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Instability suppression in viscoelastic film flows down an inclined plane lined with a deformable solid layer
1Department of Chemical Engineering, Indian Institute of Technology, Kanpur 208 016, India.
Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|November 13, 2007
Summary
The deformability of a solid layer stabilizes viscoelastic (Oldroyd-B) film flow on inclined planes, suppressing free-surface instabilities. However, increased deformability can also induce new instabilities due to elastohydrodynamic coupling.
Area of Science:
- Fluid dynamics
- Rheology
- Solid mechanics
- Non-Newtonian fluid mechanics
Background:
- Viscoelastic film flow on inclined planes exhibits free-surface instabilities, even without fluid inertia, due to liquid elasticity.
- Flow over rigid surfaces can lead to inherent instabilities in viscoelastic films.
- The interaction between fluid flow and solid deformation (elastohydrodynamics) is crucial for understanding film stability.
Purpose of the Study:
- To analyze the linear stability of viscoelastic (Oldroyd-B) film flow down an inclined plane adjacent to a deformable (neo-Hookean) solid layer.
- To investigate the stabilizing or destabilizing effects of solid deformability on free-surface and interface instabilities.
- To explore the role of elastohydrodynamic coupling in inducing or suppressing instabilities in such systems.
Main Methods:
- Low-wave-number asymptotic analysis to understand long-wavelength behavior.
- Chebyshev-Tau spectral numerical method for comprehensive analysis across all wave numbers.
- Modeling of viscoelastic liquid using the Oldroyd-B model and the solid layer using the neo-Hookean material model.
Main Results:
- Solid deformability exerts a stabilizing influence on free-surface instabilities, irrespective of the liquid film's rheology (viscoelastic or Newtonian).
- Complete suppression of free-surface instability is achievable with sufficient solid deformability.
- For pure polymeric liquids, increased solid deformability can destabilize both the free surface and the liquid-solid interface, leading to mode exchange phenomena.
- New unstable modes, absent in rigid-boundary flows, can emerge at finite Reynolds and wave numbers due to the coupling between liquid flow and solid shear waves.
- A stable operating window exists where both interfaces remain stable across all wave numbers for specific solid shear moduli.
Conclusions:
- Elastohydrodynamic coupling offers a mechanism to control film stability, either suppressing inherent viscoelastic instabilities or inducing novel instabilities.
- The deformability of the bounding solid layer is a critical parameter in managing the stability of thin films.
- This study highlights the potential for exploiting elastohydrodynamic interactions to design more stable or dynamically interesting film flows.
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