Taylor dispersion in the presence of cross flow and interfacial mass transfer

Transverse velocity gradients can enhance the effective diffusion coefficient of a scalar in the primary flow direction, a phenomenon known colloquially as Taylor dispersion. In this work, we perform Taylor dispersion analysis on a canonical pressure-driven flow in a channel with a cross flow, using both perturbation theory and Brownian dynamics simulations. Moreover, we illustrate how mass transfer at the wall affects the evolution of the scalar. By writing a one-dimensional advection-diffusion-mass-transfer equation for the cross-sectionally averaged concentration, we elucidate how the effective diffusion coefficients, effective advective velocities, and effective mass-transfer rates depend on the strength of the cross flow and the wall transfer coefficient. We perform an asymptotic analysis to investigate the limit of strong cross flow and demonstrate that, in this limit, dispersion rapidly decreases with increasing cross-flow velocity V as V^-4 and scales with the Brownian diffusivity D as D³. Additionally, we discuss the effect of the Schmidt number, the ratio of momentum to mass diffusion, which effectively controls the extent to which the cross flow affects the axial velocity profile. Finally, we describe how our results can be extended to include transverse velocities and diffusivities that are spatially nonuniform.