Shear-enhanced dispersion in Kolmogorov flow

The present study investigates the solute dispersion due to flow generated by an imposed spatially periodic forcing to enhance solute dispersion using external forcing. The imposed forcing leads to the well-known Kolmogorov flow with zero volumetric flow rate. We have adopted Gill's methodology and homogenization approach to determine the transport coefficients considering the absorption at the top wall. In the large time limit, both methodologies yield the same results in the absence of wall absorption. However, at a high rate of absorption, these results disagree and the limitation of the homogenization approach is addressed in this study. There is no solute convection in the absence of wall absorption, whereas a non-trivial downstream solute convection is predicted in the presence of wall absorption. As the forcing wavenumber q increases, the solute is convected with a lower velocity of the fluid, owing to a decrease in the amplitude of oscillation of the fluid. Consequently, solute dispersion decreases, and the dispersion becomes diffusion-dominated. At high Peclect number Pe, two highly concentrated solute clouds occur near the walls. However, these clouds do not form at low Pe owing to the uniform distribution of solute in both directions. For large β and Pe, the solute is distributed more in the downstream direction than spreading in the upstream direction. For Pe=10, the peak of mean solute concentration increases by ten times compared to Pe=1. The dispersion is maximum when q=1, i.e., if the wavenumber of the spatial forcing is unity. This study also investigates the dispersion of colloid particles in the Kolmogorov flow with the effect of shear-induced diffusivity, which is the concentration-dependent diffusivity related to both Brownian and shear motions of the particles. The Taylor dispersion theory is applied to describe the shear-induced dispersion arising from the hydrodynamics interactions and the concentration distribution of the particles. More axial spreading of the concentration distribution is predicted for shear-induced diffusion than for constant diffusion. Thus, this study demonstrates the effectiveness of external periodic forcing in enhancing shear dispersion in Kolmogorov flow.