On transport coefficients in an oscillatory Couette flow with nonlinear chemical decay reactions

A multiple-scale homogenization technique is applied to study the transport of a chemical species in oscillatory Couette flow, where the species may undergo a reversible phase exchange with the boundary walls and nonlinear chemical decay phenomena occur both within the fluid and at the boundary walls. Analytical expressions are obtained for dispersion, advection and reaction coefficients. The main purpose of this work is to visualize the effects of nonlinear chemical decay reactions and the roles of different factors or parameters on transport coefficients. Results reveal that when the nonlinearity in the mobile phase reaction (reaction in the bulk flow) increases, its corresponding reaction coefficient decreases. An increase in the order of nonlinearity in the immobile phase reaction (reaction at the boundaries) will increase the advection coefficient for large retention parameter. Higher decay reaction rates in both the mobile and the immobile phase give larger reaction coefficients. It has also been noticed that stronger kinetics will lead to higher values of the transport coefficients.