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Stability of gravity-driven free-surface flow past a deformable solid: The role of depth-dependent modulus
1Department of Chemical Engineering, Indian Institute of Technology, Kanpur 208016, India.
Physical Review. E
|May 20, 2020
Summary
This study analyzes the linear stability of a Newtonian liquid layer on an inclined plane with a deformable solid. A continuously varying shear modulus in the solid layer acts as a generalization of multi-layered solids, with stability governed by an effective shear modulus.
Area of Science:
- Fluid dynamics
- Solid mechanics
- Rheology
Background:
- Analysis of fluid flow over deformable surfaces is crucial for understanding various natural and industrial processes.
- Previous studies often simplified solid properties, limiting applicability to complex material behaviors.
Purpose of the Study:
- To investigate the linear stability of a Newtonian liquid layer on an inclined plane coated with a deformable linear elastic solid.
- To analyze the impact of a continuously varying elastic modulus on fluid-solid system stability.
- To derive analytical expressions for wave speed and identify key parameters governing instability.
Main Methods:
- Employed a low-wave-number asymptotic analysis to derive an analytical expression for the complex wave speed.
- Investigated the role of an effective shear modulus (G_eff) in determining free surface stability.
- Examined system behavior at finite wave numbers and varying ratios of viscous to elastic stresses (Γ).
Main Results:
- The continuously varying modulus solid layer generalizes multi-layered systems with constant shear moduli.
- In the low-wave-number limit, stability is dictated by G_eff, not the detailed modulus variation.
- At finite wave numbers, increased Γ leads to instability; configurations with higher shear modulus at the interface enhance stability.
Conclusions:
- A continuously varying shear modulus in the elastic substrate offers a more generalized model for fluid-solid interactions.
- The effective shear modulus is a critical parameter for predicting stability in the low-wave-number regime.
- Tailoring the spatial variation of the elastic modulus provides a means to control and manipulate fluid instabilities.
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