Enhanced electroosmotic flow, conductance and ion selectivity of a viscoplastic fluid in a hydrophobic cylindrical pore

Abstract

We have studied the electroosmotic flow (EOF) of a non-Newtonian viscoplastic fluid, modeled as a Herschel-Bulkley (H-B) fluid, through a single hydrophobic nanopore in a uniformly charged solid hydrophobic membrane separating two identical reservoirs. An interfacial slip velocity develops when the viscoplastic fluid is strained over a hydrophobic surface. It is well established in the context of Newtonian fluid that the interfacial slip at the charged surface augments the EOF. For the viscoplastic fluid, the EOF depends on the fluid behavioral index and the yield stress. We have illustrated the impact of the interfacial slip on the EOF, conductance and ion selectivity of the cylindrical nanopore at different yield stresses for both the shear thinning and the shear thickening cases of the H-B fluid. The slip velocity, characterized by the slip length, enhances the average flow and conductance of the pore and this impact is pronounced for the shear thinning case. The unyielded zone, which develops along the central line of the pore, contracts as the slip length is increased. The ion concentration polarization enhances for the shear thinning fluid, however, the slip length creates a marginal increment. The counterion selectivity of the pore is found to be significant for the Newtonian case as compared to the non-Newtonian fluid and the velocity slip enhances the ion selectivity further. We have determined an analytic solution for the EOF of a power-law fluid in a long hydrophobic tube. Our computed solution for the case of a long tube effectively coincides with this analytic solution. An increment in the pore length reduces its conductance but enhances the ion selectivity. The increment of the average EOF for the hydrophobic pore as compared to the no-slip case grows as the pore length is increased.