Consistent accounting of steric effects for prediction of streaming potential in narrow confinements

Abstract

The traditional modeling framework for determining streaming potential, when taking into consideration finite size effects, suffers from an oversight in that while the model incorporates the size effects in the ion distribution profiles, it neglects these very same effects in the flux contributions, even though diffusivities are intrinsically linked with ionic friction, which again depends on the size of the ions. This oversight may lead to inconsistent quantitative estimates through ad hoc consideration of diffusivity values, apparently independent of the specific size of the ions, which nevertheless determines the ionic profiles. We remedy this theoretical inconsistency by expressing the diffusivity in terms of the ionic radius and investigate the consequences of such a description of the diffusivity-dependent flux, consistent with the ionic distribution profiles, on streaming potential mediated flow predictions. Additionally, we consider the effects of "charge induced thickening" so that both viscosity and diffusivity are expressed as spatially varying functions. As an unintuitive implication, we also show that calculation of nonzero values of streaming potential under the purview of classical Boltzmann distributions, which consider ions to be pointlike charges, is itself a theoretical inconsistency. We believe that the simple framework presented in this paper will pave the way for more sophisticated modeling efforts in the future.