Tuning diffusioosmosis of electrolyte solutions by hydrostatic pressure

Abstract

When two reservoirs of a distinct salinity are connected by channels or pores, a fluid flow termed diffusio-osmotic is generated. This article investigates the flow emerging in an uniformly charged long slit whose thickness exceeds the local Debye screening length. Attention is focussed on the role of hydrostatic pressure drop $\Delta p$ in establishing diffusioosmosis at a finite concentration difference. For a thick slit we recover the known formula for a local diffusio-osmotic slip over a single wall, which is determined by the surface potential, salt concentration and its gradient. An equation for the global fluid flow rate $\mathcal{Q}$ is presented as a sum of the diffusio-osmotic and pressure-driven contributions. Although the diffusio-osmotic term itself remains unaffected by $\Delta p$, the nonlinear concentration and surface potential profiles along the slit, and consequently, the local slip velocity are dramatically modified. We present an equation relating the local concentration to $\mathcal{Q}$ and employ it to derive an expression describing the surface potential variation in the slit. Since $\mathcal{Q}$ can easily be tuned by $\Delta p$, the variety of possible concentration and surface potential profiles becomes very rich. Our theory provides a simple explanation of recent flow rate measurements and shows that experimental data provide rather direct information about concentration and surface potential profiles in the uniformly charged slit. The relevance of our results for sensing the salt dependence of surface potentials is discussed briefly.