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Capillary transport of two immiscible fluids in presence of electroviscous retardation

The transport of two immiscible electrolytes through a narrow confinement whose walls bear a finite surface potential is analyzed through a lumped model by considering the influence of a regulatory self‐induced axial electric field, termed as streaming potential. The presence of a surface charge on the channel walls culminates in the aqueous solutions carrying a net charge so as to make the overall system (channel and fluid) electrically neutral. The advection due to pressure driven flow or capillarity in the absence of any externally imposed electric field causes a preferential transport of net charged species. Thus, in order to render a net zero current through the system, there is an induced electric field which also retards the flow as a consequence of the force acting on the charged segments of fluid due to the streaming electric field. It is shown through a lumped model that for the situation of two distinct segments of fluids, the rate of front penetration into the capillary is strongly dependent on the relative conductivities of the two fluids. The streaming electric field evolves in accordance to the net conductivity of the channel and is responsible for dynamic changes in the retarding influence on the segments of fluid.