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A numerical study of mass transfer from laminar liquid films

Published online by Cambridge University Press:  04 September 2020

Guangzhao Zhou  and
Andrea Prosperetti Open the ORCID record for Andrea Prosperetti [Opens in a new window]
Guangzhao Zhou
Affiliation:
Department of Mechanical Engineering, University of Houston, Houston, TX77204, USA
Andrea Prosperetti*
Affiliation:
Department of Mechanical Engineering, University of Houston, Houston, TX77204, USA Faculty of Science and Technology and J. M. Burgers Center for Fluid Dynamics, University of Twente, Enschede, The Netherlands Department of Mechanical Engineering, Johns Hopkins University, Baltimore, MD 21218, USA
*
†Email address for correspondence: [email protected]
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Abstract

The paper presents results of numerical simulations of a dissolved substance diffusing out of a liquid film in a two-dimensional, gravity-driven laminar flow down a vertical solid plane. The fluid mechanic problem is solved separately subject to periodicity conditions in the flow direction. After steady-state is reached, up to a hundred copies of the calculated wave and associated flow fields are efficiently ‘glued’ together to generate a long computational domain for the diffusion process which is solved as an initial-value problem. 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 (quantified in this paper). For large waves, the contributions of the various parts of the wave – main crest, capillary waves, nearly flat substrate – 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.

JFM classification

Interfacial Flows (free surface): Thin films Waves/Free-surface Flows: Capillary waves
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 902 , 10 November 2020 , A10
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Copyright
© The Author(s), 2020. Published by Cambridge University Press

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References

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