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Non-Newtonian and viscoplastic models of a vertically-aligned thick liquid film draining due to gravity

Naire, Shailesh

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We consider theoretically the two-dimensional flow in a vertically-aligned thick liquid film supported at the top and bottom by wire frames. The film gradually thins as the liquid drains due to gravity. We focus on investigating the influence of non-Newtonian and viscoplastic effects, such as shear thinning and yield stress, on the draining and thinning of the liquid film, important in metallic and polymeric melt films. Lubrication theory is employed to derive coupled equations for a generalised Newtonian liquid describing the evolution of the film’s thickness and the extensional flow speed. We use the non-Newtonian (Power-law and Carreau)
and viscoplastic (Bingham and Herschel-Bulkley) constitutive laws to describe the flow rheology. Numerical solutions combined with asymptotic solutions predict late-time power-law thinning rate of the middle section of the film. For a Newtonian liquid, a new power law thinning rate of t -2.25 is identified. This is in comparison to a thinning rate of t -2 predicted for a thin Newtonian liquid film neglecting gravity, suggesting a weak dependence on gravity for the drainage of thicker films. For a non-Newtonian and viscoplastic liquid, varying the power law index and the yield stress influences the time scale of the thinning, but has weak dependence on the late-time thinning rate relative to the Newtonian thinning rate. The shortcomings of the Power-law model are exposed when the shear rate is low and these are resolved using the Carreau model.

Journal Article Type Article
Acceptance Date Dec 22, 2021
Online Publication Date Jan 18, 2022
Publication Date 2022-01
Journal Physics of Fluids
Print ISSN 1070-6631
Publisher AIP Publishing
Peer Reviewed Peer Reviewed
Volume 34
Issue 1
Keywords Condensed Matter Physics, Fluid Flow and Transfer Processes, Mechanics of Materials, Computational Mechanics, Mechanical Engineering
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