Multiscale Model for Electrokinetic Transport in Networks of Pores, Part I: Model Derivation

Abstract

We present an efficient and robust numerical model for the simulation of electrokinetic phenomena in porous media and microstructure networks considering a wide range of applications including energy conversion, deionization, and microfluidic-based lab-on-a-chip systems. Coupling between fluid flow and ion transport in these networks is governed by the Poisson-Nernst-Planck-Stokes equations. These equations describe a wide range of phenomena that can interact in a complex fashion when coupled in networks involving multiple pores with variable properties. Capturing these phenomena by direct simulation of the governing equations in multidimensions is prohibitively expensive. We present here a reduced-order model that treats a network of many pores via solutions to 1D equations. Assuming that each pore in the network is long and thin, we derive a 1D model describing the transport in the pore's longitudinal direction. We take into account the cross-sectional nonuniformity of potential and ion concentration fields in the form of area-averaged coefficients in different flux terms representing fluid flow, electric current, and ion fluxes. These coefficients are obtained from the solutions to the Poisson-Boltzmann equation and are tabulated against dimensionless surface charge and dimensionless thickness of the electric double layer (EDL). Although similar models have been attempted in the past, distinct advantages of the present framework include a fully conservative discretization with zero numerical leakage, fully bounded area-averaged coefficients without any singularity in the limit of infinitely thick EDLs, a flux discretization that exactly preserves equilibrium conditions, and extension to a general network of pores with multiple intersections. In part II of this two-article series, we present a numerical implementation of this model and demonstrate its applications in predicting a wide range of electrokinetic phenomena in microstructures.

Impact of network heterogeneity on electrokinetic transport in porous media

“…In our previous two-paper series, 46,47 we presented comprehensive derivation and validation of our multi-scale model that enables pore-scale simulation of nonlinear electrokinetic phenomena in porous structures. We model a porous structure as a network of micro-scale and nano-scale pores, each is to be long and thin.…”

“…We investigated the relation between U max and C ref (Figure (13)) and observed the power fits with the exponents 0.4 and 0.2 respectively for Networks Lastly, we provide insights on why U max may increase with the electrolyte salinity when C s is held fixed. Using our tabulated area-averaged coefficients, 46 we re-plottedḡ e coefficient, representing the electroosmotic velocity, with respect to 1/λ 2 D ∼ C ref for different values of C s (Figure (13c)). This diagram illustrates that for a fixed C s increasing C ref results in faster electroosmotic flow in a single channel subject to a fixed electric potential.…”

“…have not yet been analyzed, despite their being implicated in experimental observations of OLC and deionization shock waves in porous media. 31,33,34 Here, we leverage our recently developed computational framework for nonlinear electrokinetics in porous media 46,47 to begin answering these fundamental questions related to OLC in charged porous media.…”

“…We employ our previously developed computational framework 46,47 to conduct the simulations of electrokinetic transport in massive random networks of pores. In particular, we examine the internally induced flows due to random pore coupling and connectivity loops and investigate how such flows can lead to enhancement of OLC in systems subject to ICP.…”

Modelling of Ion Transport in Electromembrane Systems: Impacts of Membrane Bulk and Surface Heterogeneity

“…The research field making accent on the fluid transfer in narrow channels was only recently termed as nanofluidics but it has a quite rich history, in particular, in membrane science [194]. Nanoand microfluidics research as well as the applications in this field have experienced extensive growth in recent years [195][196][197][198][199]. 100 nm enables the occurrence of the phenomena, which are impossible at bigger length scales.…”