Three dimensional laminar dispersion in open and closed rectangular conduits

Abstract

The effect of side walls on the dispersion process in open and closed rectangular ducts is studied. As the aspect ratio increases, the steady state convection coefficient approaches an asymptotic value, obtained by neglecting side wall effects. However, the dispersion coefficient does not reduce to that for a flow with no side walls. The asymptotic steady state dispersion coefficient is about eight times larger than that obtained by neglecting side wall effects. The time dependent behavior of the convection and dispersion coefficients is also studied and it is shown that the real time required to reach the corresponding steady state value may be very large even for turbulent systems. In such cases simple constant coefficient models lead to serious error, and the present approach is a useful alternative. A simple approximate method of calculating the time dependent dispersion coefficient by adding the contribution of vertical and horizontal gradients, is shown to be useful over a wide range of operating conditions. This work provides a basis for studying three dimensional unsteady convective diffusion which occurs in various separation processes, including chromatography, electrophoresis, ultrafiltration and other systems.