Suppression of instability in liquid flow down an inclined plane by a deformable solid layer

Area of Science:

• Fluid Dynamics
• Rheology
• Materials Science

Background:

• Liquid films on inclined planes are prone to free-surface instabilities driven by fluid inertia.
• Deformable solid layers can interact with liquid flow, influencing stability through elastohydrodynamic coupling.
• Understanding these interactions is crucial for controlling thin-film flow phenomena.

Purpose of the Study:

• To analyze the linear stability of a liquid layer on a deformable viscoelastic solid.
• To investigate the impact of elastohydrodynamic coupling on free-surface and interfacial instabilities.
• To identify conditions for suppressing instabilities using soft solid coatings.

Main Methods:

• Linear stability analysis of a two-layer system (liquid on viscoelastic solid).
• Long-wave asymptotic analysis to study the effect of solid deformability.
• Numerical solutions to extend analysis to finite wavelengths and verify asymptotic predictions.

Main Results:

• Free-surface instability is suppressed in the long-wave limit as solid elasticity increases (non-dimensional parameter Gamma).
• At higher Gamma, finite-wavelength instabilities can emerge at the liquid-solid interface or free surface.
• A stable operating window exists for soft solid coatings, suppressing all instabilities across wavelengths.

Conclusions:

• Soft viscoelastic solid layers can passively suppress free-surface instabilities in liquid film flows.
• Careful selection of solid properties (shear modulus) is key to avoiding other interfacial instabilities.
• This suggests potential applications for soft coatings in controlling thin-film flows.