Diffusiophoresis in a Taylor-dispersing solute

We consider coupled solute and particle dynamics in a long, narrow, two-dimensional channel flow, where the motion of each species is the result of advection, diffusion, and diffusiophoresis. We describe the evolution of the solute and particle concentration fields at early times, distinguishing this work from existing studies that consider one-dimensional or long-time behaviors. We use a lubrication approximation to describe the particle diffusiophoresis that is driven by a solute concentration field experiencing Taylor dispersion in a background Poiseuille flow. Theoretical predictions are based on the assumption of constant zeta potential. To validate these results, we then compare the theoretical predictions at a fixed zeta potential with numerical simulation results that consider variable zeta potential, which show good agreement. Finally, we comment on the assumption of constant zeta potential for such problems.