Accounting for adsorption and desorption in lattice Boltzmann simulations

Abstract

We report a Lattice-Boltzmann scheme that accounts for adsorption and desorption in the calculation of mesoscale dynamical properties of tracers in media of arbitrary complexity. Lattice Boltzmann simulations made it possible to solve numerically the coupled Navier-Stokes equations of fluid dynamics and Nernst-Planck equations of electrokinetics in complex, heterogeneous media. With the moment propagation scheme, it became possible to extract the effective diffusion and dispersion coefficients of tracers, or solutes, of any charge, e.g., in porous media. Nevertheless, the dynamical properties of tracers depend on the tracer-surface affinity, which is not purely electrostatic and also includes a species-specific contribution. In order to capture this important feature, we introduce specific adsorption and desorption processes in a lattice Boltzmann scheme through a modified moment propagation algorithm, in which tracers may adsorb and desorb from surfaces through kinetic reaction rates. The method is validated on exact results for pure diffusion and diffusion-advection in Poiseuille flows in a simple geometry. We finally illustrate the importance of taking such processes into account in the time-dependent diffusion coefficient in a more complex porous medium.

Lattice simulation method to model diffusion and NMR spectra in porous materials

“…Here, we use a different approach, namely, the so-called "moment propagation" method, which was proposed by Frenkel and successfully applied to a number of studies on dynamics of particles in confined systems. 14,24,25 The moment-propagation method is a recursive scheme that allows us to sample all possible trajectories of the diffusing particles, rather than a subset. The computational effort scales as t × M, where t is the simulation time and M the number of lattice sites.…”

“…It is particularly attractive to use lattice models as these allow us to account for the relevant microscopic effects while being computationally much more efficient than offlattice models. The key computational advantage of the lattice approach used here is that it allows us to sample, in a single simulation, all possible diffusive trajectories, 14 rather than a single one, as would be obtained from an off-lattice simulation or from a conventional lattice simulation of the diffusion of tracers in porous media. [15][16][17] The (exponential) computational advantage of this approach turns out to be crucial for exploring the effect of multiple factors on the NMR spectra.…”

An empirical correlation of the longitudinal and transverse dispersion coefficients for flow through random particle packs

“…This band broadening phenomenon is governed by the pore scale convection and diffusion (called dispersion), which is crucial in many technological applications, such as separation, contaminant transport, oil production, geological CO 2 sequestration, fuel cells, nutrient transport. The dispersion behavior depends on the pore structure (Bacri et al, 1987;Kandhai et al, 2002;Schure and Maier, 2006;Willingham et al, 2008;Maier et al, 2008;Khirevich et al, 2012;Jourak et al, 2013), fluid properties (Delgado, 2006), surface reaction (Augier et al, 2008;Fridjonsson et al, 2011;Varloteaux et al, 2013;Levesque et al, 2013). The dispersion behaviors along and perpendicular to the mean flow are different, and they are characterized by the longitudinal and transverse dispersion coefficients, respectively.…”

Bottom-up model of adsorption and transport in multiscale porous media

“…Fluid mechanics such as computational fluid dynamics, which relies on Navier-Stokes and Boltzmann equations, is not suited as it assumes that the flow regime at the field scale remains valid at vanishing scales and does not account for adsorption and the wide range of confined fluid states [11][12][13]. Recently, Levesque et al [14] have attempted to account for adsorption in the mesoscopic equations of lattice Boltzmann dynamics [15] while Albaalbaki and Hill have integrated adsorption in continuum models with diffusion processes [16]. Homogenization methods also allow inserting adsorption effects in transport at a given scale [17,18].…”