies of components. We obtain governing equations for each component of the medium. This is not a system of conservation laws. Nevertheless, using Hamilton's principle we are able to obtain a complete set of Rankine-Hugoniot conditions. In particular, for the gas dynamics they coincide with classical jump conditions of conservation of momentum and energy. For the two-fluid case, the jump relations do not involve the conservation of the total momentum and the total energy.
Henri Gouin, Sergey Gavrilyuk. Hamilton's Principle and Rankine-Hugoniot Conditions for General Motions of Mixtures. Meccanica, Springer Verlag, 1999, 34 (1), pp.39-47. <10.1023/A:1004370127958>. <hal-00249829>
Médale Marc, Marc Jaeger, Ahmed Kaiss. Finite element analysis of the action of buoyancy-induced and thermocapillary flow on the melting of tin in a 2D square cavity. Computer Assisted Mechanics and Engineering Sciences, 1999. Plus de détails...
A finite element model has been developed for the computation of melting/solidifying process under the combined action of buoyancy and surface tension forces. Validated on the square cavity benchmark of Gobin and Le Quéré (Bertrand et al. [1], Gobin and Le Quéré [2]), the numerical model is used to extend this previous analysis to the free surface case where surface tension can drive the flow (capillary flow). A comparison of the results obtained for three types of boundary conditions applied at the top of the melting pool is performed. It shows that in the studied case of tin where the thermal Bond number is moderated (Bo=200), the flow is still mainly dominated by buoyancy effect as long as the melted pool is deep enough like in the square cavity case of the above mentioned benchmark.
Médale Marc, Marc Jaeger, Ahmed Kaiss. Finite element analysis of the action of buoyancy-induced and thermocapillary flow on the melting of tin in a 2D square cavity. Computer Assisted Mechanics and Engineering Sciences, 1999. <hal-01282058>
Journal: Computer Assisted Mechanics and Engineering Sciences
Gang Chen, Christian Kharif, Stéphane Zaleski, Jie Li. Two-dimensional Navier–Stokes simulation of breaking waves. Physics of Fluids, American Institute of Physics, 1999, 11 (1), pp.121-133. Plus de détails...
Numerical simulations describing plunging breakers including the splash-up phenomenon are presented. The motion is governed by the classical, incompressible, two-dimensional Navier–Stokes equation. The numerical modeling of this two-phase flow is based on a piecewise linear version of the volume of fluid method. Capillary effects are taken into account such as a nonisotropic stress tensor concentrated near the interface. Results concerning the time evolution of liquid–gas interface and velocity field are given for short waves, showing how an initial steep wave undergoes breaking and successive splash-up cycles. Breaking processes including overturning, splash-up and gas entrainment, and breaking induced vortex-like motion beneath the surface and energy dissipation, are presented and discussed. It is found that strong vorticities are generated during the breaking process, and that more than 80% of the total pre-breaking wave energy is dissipated within three wave periods. The numerical results are compared with some laboratory measurements, and a favorable agreement is found.
Gang Chen, Christian Kharif, Stéphane Zaleski, Jie Li. Two-dimensional Navier–Stokes simulation of breaking waves. Physics of Fluids, American Institute of Physics, 1999, 11 (1), pp.121-133. <10.1063/1.869907>. <hal-01307123>
Henri Gouin, Witold Kosinski. Boundary conditions for a capillary fluid in contact with a wall. Archives of Mechanics, 1998, 50 (5), pp. 907-916. Plus de détails...
Contact of a fluid with a solid or an elastic wall is investigated. The wall exerts molecular forces on the fluid which is locally strongly nonhomogeneous. The problem is approached with a fluid energy of the second gradient form and a wall surface energy depending on the value of the fluid density at the contact. From the virtual work principle are obtained limit conditions taking into account the fluid density, its normal derivative to the wall and the curvature of the surface
Henri Gouin, Witold Kosinski. Boundary conditions for a capillary fluid in contact with a wall. Archives of Mechanics, 1998, 50 (5), pp. 907-916. <hal-00255841>
One derives the governing equations and the Rankine - Hugoniot conditions for a mixture of two miscible fluids using an extended form of Hamilton's principle of least action. The Lagrangian is constructed as the difference between the kinetic energy and a potential depending on the relative velocity of components. To obtain the governing equations and the jump conditions one uses two reference frames related with the Lagrangian coordinates of each component. Under some hypotheses on flow properties one proves the hyperbolicity of the governing system for small relative velocity of phases.
Henri Gouin. Energy of interaction between solid surfaces and liquids. Journal of Physical Chemistry B, American Chemical Society, 1998, 102 (7), pp.1212-1218. Plus de détails...
We consider the wetting transition on a planar surface in contact with a semi-infinite fluid. In the classical approach, the surface is assumed to be solid, and when interaction between solid and fluid is sufficiently short-range, the contribution of the fluid can be represented by a surface free energy with a density of the form Phi( rho_s), where rho_s is the limiting density of the fluid at the surface. In the present paper we propose a more precise representation of the surface energy that takes into account not only the value of rho_s but also the contribution from the whole density profile rho(z) of the fluid, where z is the coordinate normal to the surface. The specific value of the functional of rho_s at the surface is expressed in mean-field approximation through the potentials of intermolecular interaction and some other parameters of the fluid and the solid wall. An extension to the case of fluid mixtures in contact with a solid surface is proposed.
Henri Gouin. Energy of interaction between solid surfaces and liquids. Journal of Physical Chemistry B, American Chemical Society, 1998, 102 (7), pp.1212-1218. <10.1021/jp9723426>. <hal-00222180>
Sergey Gavrilyuk, Henri Gouin, Yurii Perepechko. A variational principle for two-fluid models. Comptes rendus de l’Académie des sciences. Série IIb, Mécanique, physique, astronomie, Elsevier, 1997, 324 (8), pp.483-490. Plus de détails...
A variational principle for two-fluid mixtures is proposed. The Lagrangian is constructed as the difference between the kinetic energy of the mixture and a thermodynamic potential conjugated to the internal energy with respect to the relative velocity of phases. The equations of motion and a set of Rankine-Hugoniot conditions are obtained. It is proved also that the convexity of the internal energy guarantees the hyperbolicity of the one-dimensional equations of motion linearized at rest.
Sergey Gavrilyuk, Henri Gouin, Yurii Perepechko. A variational principle for two-fluid models. Comptes rendus de l’Académie des sciences. Série IIb, Mécanique, physique, astronomie, Elsevier, 1997, 324 (8), pp.483-490. <10.1016/S1251-8069(97)80186-8>. <hal-00239305>
Journal: Comptes rendus de l’Académie des sciences. Série IIb, Mécanique, physique, astronomie
Francesco Dell'Isola, Henri Gouin, Giacomo Rotoli. Nucleation of spherical shell-like interfaces by second gradient theory: numerical simulations. European Journal of Mechanics - B/Fluids, Elsevier, 1996, 15 (4), pp.545-568. Plus de détails...
The theory of second gradient fluids (which are able to exert shear stresses also in equilibrium conditions) allows us: (i) to describe both the thermodynamical and the mechanical behavior of systems in which an interface is present; (ii) to express the surface tension and the radius of microscopic bubbles in terms of a functional of the chemical potential; (iii) to predict the existence of a (minimal) nucleation radius for bubbles. Moreover, the above theory supplies a 3D-continuum model which is endowed with sufficient structure to allow the construction of a 2D-shell-like continuum representing a consistent approximate 2D-model for the interface between phases. In this paper we use numerical simulations in the framework of second gradient theory to obtain explicit relationships for the surface quantities typical of 2D-models. In particular, for some of the most general two-parameter equations of state, it is possible to obtain the curves describing the relationship between the surface tension, the thickness, the surface mass density and the radius of the spherical interfaces between fluid phases of the same substance. These results allow us to predict the (minimal) nucleation radii for this class of equations of state.
Francesco Dell'Isola, Henri Gouin, Giacomo Rotoli. Nucleation of spherical shell-like interfaces by second gradient theory: numerical simulations. European Journal of Mechanics - B/Fluids, Elsevier, 1996, 15 (4), pp.545-568. <hal-00393974>
Francesco Dell'Isola, Henri Gouin, Pierre Seppecher. Radius and surface tension of microscopic bubbles by second gradient theory. Comptes rendus de l’Académie des sciences. Série IIb, Mécanique, Elsevier, 1995, 320, pp.5. Plus de détails...
The classical theory of Laplace is not suitable for describing the behavior of microscopic bubbles. The theory of second gradient fluids (which are able to exert shear stresses in equilibrium conditions) allows us to obtain a new expression for surface tension and radius of these bubbles in terms of functionals of the chemical potential. This relationship allows us to generalize the results of Cahn-Hilliard and Tolman.
Francesco Dell'Isola, Henri Gouin, Pierre Seppecher. Radius and surface tension of microscopic bubbles by second gradient theory. Comptes rendus de l’Académie des sciences. Série IIb, Mécanique, Elsevier, 1995, 320, pp.5. <hal-00308860>
Journal: Comptes rendus de l’Académie des sciences. Série IIb, Mécanique
Pierre Casal, Henri Gouin. Vibrations of liquid drops in film boiling phenomena: the mathematical model.. International Journal of Engineering Science, Elsevier, 1994, 32 (10), pp.1553-1560. Plus de détails...
Flattened liquid drops poured on a very hot surface evaporate quite slowly and float on a film of their own vapour. In the cavities of a surface, an unusual type of vibrational motions occurs. Large vibrations take place and different forms of dynamic drops are possible. They form elliptic patterns with two lobes or hypotrochoid patterns with three lobes or more. The lobes are turning relatively to the hot surface. We present a model of vibrating motions of the drops. Frequencies of the vibrations are calculated regarding the number of lobes. The computations agree with experiments.
Pierre Casal, Henri Gouin. Vibrations of liquid drops in film boiling phenomena: the mathematical model.. International Journal of Engineering Science, Elsevier, 1994, 32 (10), pp.1553-1560. <10.1016/0020-7225(94)90163-5>. <hal-00258503>
Journal: International Journal of Engineering Science
Henri Gouin. Dynamics effects in gradient theory for fluid mixtures. IMA Volumes in Mathematics and its Applications, 1993, 52, pp.111-121. Plus de détails...
We propose a new method to study motions of mixtures in fluid interfaces. We extend the equations of equilibrium in interfaces and the results associated with travelling waves for van der Waals like fluids. Maxwell rule is extended to interfaces of fluid mixtures out of equilibrium. Formulae like Clapeyron relation are obtained for isothermal layers.
Henri Gouin. Dynamics effects in gradient theory for fluid mixtures. IMA Volumes in Mathematics and its Applications, 1993, 52, pp.111-121. <hal-00269176>
Journal: IMA Volumes in Mathematics and its Applications
Henri Gouin. Variational Theory of Mixtures in Continuum Mechanics. European Journal of Mechanics - B/Fluids, Elsevier, 1990, 9 (5), pp.469-491. Plus de détails...
In continuum mechanics, the equations of motion for mixtures are derived through the use of Hamilton's extended principle which regards the mixture as a collection of distinct continua. The internal energy is assumed to be a function of densities, entropies and successive spatial gradients of each constituent. We first write the equations of motion for each constituent of an inviscid miscible mixture of fluids without chemical reactions or diffusion. Our work leads to the equations of motion in an universal thermodynamic form in which interaction terms subject to constitutive laws, difficult to interpret physically, do not occur. For an internal energy function of densities, entropies and spatial gradients, an equation describing the barycentric motion of the constituents is obtained. The result is extended for dissipative mixtures and an equation of energy is obtained. A form of Clausius-Duhem's inequality which represents the second law of thermodynamics is deduced. In the particular case of compressible mixtures, the equations reproduce the classical results. Far from critical conditions, the interfaces between different phases in a mixture of fluids are layers with strong gradients of density and entropy. The surface tension of such interfaces is interpreted.
Henri Gouin. Variational Theory of Mixtures in Continuum Mechanics. European Journal of Mechanics - B/Fluids, Elsevier, 1990, 9 (5), pp.469-491. <hal-00306965>
Pierre Casal, Henri Gouin. Invariance Properties of Inviscid Fluids of Grade n. Lecture Notes in Physics, TAYLOR & FRANCIS LTD, 1989, 344, pp.85-98. Plus de détails...
Fluids of grade n are continuous media in dynamic changes of phases avoiding the surfaces of discontinuity and representing the capillary layers in liquid-vapour interfaces. We recall the thermodynamic form of the equation of motion for inviscid fluids of grade n. First integrals and theorems of circulation are deduced. A general classification of flows is proposed.
Pierre Casal, Henri Gouin. Invariance Properties of Inviscid Fluids of Grade n. Lecture Notes in Physics, TAYLOR & FRANCIS LTD, 1989, 344, pp.85-98. <10.1007/BFb0024930>. <hal-00266215>
Henri Gouin. Thermodynamic form of the equation of motion for perfect fluids of grade n. Comptes Rendus de l'Academie des Sciences Serie II, 1987, 305 (II), pp.833-838. Plus de détails...
We propose a thermodynamic form of the equation of motion for perfect fluids of grade n which generalizes the one given by J. Serrin in the case of perfectly compressible fluids. First integrals and circulation theorems are deduced and a classification of the flows is given.
Henri Gouin. Thermodynamic form of the equation of motion for perfect fluids of grade n. Comptes Rendus de l'Academie des Sciences Serie II, 1987, 305 (II), pp.833-838. <hal-00488912>
Journal: Comptes Rendus de l'Academie des Sciences Serie II
Henri Gouin. Utilization of the second gradient theory in continuum mechanics to study motions and thermodynamics of liquid-vapor interfaces. Manuel G. Velarde. Plenum Publishing Corporation, pp.16, 1987, Physicochemical Hydrodynamics, Series B - Physics, Vol 174, Interfacial Phenomena. Plus de détails...
A thermomechanical model of continuous fluid media based on second gradient theory is used to study motions in liquid-vapor interfaces. At equilibrium, the model is shown to be equivalent to mean-field molecular theories of capillarity. In such fluids, conservative motions verify first integrals that lead to Kelvin circulation theorems and potential equations. The dynamical surface tension of liquid-vapor interfaces is deduced from viscous fluid equations. The result provides and explains the Marangoni effect.
Henri Gouin. Utilization of the second gradient theory in continuum mechanics to study motions and thermodynamics of liquid-vapor interfaces. Manuel G. Velarde. Plenum Publishing Corporation, pp.16, 1987, Physicochemical Hydrodynamics, Series B - Physics, Vol 174, Interfacial Phenomena. <hal-00614568>
Henri Gouin, Jean-François Debieve. Variational Principle Involving the Stress Tensor in Elastodynamics. International Journal of Engineering Science, Elsevier, 1986, 24 (7), pp.1057-1066. Plus de détails...
In the mechanics of inviscid conservative fluids, it is classical to generate the equations of dynamics by formulating with adequate variables, that the pressure integral calculated in the time-space domain corresponding to the motion of the continuous medium is stationary. The present study extends this principle to the dynamics of large deformations for isentropic motions in thermo-elastic bodies: we use a new way of writing the equations of motion in terms of potentials and we substitute the trace of the stress tensor for the pressure term.
Henri Gouin, Jean-François Debieve. Variational Principle Involving the Stress Tensor in Elastodynamics. International Journal of Engineering Science, Elsevier, 1986, 24 (7), pp.1057-1066. <10.1016/0020-7225(86)90001-7>. <hal-00303656>
Journal: International Journal of Engineering Science
Henri Gouin. Compressible Fluids: the discontinuity of the vorticity vector on a shock wave in thermodynamical variables.. Comptes rendus hebdomadaires des séances de l'Académie des sciences, Elsevier, 1973, 276 (Serie A), pp.1377-1380. Plus de détails...
The discontinuity of the vorticity is written as a function of the vector T grad s, (where T is the temperature and s the specific entropy). The expression is obtained thanks to potential equations and independently of the mass conservation and the equation of momentum balance.
Henri Gouin. Compressible Fluids: the discontinuity of the vorticity vector on a shock wave in thermodynamical variables.. Comptes rendus hebdomadaires des séances de l'Académie des sciences, Elsevier, 1973, 276 (Serie A), pp.1377-1380. <hal-00276736>
Journal: Comptes rendus hebdomadaires des séances de l'Académie des sciences