Bridging molecular and continuous descriptions: the case of dynamics in clays

Abstract

The theory of transport in porous media such as clays depends on the level of description. On the macroscopic scale,hydrodynamics equations are used. These continuous descriptions are convenient to model the fluid motion in a confined system. Nevertheless, they are valid only if the pores of the material are much larger than the molecular size of the components of the system. Another approach consists in using molecular descriptions. These two methods which correspond to different levels of description are complementary. The link between them can be clarified by using a coarse-graining procedure where the microscopic laws are averaged over fast variables to get the long time macroscopic laws. We present such an approach in the case of clays. Firstly, we detail the various levels of description and the relations among them, by emphasizing the validity domain of the hydrodynamic equations. Secondly, we focus on the case of dehydrated clays where hydrodynamics is not relevant. We show that it is possible to derive a simple model for the motion of the cesium ion based on the difference on time scale between the solvent and the solute particles.

Electrokinetics: insights from simulation on the microscopic scale

“…Marry et al introduced a Green-Kubo formula for the electro-osmotic response and used equilibrium molecular simulations to determine the electro-osmotic velocity profile between montmorillonite surfaces separated by thin water films (from 2 to 4 nm) [42,43,124]. Although the convergence of the Green-Kubo integrals was rather slow, they found that these could only be explained if slip boundary conditions were introduced, even though with a small slip length, as illustrated in Figure 6.…”

Multiscale modelling of transport in clays from the molecular to the sample scale

“…On the other hand, one should make the link between the various levels of description, exploiting more accurate models to calibrate coarser ones retaining the relevant information on larger scales. This "bottom-up" strategy includes for example using ab initio calculations to parametrize force fields (Cygan et al, 2004), or molecular simulation to derive simple kinetic models (Rotenberg et al, 2007a,b;Dufrêche et al, 2010;Carof et al, 2014). Even though all the references cited above are applications to clay minerals, this strategy is of course very general and has been successful in many other contexts.…”

Coarse graining the dynamics of nano-confined solutes: the case of ions in clays

“…As an example of extremely confined solute, we investigate the case of cesium ions confined in the interlayer porosity of montmorillonite clays, with a very low water content (a single water layer with 6 water molecules per ion), for which previous attempts to build a continuous solvent model failed to reproduce the dynamics predicted by molecular simulations [5,6]. We first derive a Generalized Langevin Equation (GLE) for the motion of a solute in an external potential using the Mori-Zwanzig formalism.…”

“…In a previous work, we have investigated the possibility to describe this confined motion by a continuous solvent model in which the ion evolves in the Potential of Mean Force (PMF), which captures the average effect of all its environment (clay surfaces, water molecules and other ions). The effect of a thermalizing bath is then accounted for via a constant and uniform friction and random forces [5,6]. The resulting model corresponds to simple Langevin Dynamics (for simplicity we write it here in the one-dimensional case):…”

“…Figure 2 compares the Velocity Autocorrelation Function (VACF) from Molecular Dynamics (MD) simulations with the results of Langevin dynamics in the PMF extracted from molecular simulations, for several values of the friction coefficient. It shows that no choice of friction allows to capture simultaneously the initial decay, the depth and the position of the minimum [5,6]. An underlying assumption of the Langevin equation 1is the decoupling of time scales between the solute (ion) and its environment, which may not be achieved under extreme confinement conditions, despite the larger mass of the cesium ion compared to that of water molecules.…”