Wall-mode instability in plane shear flow of viscoelastic fluid over a deformable solid

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
Paresh ChokshiV Kumaran

Abstract

The linear stability analysis of a plane Couette flow of an Oldroyd-B viscoelastic fluid past a flexible solid medium is carried out to investigate the role of polymer addition in the stability behavior. The system consists of a viscoelastic fluid layer of thickness R, density ρ, viscosity η, relaxation time λ, and retardation time βλ flowing past a linear elastic solid medium of thickness HR, density ρ, and shear modulus G. The emphasis is on the high-Reynolds-number wall-mode instability, which has recently been shown in experiments to destabilize the laminar flow of Newtonian fluids in soft-walled tubes and channels at a significantly lower Reynolds number than that for flows in rigid conduits. For Newtonian fluids, the linear stability studies have shown that the wall modes become unstable when flow Reynolds number exceeds a certain critical value Re(c) which scales as Σ(3/4), where Reynolds number Re=ρVR/η,V is the top-plate velocity, and dimensionless parameter Σ=ρGR(2)/η(2) characterizes the fluid-solid system. For high-Reynolds-number flow, the addition of polymer tends to decrease the critical Reynolds number in comparison to that for the Newtonian fluid, indicating a destabilizing role for fluid viscoelasticity. Numer...Continue Reading

References

Oct 6, 2000·Physical Review Letters·V Kumaran, R Muralikrishnan
Aug 18, 2004·Journal of Colloid and Interface Science·Matthew D Eggert, Satish Kumar
Jul 23, 2008·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Paresh Chokshi, V Kumaran

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Citations

Oct 23, 2021·Journal of Physics. Condensed Matter : an Institute of Physics Journal·Ivan C Christov

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