Colloidal shadows reveal hidden solute transport

Abstract

An object releasing a chemical into a surrounding flow leaves behind a plume that encodes the rate of release, but for most solutes, that plume is invisible. Classical transport theory describes this configuration through a self-similar concentration boundary layer whose structure has never been resolved experimentally in forced flow at low Reynolds number: a century of measurements at these conditions has returned integrated transfer rates rather than the field itself. Here we show that both the field and the information it carries are experimentally accessible. Around hydrogel posts photopatterned inside a microfluidic channel, a released solute drives suspended colloidal particles away by diffusiophoresis, i.e., their drift along chemical gradients, carving a particle-free ``shadow'' downstream. Using a fluorescent solute, we resolve the concentration field around the post and recover the classical self-similar structure of convective mass transfer. For an invisible surfactant, the width of the shadow, benchmarked against a directly imaged solute on the same platform, then serves as a proxy for the dimensionless rate of mass transfer from the post. Finally, comparing two orientations of a triangular post tests a classical prediction by Brenner: the local concentration fields rearrange, yet no orientation dependence of the integrated transfer rate is resolved. For solute--tracer pairs whose diffusiophoretic response is known, colloidal shadows thus turn ordinary tracer particles into quantitative reporters of chemical exchange that cannot be observed directly.