Upscaling of dispersion in gas-liquid absorption on an inclined surface

We extend the Taylor-Aris dispersion theory to upscale the gas absorption into a viscous incompressible liquid flowing along an inclined surface. A reduced-order model of advection-dispersion-reaction is developed with the aid of Reynolds decomposition and cross-sectional averaging techniques. The upscaled model allowed evaluation of the dispersion, advection, and absorption kinetics as a function of the Peclet number (Pe) and the Damköhler number (Da). The transport and kinetics parameters for the limiting cases of nonabsorption and absorption dominant are also evaluated. The upscaled model is solved analytically, and the obtained solution is used to evaluate the upscaled mass transfer between the gas and liquid. The results for the overall Sherwood number identify three regions: (i) advection dominant, (ii) transition where both advection and absorption play a role, and (iii) absorption dominant. The scaling relation between the Sherwood number (Sh) and the Da for the last region was determined to follow Sh∼Da^{1/2}. It is also revealed that in the first two regions, the Sherwood number versus the Peclet number exhibits a bell-shaped (or Gaussian) behavior, suggesting an optimal Pe that maximizes mass transfer between gas and liquid in these regions. The model and insights presented have the potential to be applied in a wide range of industrial separation processes involving the interaction of a gas exposed to a liquid flowing downward on an inclined surface under gravity.