(412g) Dispersion in Steady Two-Dimensional Flows through a Parallel-Plate Channel
We applied the macro-transport equation to examine dispersion in a two-dimensional pressure-driven flow in a heterogeneous channel comprising alternating shear-free and no-slip regions, relevant to electroosmotic flows and flows in superhydrophobic environments. The results therefrom were compared with those obtained from a unidirectional Poiseuille flow in a homogeneously no-slip channel, in which case we recovered the classical constant dispersivity with no zero advection speed correction. In contrast, in the heterogeneous channel the dispersion coefficient changes from zero to a finite value when the flow transitions from plug-like in the shear-free section to parabolic in the no-slip region. The mean velocity faithfully represents the advection speed in each region far away from the shear-free-no-slip transition, at which a localized negative correction is found to account for the decrease in the velocity. We further substituted the transport coefficients into the macro-transport equation to compute the evolution of the concentration profile. The evolution predicted by the macro-transport equation agrees well with that obtained by numerically solving the two-dimensional advection-diffusion equation. We found that while the shear-free section suppresses band broadening, the following no-slip section may lead to a wider band compared to an otherwise homogeneously no-slip channel. This suggests caution being exercised in controlling band broadening in channels with surface heterogeneities, such as encountered in capillary electrophoresis.