Cross-streamline diffusiophoretic migration of colloids in Taylor-dispersed channel flows

Abstract

Diffusiophoretic transport of colloids in pressure-driven channel flow is commonly analysed in two limits: an early-time regime in which the solute field is fully two-dimensional, and a late-time macrotransport regime in which cross-sectional homogenization leaves only a weak axial bias on the particles. For colloids, however, many experiments operate in the broad intermediate window \(a^2/D_{\mathrm s}\ll t\ll a^2/D_{\mathrm p}\): the solute has entered the Taylor-dispersion regime, but the particles remain effectively non-diffusive across the gap. We show that the Taylor-dispersed solute retains a residual transverse gradient that is P\'eclet-enhanced relative to the axial gradient and decays only as \(t^{-1/2}\). This gradient is small in the solute concentration but large enough in \(\nabla\ln c\) to drive cross-streamline migration of colloids. Attractive fronts (\(c_{\mathrm f}>c_{\mathrm i}\)) move particles toward faster centreline streamlines, sharpening the leading edge and accelerating removal; repulsive fronts (\(c_{\mathrm f}<c_{\mathrm i}\)) move particles toward slower near-wall streamlines, broadening the trailing edge and delaying removal. Direct simulations and microfluidic experiments confirm these front-sharpening and front-broadening dynamics. An asymptotic Taylor-regime solute field, combined with a non-diffusive trajectory model, captures the observed front geometries, density profiles, and removal dynamics. The results show that Taylor-dispersed solute fields can remain dynamically two-dimensional for particles, even when their concentration is nearly cross-sectionally uniform.