Ion transport through deformable porous media: derivation of the macroscopic equations using upscaling

We study the upscaling or homogenization of the transport of a multicomponentelectrolyte in a dilute Newtonian solvent through a deformable porous medium.The pore scale interaction between the flow and the structure deformation is taken into account.After a careful adimensionalization process, we first consider so-called equilibrium solutions,in the absence of external forces, for which the velocity and diffusive fluxes vanish andthe electrostatic potential is the solution of a Poisson-Boltzmann equation.When the motion is governed by a small static electric field and small hydrodynamic and elastic forces,we use O'Brien's argument to deduce a linearized model. Then we perform the homogenizationof these linearized equations for a suitable choice of time scale. It turns out thatthe deformation of the porous medium is weakly coupled to the electrokinetics systemin the sense that it does not influence electrokinetics although the latter one yieldsan osmotic pressure term in the mechanical equations. As a byproduct we find that theeffective tensor satisfies Onsager properties, namely is symmetric positive definite

Identification des contributions enthalpiques a l'origine de la sélectivité en extraction liquide/liquide

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Models of electrolyte solutions from molecular descriptions: The example of NaCl solutions

We present a method to derive implicit solvent models of electrolyte solutions from all-atom descriptions; providing analytical expressions of the thermodynamic and structural properties of the ions consistent with the underlying explicit solvent representation. Effective potentials between ions in solution are calculated to perform perturbation theory calculations, in order to derive the best possible description in terms of charged hard spheres. Applying this method to NaCl solutions yields excellent agreement with the all-atom model, provided ion association is taken into account.Comment: 4 pages, 5 figure

Influence of the volume fraction on the electrokinetic properties of maghemite nanoparticles in suspension

Special issue in Honour of Pierre TURQInternational audienceWe used several complementary experimental and theoretical tools to characterise the charge properties of well-definedmaghemite nanoparticles in solution as a function of the volume fraction. The radius of the nanoparticles is equal to 6 nm.The structural charge was measured from chemical titration and was found high enough to expect some counterions tobe electrostatically attracted to the surface, decreasing the apparent charge of the nanoparticle. Direct-current conductivitymeasurements were interpreted by an analytical transport theory to deduce the value of this apparent charge, denoted here by‘dynamic effective charge’. This dynamic effective charge is found to decrease strongly with the volume fraction. In contrast,the ‘static’ effective charge, defined thanks to the Bjerrum criterion and computed from Monte Carlo simulations turns outto be almost independent of the volume fraction. In the range of Debye screening length and volume fraction investigatedhere, double layers around nanoparticles actually interact with each other. This strong interaction between nanocolloidalmaghemite particles is probably responsible for the experimental dependence of the electrokinetic properties with the volumefraction

Charge Properties of TiO2 Nanotubes in NaNO3 Aqueous Solution

Charging of material surfaces in aqueous electrolyte solutions is one of the most important processes in the interactions between biomaterials and surrounding tissue. Other than a biomaterial, titania nanotubes (TiO2 NTs) represent a versatile material for numerous applications such as heavy metal adsorption or photocatalysis. In this article, the surface charge properties of titania NTs in NaNO3 solution were investigated through electrophoretic mobility and polyelectrolyte colloid titration measuring techniques. In addition, we used high-resolution transmission electron microscopy imaging to determine the morphology of TiO2 NTs. A theoretical model based on the classical density functional theory coupled with the charge regulation method in terms of mass action law was developed to understand the experimental data and to provide insights into charge properties at different physical conditions, namely, pH and NaNO3 concentration. Two intrinsic protonation constants and surface site density have been obtained. The electrostatic properties of the system in terms of electrostatic potentials and ion distributions were calculated and discussed for various pH values. The model can quantitatively describe the titration curve as a function of pH for higher bulk salt concentrations and the difference in the equilibrium amount of charges between the inner and outer surfaces of TiO2 NTs. Calculated counterion (NO3–) distributions show a pronounced decrease of NO3– ions for high bulk pH (both inside and outside TiO2 NT) because of the strong electric field. With the decrease of bulk pH or the increase of the salt concentration, NO3– is able to accumulate near the TiO2 NTs surfaces

On the fluid-fluid phase separation in charged-stabilized colloidal suspensions

We develop a thermodynamic description of particles held at a fixed surface potential. This system is of particular interest in view of the continuing controversy over the possibility of a fluid-fluid phase separation in aqueous colloidal suspensions with monovalent counterions. The condition of fixed surface potential allows in a natural way to account for the colloidal charge renormalization. In a first approach, we assess the importance of the so called ``volume terms'', and find that in the absence of salt, charge renormalization is sufficient to stabilize suspension against a fluid-fluid phase separation. Presence of salt, on the other hand, is found to lead to an instability. A very strong dependence on the approximations used, however, puts the reality of this phase transition in a serious doubt. To further understand the nature of the instability we next study a Jellium-like approximation, which does not lead to a phase separation and produces a relatively accurate analytical equation of state for a deionized suspensions of highly charged colloidal spheres. A critical analysis of various theories of strongly asymmetric electrolytes is presented to asses their reliability as compared to the Monte Carlo simulations