Modélisation numérique des instabilités électro-convectives au voisinage d'une membrane échangeuse d'ions
Thermodynamique statistique des solutions électrolytiques appliquée aux procédés de séparation membranaire
Publications scientifiques au M2P2
Pierre Magnico. Electro-Kinetic Instability in a Laminar Boundary Layer Next to an Ion Exchange Membrane. International Journal of Molecular Sciences, MDPI, 2019, 20 (10), pp.2393. ⟨10.3390/ijms20102393⟩. ⟨hal-02177052⟩ Plus de détails...
The electro-kinetic instability in a pressure driven shear flow near an ion exchange membrane is considered. The electrochemical system, through which an electrical potential drop is applied, consists in a polarization layer in contact with the membrane and a bulk. The numerical investigation contained two aspects: analysis of the instability modes and description of the Lagrangian transport of fluid and ions. Regarding the first aspect, the modes were analyzed as a function of the potential drop. The analysis revealed how the spatial distribution of forces controls the dynamics of vortex association and dissociation. In particular, the birth of a counter-clockwise vortex between two clockwise vortices, and the initiation of clusters constituting one or two envelopes wrapping a vortex group, were examined. In regards to the second aspect, the trajectories were computed with the fourth order Runge Kutta scheme for the time integration and with the biquadratric upstream scheme for the spatial and time interpolation of the fluid velocity and the ion flux. The results for the periodic mode showed two kinds of trajectories: the trochoidal motion and the longitudinal one coupled with a periodic transverse motion. For the aperiodic modes, other mechanisms appeared, such as ejection from the mixing layer, trapping by a growing vortex or merging vortices. The analysis of the local velocity field, the vortices' shape, the spatial distribution of the forces and the ion flux components explained these trajectories.
Pierre Magnico. Electro-Kinetic Instability in a Laminar Boundary Layer Next to an Ion Exchange Membrane. International Journal of Molecular Sciences, MDPI, 2019, 20 (10), pp.2393. ⟨10.3390/ijms20102393⟩. ⟨hal-02177052⟩
Journal: International Journal of Molecular Sciences
Pierre Magnico. Spatial distribution of mechanical forces and ionic flux in electro-kinetic instability near a permselective membrane. Physics of Fluids, American Institute of Physics, 2018, 30 (1), pp.014101. ⟨10.1063/1.5007930⟩. ⟨hal-02114498⟩ Plus de détails...
This paper is devoted to the numerical investigation of electro-kinetic instability in a polarization layer next to a cation-exchange membrane. An analysis of some properties of the electro-kinetic instability is followed by a detailed description of the fluid flow structure and of the spatial distribution of the ionic flux. In this aim, the Stokes-Poisson-Nernst-Planck equation set is solved until the Debye length scale. The results show that the potential threshold of the marginal instability and the current density depend on the logarithm of the concentration at the membrane surface. The size of the stable vortices seems to be an increasing function of the potential drop. The fluid motion is induced by the electric force along the maximum concentration in the extended space charge (ESC) region and by the pressure force in the region around the inner edge of the ESC layer. Two spots of kinetic energy are located in the ESC region and between the vortices. The cationic motion, controlled by the electric field and the convection, presents counter-rotating vortices in the stagnation zone located in the fluid ejection region. The anion transport is also characterized by two independent layers which contain counter-rotating vortices. The first one is in contact with the stationary reservoir. In the second layer against the membrane, the convection, and the electric field control, the transversal motion, the Fickian diffusion, and the convection are dominant in the longitudinal direction. Finally, the longitudinal disequilibrium of potential and pressure along the membrane is analyzed.
Pierre Magnico. Spatial distribution of mechanical forces and ionic flux in electro-kinetic instability near a permselective membrane. Physics of Fluids, American Institute of Physics, 2018, 30 (1), pp.014101. ⟨10.1063/1.5007930⟩. ⟨hal-02114498⟩
Pierre Magnico. Ion transport dependence on the ion pairing/solvation competition in cation-exchange membranes. Journal of Membrane Science, Elsevier, 2015, 483, pp.112-127. ⟨10.1016/j.memsci.2015.01.051⟩. ⟨hal-01298876⟩ Plus de détails...
Effect of ion-pairing on ion partitioning at equilibrium and on transport properties is studied by means of the Poisson–Nernst–Planck (PNP) equations. Owing to the low electrolyte solution relative permittivity (εSεS) and the high ion density in the membrane, the excess terms of the chemical potential must be computed. In this aim, the density functional theory and the binding mean sphere approximation were used in order to extend the PNP equations and to compute the association constant. The counter-ion/fixed-charge-group pairing and the counter-ion/co-ion one were examined. In the case of monovalent fixed charge, the total density of co-ion and the free one decreases with εSεS owing to the solvation contribution. So that it induces a decrease of the membrane system conductivity. If the counter-ion/co-ion pairing is considered, the free co-ion density and the conductivity increase when εSεS reaches small values. However in the ohmic regime, this dependence of the conductivity towards the free co-ion density is not always fulfilled.
Pierre Magnico. Ion transport dependence on the ion pairing/solvation competition in cation-exchange membranes. Journal of Membrane Science, Elsevier, 2015, 483, pp.112-127. ⟨10.1016/j.memsci.2015.01.051⟩. ⟨hal-01298876⟩
Pierre Magnico. Influence of the ion-solvent interactions on ionic transport through ion-exchange-membranes. Journal of Membrane Science, Elsevier, 2013, 442, pp.272-285. ⟨10.1016/j.memsci.2013.04.003⟩. ⟨hal-00968171⟩ Plus de détails...
Ionic transport through ionic exchange membrane cannot be interpreted by the Nernst-Planck equation if the ion density is high, particularly in the membrane. In order to extend the density range, excess terms must be added to the chemical potential. These terms are computed by considering charged hard spheres embedded in a dielectric continuum. In this aim and owing to heterogeneity of the electrolytic solution the density function theory (DFT) is used. A previous work has been carried out with a homogeneous and amorphous solvent. Here an extension including the finite size of the solvent molecule and the local dielectric properties via the dielectric coefficient is presented. The electro-osmosis is also examined. The selectivity at equilibrium, the density profiles and the voltammograms are analysed. The numerical results obtained with NaCl and CaCl2 show that the physical properties of the solvent decrease the selectivity and increases the conductivity of the membrane systems. In the same time, the dielectric properties increase the electro-osmotic effects on the ionic transport. The approach described in this work can be used to study the solvent confinement effect inside the membrane on the ionic transport.
Pierre Magnico. Influence of the ion-solvent interactions on ionic transport through ion-exchange-membranes. Journal of Membrane Science, Elsevier, 2013, 442, pp.272-285. ⟨10.1016/j.memsci.2013.04.003⟩. ⟨hal-00968171⟩
Pierre Magnico. Ion size effects on electric double layers and ionic transport through ion-exchange membrane systems. Journal of Membrane Science, Elsevier, 2012, 415, pp.412-423. ⟨10.1016/j.memsci.2012.05.025⟩. ⟨hal-00968166⟩ Plus de détails...
The density function theory is used to study the density profiles and the transport properties of an ion-exchange membrane system submitted to an electric potential drop. As the ionic density increases, hard sphere interaction between ions becomes dominant and the ion size must be taken into account. The results show that the density distribution and the transport properties depend on the bulk electrolyte density. At equilibrium the charge inside the electric double layer (EDL) adjacent to the membrane decreases and the membrane electric potential increases as the bulk density increases. For high bulk density of unsymmetric electrolyte, secondary charge layers are observed inside the EDL. In the membrane the anion-density-to-bulk-density ratio increases when the bulk density increases from small to moderate values owing to the membrane potential increase. But it decreases abruptly at high bulk density values owing to the increase of the non-ideal electrostatic interaction. At a given electric potential drop, the current/voltage curves follow the variation of this ratio with respect to the bulk density at equilibrium. As the current density approaches the limiting one, the amplitude of the secondary charge layers decreases and the EDL thickness increases.
Pierre Magnico. Ion size effects on electric double layers and ionic transport through ion-exchange membrane systems. Journal of Membrane Science, Elsevier, 2012, 415, pp.412-423. ⟨10.1016/j.memsci.2012.05.025⟩. ⟨hal-00968166⟩
Pierre Magnico, P. Fongarland. CFD simulations of two stirred tank reactors with stationary catalytic basket. Chemical Engineering Science, Elsevier, 2006, 61 (4), pp.1217-1236. ⟨10.1016/j.ces.2005.07.025⟩. ⟨hal-01089397⟩ Plus de détails...
Among the different systems used for laboratory kinetic investigation, stationary catalytic basket stirred tank reactors (SCBSTRs) allow one to study triphasic reactions involving shaped catalyst with large size. The hydrodynamics of these complex reactors is not well known and has been studied experimentally in only a few cases. Despite the difference in the design of two commercial SCBSTRs reported in these works, the local measurements of the liquid–solid mass transfer coefficient inside the catalytic basket revealed the same velocity profile. The aim of the present work is therefore to investigate more accurately the hydrodynamics of the two reactors by means of CFD in order to compare the effect of the blade/baffle hydrodynamic interaction on the flow pattern. Owing to the geometrical complexity of the reactors, the hydrodynamic investigation is based on the kk–εε model and the Brinkman–Forsheimer equations. The agreement at the local level with the experimental data (PIV and mass transfer measurements) validates this preliminary work performed with the standard values of the parameters present in the turbulent model and the Brinkman–Forsheimer equations. The simulations reveal in both reactors a ring-shaped vortex around the impeller in the agitation region. The high axial location of its centre induces a reverse flow at the tips of the basket. Owing to the fluid friction in the porous medium, the azimuthal flow in the core region is transformed into a radial flow in the basket where the flow decreases abruptly. Vertical vortices are located at the blade tips and at the downstream face of the baffles or they are located in the basket on both sides of the baffles, depending on the design and the location of the baffles. At the inner radius interface of the basket, the vertical blade impeller induces a rather homogeneous velocity profile, but the pitched blade impeller imposes a high velocity at the plane of symmetry. Therefore the simulations demonstrate that two different local velocity patterns and two different porous media may induce the same mass transfer properties.
Pierre Magnico, P. Fongarland. CFD simulations of two stirred tank reactors with stationary catalytic basket. Chemical Engineering Science, Elsevier, 2006, 61 (4), pp.1217-1236. ⟨10.1016/j.ces.2005.07.025⟩. ⟨hal-01089397⟩