Taylor Dispersion and Concentration Profiles of Solutes in the Capillary Transport of Active Liquids

In this paper, we develop a theory to capture Taylor dispersion and concentration profiles of a solute band transporting in a circular capillary in the presence of a background active fluid flow. Specifically, we consider active liquids containing active particles with vortex defects: under such circumstances, our recent calculations have revealed the generation of (diffusioosmosis-like) induced pressure-gradient-driven fluid flow in the presence of an axial gradient in the activity (or concentration of the active particles). This paper, therefore, captures the solute transport in such activity-gradient-triggered induced pressure-driven background flows. We obtain analytical results for the overall velocity, the Taylor dispersion coefficient (or effective diffusivity), and concentration profiles of the solute band. We compare our findings with the results of the solute transport in the presence of the background pressure-driven Hagen Poiseuille flow (having the same magnitude of pressure gradient as the activity gradient in active flows) and identify smaller Taylor dispersion (and hence lesser spread of the solute bands) and smaller average velocity (hence slower transport of the solute band-an effect that becomes more magnified at larger Peclet numbers) for the case of solute transport in background active liquid flows.