Diffusioosmotic dispersion in a long, narrow channel

Solute-surface interactions have garnered considerable interest in recent years as a novel control mechanism for driving unique fluid dynamics transport with potential applications to fields such as biomedicine, the development of microfluidic devices, and enhanced oil recovery. In this study, we will discuss dispersion induced by the diffusioosmotic motion near a charged wall in the presence of a solute concentration gradient. Here, we introduce a Gaussian plug of salt at the center of a channel with no background flow. The gradient in solute concentration drives a diffusioosmotic slip flow at the walls, which results in a recirculating flow in the channel; this, in turn, drives an advective flux of the solute concentration. This effect introduces cross-stream diffusion of the solute, altering the effective diffusivity. We will present theoretical predictions for the solute dynamics using a multiple-timescale analysis to quantify the dispersion driven by the solute-surface interactions. In addition, we will present numerical simulations to validate our theoretical predictions. Finally, we will comment on the effective diffusivity and long-time dynamics.