A Numerical Study of Mass Transfer from Laminar Liquid Films

The process of a dissolved substance diffusing out of a liquid film in two-dimensional, gravity-driven laminar flow down a vertical solid plane is numerically simulated. The fluid mechanic problem is solved separately subject to periodicity conditions in the flow direction. After steady-state is reached, many copies of the calculated flow fields are efficiently “glued” together to generate a long computational domain for simulation of mass transfer. This approach renders it possible to follow the diffusion process over a long distance and to elucidate its various stages. It is found that large and small waves, with a maximum liquid velocity larger or smaller than the wave speed, respectively, behave differently. For the latter, the Sherwood number reaches an asymptotic value by the time the film still contains a significant amount of solute. From this point on, the mass transfer is very similar to that of a flat film with a smaller thickness. For large waves, the contributions of the various parts of the wave evolve differently with time and conditions and may negatively affect the mass transfer process if they get out of balance. Thus, the presence of recirculation is, in and by itself, insufficient to judge the mass transfer performance of a falling film.