We revisit the classical problem of diffusion-limited ion transport to a membrane (or electrode) by considering the effects of charged side walls. Using simple mathematical models and numerical simulations, we identify three basic mechanisms for over-limiting current in a microchannel: (i) surface conduction carried by excess counterions, which dominates for very thin channels, (ii) convection by electro-osmotic flow on the side walls, which dominates for thicker channels and transitions to (iii) electro-osmotic instability on the membrane end in very thick channels. These intriguing electrokinetic phenomena may find applications in biological separations, water desalination, and electrochemical energy storage.

Most electrochemical processes, such as electrodialysis, are limited by diffusion, but in porous media, surface conduction and electroosmotic flow also contribute to ionic flux. In this article, we report experimental evidence for surface-driven overlimiting current (faster than diffusion) and deionization shocks (propagating salt removal) in a porous medium. The apparatus consists of a silica glass frit (1 mm thick with a 500 nm mean pore size) in an aqueous electrolyte (CuSO4 or AgNO3) passing ionic current from a reservoir to a cation-selective membrane (Nafion). The current-voltage relation of the whole system is consistent with a proposed theory based on the electroosmotic flow mechanism over a broad range of reservoir salt concentrations (0.1 mM to 1.0 M) after accounting for (Cu) electrode polarization and pH-regulated silica charge. Above the limiting current, deionized water (≈10 μM) can be continuously extracted from the frit, which implies the existence of a stable shock propagating against the flow, bordering a depleted region that extends more than 0.5 mm across the outlet. The results suggest the feasibility of shock electrodialysis as a new approach to water desalination and other electrochemical separations.

The conductivity of highly charged membranes is nearly constant, due to counterions screening pore surfaces. Weakly charged porous media, or “leaky membranes,” also contain a significant concentration of coions, whose depletion at high current leads to ion concentration polarization and conductivity shock waves. To describe these nonlinear phenomena in the absence of electro‐osmotic flow, a simple leaky membrane model is formulated, based on macroscopic electroneutrality and Nernst–Planck ionic fluxes. The model is solved in cases of unsupported binary electrolytes: steady conduction from a reservoir to a cation‐selective surface, transient response to a current step, steady conduction to a flow‐through porous electrode, and steady conduction between cation‐selective surfaces in cross flow. The last problem is motivated by separations in leaky membranes, such as shock electrodialysis. The article begins with a tribute to Neal Amundson, whose pioneering work on shock waves in chromatography involved similar mathematics. © 2013 American Institute of Chemical Engineers AIChE J, 59: 3539–3555, 2013

Objective Venous thromboembolism frequently results in thrombi formation near or within the pocket of a venous valve as the result of recirculating hemodynamics, which has been largely attributed to hypoxia-induced tissue factor (TF) expression. Numerical models are now capable of assessing the spatiotemporal behavior of the TF initiated coagulation cascade under non-uniform hemodynamics. The aim of this study was to use such a numerical simulation to analyze the degree and location of thrombin formation with respect to tissue factor position in the presence of disturbed flow induced by an open venous valve. Method Thrombin formation was simulated using a computational model that captures the hemodynamics, kinetics and chemical transport of 22 biochemical species. Disturbed flow is described by the presence of a valve in the equilibrium phase of the valve cycle with leaflets in a fully open position. Three different positions of TF downstream of the valve opening were investigated. Results The critical amount of TF required to initiate a thrombotic response is reduced by up to 80% when positioned underneath the recirculating regions near the valve opening. Additionally, due to the increased surface area of the open valve cusp, in conjunction with recirculating hemodynamics, it was observed that thrombin is generated inside the valve pocket even when the exposed region of TF is downstream of the valve. Conclusions The presence of pro-thrombotic surface reactions, in conjunction with recirculating hemodynamics, provides an additional mechanism for thrombus formation in venous valves, which does not require direct damage or dysfunction to the valve itself.

An expanded computational model of surface induced thrombin generation was developed that includes hemodynamic effects, 22 biochemical reactions and 44 distinct chemical species. Surface binding of factors V, VIII, IX, and X was included in order to more accurately simulate the formation of the surface complexes tenase and prothrombinase. In order to model these reactions, the non-activated, activated and inactivated forms were all considered. This model was used to investigate the impact of surface bound heparin on thrombin generation with and without the additive effects of thrombomodulin (TM). In total, 104 heparin/TM pairings were evaluated (52 under venous conditions, 52 under arterial conditions), the results demonstrating the synergistic ability of heparin and TM to reduce thrombin generation. Additionally, the role of circulating tissue factor (TFp) was investigated and compared to that of surface-bound tissue factor (TFs). The numerical results suggest that circulating TF has the power to amplify thrombin generation once the coagulation cascade is already initiated by surface-bound TF. TFp concentrations as low as 0.01 nM were found to have a significant impact on total thrombin generation.