The hydrodynamic dispersion of a solute band for a fully developed laminar flow in a microchannel under steady state is studied theoretically. The mean velocity profile for the Hagen-Poiseuille flow is obtained for a no-flux boundary condition at the flat wall and an irreversible chemical reaction of first order at the curved wall of the microchannel. The convective diffusion equation is solved for the appropriate initial and boundary conditions. The generalized dispersion model was thus used to obtain analytical solutions for the transport parameters such as concentration profiles, convection and dispersion coefficients as well as exchange coefficient (mass transfer) at the channel boundary. Results are presented graphically for several cases. A parametric study of the transport properties was performed by varying the Damkoehler number which influences the long term values of the transport coefficients. A Damkoehler number is a ratio of the characteristic liquid residence time to the reaction time. Results are presented graphically for the exchange coefficient, dispersion coefficient and the transport coefficient over dimensionless time. Also the influence of the Damkoehler number on the time dependence of the convection and transport coefficients is presented graphically. It is observed that the dispersion coefficient decreases with the increase in the Damkoehler number while the exchange and convection coefficients increase together with the Damkoehler number. The time evaluation of the dimensionless concentration profiles at the channel inlet is presented. The result shows that the mean concentration is smaller for a higher Damkoehler number but, at the same time, its location moves faster along the channel. It is shown that the mean concentration spreads over time while the maximum concentration decreases.
The analytical result presented in the paper on the hydrodynamic dispersion may be useful for the microfluidics.