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We present an efficient and robust numerical model for simulation ofelectrokinetic phenomena in porous networks over a wide range of applicationsincluding energy conversion, desalination, and lab-on-a-chip systems. Couplingbetween fluid flow and ion transport in these networks is governed by thePoisson-Nernst-Planck-Stokes equations. These equations describe a wide rangeof transport phenomena that can interact in complex and highly nonlinear waysin networks involving multiple pores with variable properties. Capturing thesephenomena by direct simulation of the governing equations in multipledimensions is prohibitively expensive. We present here a reduced ordercomputational model that treats a network of many pores via solutions to 1Dequations. Assuming that each pore in the network is long and thin, we derive a1D model describing the transport in pore's longitudinal direction. We takeinto account the non-uniformity of potential and ion concentration profilesacross the pore cross-section in the form of area-averaged coefficients indifferent flux terms representing fluid flow, electric current, and ion fluxes.Distinct advantages of the present framework include: a fully conservativediscretization, fully bounded tabulated area-averaged coefficients without anysingularity in the limit of infinitely thick electric double layers (EDLs), aflux discretization that exactly preserves equilibrium conditions, andextension to general network of pores with multiple intersections. Byconsidering a hierarchy of canonical problems with increasing complexity, wedemonstrate that the developed framework can capture a wide range of phenomena.Example demonstrations include, prediction of osmotic pressure built up in thinpores subject to concentration gradient, propagation of deionization shocks andinduced recirculations for intersecting pores with varying properties.

A multi-scale model for electrokinetic transport in networks of micro-scale and nano-scale pores