Exact solutions for quantifying spreading of chemotactic and diffusiophoretic species under a hydrodynamic flow

The transport of microorganisms by chemotaxis is described by the same "log-sensing" response as colloids undergoing diffusiophoresis, despite their completely different mechanistic origins. In this talk, we employ a recent macrotransport theory to analyze the advective-diffusive transport of a chemotactic or diffusiophoretic colloidal species in a uniform circular tube under a steady pressure-driven flow and transient solute gradient. We derive exact solutions to the macrotransport equation, enabling efficient quantification of the large parameter space in chemotactic/diffusiophoretic colloid transport. First, we show that while hydrodynamic flow enhances colloid spreading in most cases, it can reduce colloid spreading for strongly solute-repelled colloids. Second, the minimum spreading for strongly solute-repelled colloids occurs in the intermediate hydrodynamic flow regime, contrasting the minimum for solute-attracted colloids which is attained in the absence of a hydrodynamic flow. Third, the macrotransport theory predicts new regimes of anomalous diffusion with a hybrid, linear-log-sensing chemotactic model, which otherwise cannot be realized with the traditional log-sensing relation.