Shah, R. A. and Gaskel, P. and Veremieiev, S. (2017) 'Free surface thin film flow of a Sisko’s fluid over a surface topography.', Journal of applied fluid mechanics., 10 (1). pp. 307-317.
The flow of a thin film down an inclined surface over topography is considered for the case of liquids with Sisko’s model viscosity. For the first time lubrication theory is used to reduce the governing equations to a non-linear evolution equation for a current of a Sisko’s model non-Newtonian fluid on an inclined plane under the action of gravity and the viscous stresses. This model is solved numerically using an efficient Full Approximation Storage (FAS) multigrid algorithm. Free surface results are plotted and carefully examined near the topography for different values of power-law index np, viscosity parameter m, the aspect ratio A and for different inclination angle of the plane with the horizontal. Number of complications and additional physical effects are discussed that enrich real situations. It is observed that the flows into narrow trenches develop a capillary ridge just in front of the upstream edge of a trench followed by a small trough. For relatively small width trenches, the free surface is almost everywhere flat as the dimensional width of the trench is much smaller than the capillary length scale. In this region, surface tension dominates the solution and acts so as to stretch a membrane across the trench leading to smaller height deviations. The ridge originates from the topographic forcing which works to force fluid upstream immediately prior to the trench before helping to accelerate it over. The upstream forcing slows down the fluid locally and increases the layer thickness.
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|Publisher Web site:||https://doi.org/10.18869/acadpub.jafm.73.238.26727|
|Publisher statement:||This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.|
|Date accepted:||10 September 2016|
|Date deposited:||19 July 2017|
|Date of first online publication:||01 January 2017|
|Date first made open access:||No date available|
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