Thermocapillarity Motion of a Droplet within a Permeable Cavity

Document Type : Research article

Authors

Department of Mathematics and Computer, Faculty of Science, Alexandria University, Alexandria, Egypt

Abstract

The thermocapillarity motion of a non-deformable spherical droplet embedded in a concentric
permeable spherical cavity, filled with a Newtonian viscous fluid, and subjected to a uniformly
prescribed temperature gradient, is investigated analytically. The energy and momentum field
equations are resolved within the quasi-steady limit, considering small Péclet and Reynolds
numbers. Additionally, in this investigation, it is assumed that the capillary number at the droplet
interface is small, ensuring the perpetuation of the droplet's spherical shape throughout its motion.
We have derived normalized thermocapillarity velocity results across a broad spectrum of relative
thermal conductivity values, cavity permeabilities, and viscosity ratios. The obtained normalized
thermocapillarity velocity is emphasized using graphs and tables, allowing for a comparison with
existing literature data. Additionally, specific cases available in the literature have been examined
to further validate our findings. This study is inspired by diverse flow situations, including particle
deposition in processes like reverse osmosis, dialysis, and within various biological organs where
fluid traverses’ membranes or cell cavity walls.

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Alexandria Journal of Science and Technology

Articles in Press, Accepted Manuscript
Available Online from 29 April 2024

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