An analysis of advective diffusion in branching channels

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Abstract
Solutions to the steady advection–diffusion equation in a branching channel are obtained for both uniform and spatially varying flow fields and for two channel geometries. An interesting feature of the solutions is that anisotropy of the dispersion coefficients in the direction of the streamlines may be accounted for. The analysis reveals that mixing is confined to a distance, b2U/π2KN, downstream of the junction in the advection-dominated case and a distance, KS/U, upstream in the diffusion-dominated situation, KS and KN being the diffusivities along and across the flow respectively, U the characteristic velocity of the flow, and b the breadth of channel downstream of the junction.

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