Streaming potential and associated electrokinetic effects of power-law fluid in a soft nanochannel with pH-regulated polyelectrolyte layers

In this article, we investigate the streaming potential assisted pressure-driven flow of a power-law fluid through a soft nanochannel. The ion and flow permeable polyelectrolyte layers (PELs) grafted on the supporting rigid walls contain zwitterionic functional groups and, thus, the volume charge of the PEL depends on pH and ionic concentration of the bulk electrolyte. Our mathematical model combines the nonlinear Poisson−Boltzmann equation for electrostatic potential, the Darcy−Brinkman equation for flow within the PEL and the Cauchy momentum equation for the bulk fluid. We employ a numerical scheme based on the finite difference method to determine the flow profiles and streaming potential and subsequently measured the electroviscous effect and energy conversion efficiency. Furthermore, we derive simplified analytical results for these quantities under weakly charged pH-regulated PEL conditions and a Newtonian background electrolyte. We further demonstrate the dependence of fluid rheological behavior, pH, concentration of bulk electrolyte, etc., on the strength of induced streaming field as well as associated electrokinetic phenomena.