Taylor dispersion in oscillatory flow in rectangular channels

This paper focuses on exploring the effect of the side walls on dispersion in oscillatory Poiseuille flows in rectangular channels. The method of multiple time scales with regular expansions is utilized to obtain analytical expressions for the effective dispersivity D-3D*. The dispersion coefficient is of the form D-3D*/Pe(2) = f(Omega equivalent to omega h(2)/D, Sc equivalent to D/v, chi equivalent to w/h) where Pe equivalent to < u > h/D, < u > is the root mean square of the cross-section averaged velocity, omega is the angular velocity, 2w and 2h are, respectively, the width and the height of the cross-section. D is the solute diffusivity, and v is the fluid kinematic viscosity. The analytical results are compared with full numerical simulations and asymptotic expressions. Also effect of various parameters on dispersion coefficient is explored. For small oscillation frequency Omega the dispersion coefficient approaches the time averaged dispersion of the Poiseuille flow and for large Omega, D-3D* scales as Pe(2)/Omega(2) where Pe = < u > h/D. Due to its relative simplicity, the 2D model is frequently utilized for calculating dispersion in channels. However at small dimensionless frequencies the 20 model can significantly underestimate the dispersion, particularly for channels with large chi. At large Omega the dispersion coefficient predicted from the 20 model becomes reasonably accurate, particularly for channels with large chi. For a square channel, the 20 prediction is reasonably accurate for all frequencies. The results of this study will enhance our understanding of transport in microscale systems that are subjected to oscillating flows, and potentially aid technological advances in diverse areas relevant to microfluidic devices. (C) 2014 Elsevier Ltd. All rights reserved.