Coarse-grained simulations of charge, current and flow in heterogeneous media

Abstract

We present a coarse-grained simulation method for complex charged systems. This mesoscopic model couples a hydrodynamic description to a free energy functional accounting for the interactions between solvent(s) and charged solutes. It is implemented in a hybrid lattice-based algorithm, whereby the evolution of the overall mass and momentum is taken care of via a Lattice Boltzmann scheme, whereas the composition and ionic concentrations are updated using the link-flux method. Several applications illustrate the power of this coarse-grained model for charged heterogeneous media: the transport of charged tracers in charged porous media, the deformation of an oil droplet in water under the effect of an applied electric field, and the distribution of ions at an oil-water interface as a function of their affinity for both solvents.

Entropically induced asymmetric passage times of charged tracers across corrugated channels

“…Such feature reminds the one observed for tracers in a porous media obtained by coarse-grained numerical simulations. 34,35 Interestingly, such a modulation in the MFPT for charged tracers vanishes for κh 0 ≪ 1 as well as for κh 0 ≫ 1, in agreement with the entropic electrokinetic regime observed for tracers under external forcing 8 and under chemical potential gradients. 9 We can gain insight in the dependence of the MFPT on κ by analyzing the effective barrier experienced by the tracers, quantified by the free energy difference ∆A q as defined in Eq.…”

Accounting for adsorption and desorption in lattice Boltzmann simulations

“…Several fractions of adsorbed tracers, or sorption strength, f a , defined in Eq. (14), are presented: black circles, 0%, i.e., without adsorption; red squares, 30%; green diamonds, 79%; and blue triangles, 97%. coefficient is again given by the fraction of free particles times their bulk diffusion coefficient.…”

“…The issue of averaging over initial conditions in Eq. (5) can be handled elegantly and efficiently using the moment propagation method [12,15,16], which was recently extended to charged tracers [14,[17][18][19][20][21].…”

“…(1) and (2), e.g., with a finite element method, for all possible initial conditions, which is computationally intractable for complex systems such as heterogeneous porous media. An alternative is to deduce K and D(t) from the tracer velocity autocorrelation function (VACF) following [11][12][13][14] …”

Lattice-Boltzmann-Langevin simulations of binary mixtures

“…Such an approach, using fluxes defined on lattice links, has been proposed to study the electrokinetic equations in the absence of fluctuations in [37,38]. Alternative finite volume schemes may also be found in the context of reaction-diffusion systems [19].…”