Streaming potential-modulated capillary filling dynamics of immiscible fluids

The pressure driven transport of two immiscible electrolytes in a narrow channel with prescribed surface potential (zeta potential) is considered under the influence of a flow-induced electric field. The latter consideration is non-trivially and fundamentally different from the problem of electric field-driven motion (electroosmosis) of two immiscible electrolytes in a channel in a sense that in the former case, the genesis of the induced electric field, termed as streaming potential, is the advection of ions in the absence of any external electric field. As the flow occurs, one fluid displaces the other. Consequently, in cases where the conductivities of the two fluids differ, imbibition dynamically alters the net conductivity of the channel. We emphasize, through numerical simulations, that the alteration in the net conductivity has a significant impact on the contact line dynamics and the concomitant induced streaming potential. The results presented herein are expected to shed light on multiphase electrokinetics devices.