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Shivam Sahu1, V Shankar1

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Summary
This summary is machine-generated.

The stability of a liquid layer flowing over a deformable solid bilayer is primarily determined by the bilayer's effective shear modulus, not the adjacent solid's properties. Decreasing this modulus below a critical value stabilizes the free surface.

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Area of Science:

  • Fluid Dynamics
  • Solid Mechanics
  • Interfacial Phenomena

Background:

  • Elastohydrodynamic coupling in fluid flow over deformable surfaces is crucial for understanding interfacial stability.
  • Previous studies on plane Couette flow showed solid layer nature significantly impacts flow instability.
  • The behavior of free-surface flows over elastic materials requires further investigation, particularly concerning bilayer substrates.

Purpose of the Study:

  • To investigate the elastohydrodynamic coupling between a Newtonian liquid layer and a deformable solid bilayer on an inclined plane.
  • To analyze the stability of the liquid layer's free surface and the liquid-solid interface.
  • To determine the influence of bilayer properties and fluid/solid inertia on system stability.

Main Methods:

  • Temporal linear stability analysis of the coupled solid-fluid system.
  • Long-wave asymptotic analysis to derive analytical expressions for complex wavespeed.
  • Numerical shooting method to solve governing differential equations and find stability criteria.

Main Results:

  • Free-surface stability in the long-wave limit is insensitive to the adjacent solid's properties but depends on the effective shear modulus (Geff) of the bilayer.
  • Decreasing Geff below a critical value stabilizes the free-surface instability.
  • At finite wave numbers, wall deformability and inertia induce additional instabilities sensitive to bilayer layer arrangement; these can be delayed by manipulating layer properties.

Conclusions:

  • The effective shear modulus of a solid bilayer is a key parameter for controlling free-surface stability in inclined liquid flows.
  • Bilayer properties and layer arrangement can be tuned to suppress instabilities and delay their onset.
  • Dissipative effects within solid layers also influence stability and can be leveraged for instability suppression, enhancing control over interfacial phenomena.