Steady bilayer channel and free-surface isothermal film flow over topography

Abdalla, A.A.; Veremieiev, S.; Gaskell, P.H.

Abstract

Two flow configurations, involving bilayers, are explored systematically: through an inclined channel comprised of two planar surfaces in parallel alignment and down an inclined plane. Both liquid layers are assumed to be perfectly immiscible and the lower rigid bounding surface contains locally defined steep-sided topographical features – either a step-up/-down or a trench. A common governing equation-set based on the long-wave approximation and depth-averaging is derived, embodying the more general case of a system of n-layers, and solved numerically. Results for the particular case of flow in a vertically aligned channel are found to be indistinguishable from corresponding solutions in the literature; those for the case of a step-up and non-zero Reynolds number having not been reported hitherto. New to this, the case of flow in a inclined channel is investigated as is the situation when, in horizontal alignment, the channel’s upper planar bounding surface moves with a constant speed inducing a shear flow. Gravity-driven bilayer film flow reveals a number of interesting features dependent on the fluid properties, the Reynolds number and the ratio of the upper to lower liquid layer thickness, with parallels drawn to the practically relevant cascade/slide-coating mode of multi-layer thin-film deposition. In the limit when both layers have identical properties the corresponding equivalent single layer solution is recovered exactly.

Citation

Abdalla, A., Veremieiev, S., & Gaskell, P. (2018). Steady bilayer channel and free-surface isothermal film flow over topography. Chemical Engineering Science, 181, 215-236. https://doi.org/10.1016/j.ces.2018.01.031

• Journal Article Type: Article
• Acceptance Date: Jan 22, 2018
• Online Publication Date: Feb 10, 2018
• Publication Date: May 1, 2018
• Deposit Date: Feb 16, 2018
• Publicly Available Date: Feb 10, 2019
• Journal: Chemical Engineering Science
• Print ISSN: 0009-2509
• Publisher: Elsevier
• Peer Reviewed: Peer Reviewed
• Volume: 181
• Pages: 215-236
• DOI: https://doi.org/10.1016/j.ces.2018.01.031