Nonlinear electrokinetic transport in microscale and nanoscale porous structures [electronic resource]
Keywords: Mechanical Engineering.

We present an efficient and robust numerical model for simulation of electrokinetic phenomena in networks of pores over a wide range of applications including energy conversion, desalination, and 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 transport phenomena that can interact in complex and highly nonlinear ways in networks involving multiple pores with variable properties. Capturing these phenomena by direct simulation of the governing equations in multiple dimensions is prohibitively expensive. We present here a reduced order computational 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 pore's longitudinal direction. We take into account the non-uniformity of potential and ion concentration profiles across the pore cross-section in the form of area-averaged coefficients in different flux terms representing fluid flow, electric current, and ion fluxes. Distinct advantages of the present framework include: (1) a fully conservative discretization, (2) covering the entire range of electric double layer (EDL) to pore size ratio, (3) fully bounded tabulated area-averaged coefficients and driving potentials without any singularity in the limit of zero concentration, (4) a well-balanced flux discretization that exactly preserves equilibrium conditions in the absence of driving forces, (5) multi-step and efficient computational algorithms that avoids inversion of large matrices derived from conservation laws over the whole network, and (6) extension to general network of pores with multiple intersections. We have verified our model against direct numerical simulations of deionization shock in micropore-membrane junction and concentration polarization in micro-nano-micro pore junction subject to pressure gradient. Our model reveals the same scaling laws for temporal variation of shock distance and shock thickness in micropore-membrane junction, which have been predicted by analytical theory and validated by experiments. By considering a wide range of canonical problems with increasing complexity, we demonstrate that the developed model can predict a wide range of phenomena. For pores subject to concentration gradients, the model captures the induced osmotic pressure in the limit of thin pores, and allows the quantification of induced pressure in non-ideal limit (pore with finite size). It captures current rectification in conical nano-pores subject to axial electric field and demonstrates that advection transport can play a role in increasing the rectified current and would not be negligible in high applied potentials. Our model is capable of predicting phenomena such as stationary shocks in H-junction network, and internally induced flow loops when pores with different sizes are connected in parallel. The developed methodology enables robust and efficient simulation of electrokinetic transport in massive networks of pores, with orders of magnitude lower computational cost than brute force approach. As opposed to direct numerical simulations that require extensive supercomputing resources, this model can be utilized for simulation of porous networks with arbitrary topology on a desktop computer. Our simulations of massive network of pores reveal the inherent impact of pore size variability and pore-pore coupling on overlimiting transport through porous structures. At low surface conduction, when sufficiently large potential is applied, we demonstrate that electrokinetic transport in a porous network can be dominated by advection mechanism via internally induced flow loops. We illustrate how the homogenized model that misses the advection effect can mispredict the system behavior and lead to a wrong solution. Furthermore, using the developed model we explore the dependency of system response on parameters associated with network topology and electrolyte salinity. Our model provides an efficient tool to study the complex physics that could occur in porous structures, and understand physical trends that can inspire design of efficient porous materials.