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Title: Effect of wall deformability on the stability of surfactant-laden visco-elastic liquid film falling down an inclined plane
Authors: Baingne M.
Sharma, Gaurav
Published in: Journal of Non-Newtonian Fluid Mechanics
Abstract: The stability behavior of a visco-elastic (Upper Convected Maxwell) liquid film flowing down an inclined plane is examined using the standard normal mode linear stability analysis in creeping flow limit. The inclined plane is coated with a deformable solid layer, and the gas-liquid interface is covered with a monolayer of an insoluble surfactant. There exist three modes of instabilities for this composite fluid-solid system: (i) the free surface gas-liquid (GL) mode, (ii) the surfactant or Marangoni mode, and (iii) the liquid-solid (LS) mode. Previous studies have shown that the Marangoni mode remains stable for film flowing down a rigid inclined plane. We show that when the rigid wall is replaced by a deformable wall, the Marangoni mode becomes unstable when a non-dimensional deformability parameter, defined as G=?V/EsR, increases above a threshold value (?, V, Es, and R are fluid viscosity, free-surface velocity, shear modulus of soft solid layer, and fluid thickness, respectively). It is well known that the GL mode remains stable for Newtonian liquid film at zero Reynolds number, but becomes unstable for a visco-elastic film flowing past a rigid inclined plane even in creeping flow limit purely because of fluid elasticity. Previous studies have shown that the presence of soft solid layer can suppress this free surface GL mode instability. The presence of surfactant also has a stabilizing effect on this GL mode instability in rigid limit. Here, we evaluate whether a soft solid coating can be used to obtain a stable flow configuration for a surfactant-covered visco-elastic film as well particularly (i) in view of the above mentioned Marangoni mode destabilization observed solely due to wall deformability, and (ii) when the surfactant stabilizing contribution remains insufficient to suppress the free-surface instability. We demonstrate that there exists a window in terms of parameter G where the free surface GL mode instability is suppressed without exciting any other mode. We also identify the parameter regimes where it is not possible to achieve stable film flow, however, in these cases, we show that the Marangoni mode can be selectively destabilized by appropriately selecting the thickness and shear modulus of solid layer. © 2019 Elsevier B.V.
Citation: Journal of Non-Newtonian Fluid Mechanics(2019), 269(): 1-16
Issue Date: 2019
Publisher: Elsevier B.V.
Keywords: Fluid-solid interactions
Free-surface instability
Marangoni instability
Neo-Hookean solid
Visco-elastic film
Wall deformability
ISSN: 3770257
Author Scopus IDs: 57193552265
Author Affiliations: Baingne, M., Department of Chemical Engineering, Indian Institute of Technology Roorkee, Roorkee, 247 667, India
Sharma, G., Department of Chemical Engineering, Indian Institute of Technology Roorkee, Roorkee, 247 667, India
Corresponding Author: Sharma, G.; Department of Chemical Engineering, Indian Institute of Technology RoorkeeIndia; email:
Appears in Collections:Journal Publications [CH]

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