Solute dispersion in channels with periodically varying apertures

We study solute dispersion in channels with periodically varying apertures. Based on an approximate analytical solution of the flow equation, we study the impact of the geometry and molecular diffusion on effective solute dispersion analytically using the method of local moments. We also study the problem numerically using a random walk particle tracking method. For transport in parallel shear flow, the effective dispersion coefficient is dependant on the square of the Peclet number. Here, when the fluctuation of the channel aperture becomes comparable with the channel width, the effective dispersion coefficients show a more complex dependence on the Peclet number and the pore geometry. We find that for a fixed flow rate, periodic fluctuations of the channel aperture can lead to both a decrease and an increase in effective dispersion.