Effects of nonlinear chemical reactions on the transport coefficients associated with steady and oscillatory flows through a tube

The paper concerns with the determination of effective transport coefficients associated with the oscillatory flow through a tube where a solute undergoes nonlinear chemical reactions both within the fluid and at the boundary. Method of homogenization, a multiple-scale method of averaging, is adopted to derive the transport equation that contains advection, diffusion and reaction. The resultant equation shows how the transport coefficients are influenced by the rate and degree of the nonlinear chemical reaction. Two different nonlinear reactions are considered at the bulk flow and the boundary. The reactions at the boundary may be reversible and irreversible in nature. Several facts are established from the model by fixing the rate or degree of the nonlinear reactions. Results demonstrate that the reaction at the boundary is more influential than the bulk-flow reaction in determining the transport coefficients. Also fluid-phase reaction coefficient diminishes as the nonlinearity increases, whereas the trend is opposite for the nonlinear wall-phase reaction coefficient. Different controlling parameters are found to play significant role on the transport coefficients when the ratio of wall-phase concentration to the fluid-phase concentration is low.