The critical wall velocity for stabilization of plane Couette–Poiseuille flow of viscoelastic fluids

✍ Scribed by Miguel Moyers-Gonzalez; Ian Frigaard

• Publisher: Elsevier Science
• Year: 2010
• Tongue: English
• Weight: 929 KB
• Volume: 165
• Category: Article
• ISSN: 0377-0257
• DOI: 10.1016/j.jnnfm.2010.01.005

✦ Synopsis

Plane Couette flow of a Newtonian fluid is linearly stable with respect to linear disturbances and plane Poiseuille flow becomes linearly unstable when the critical Reynolds number exceeds Re c = 11544. As the Couette component is increased in a plane Couette-Poiseuille flow, it is known that the flow becomes absolutely stable for wall velocities above a critical value. It is suspected that a similar stabilization occurs for viscoelastic fluids.

In this paper we show numerically that the plane Couette-Poiseuille flow of Oldroyd-B and modified FENE Chilcott-Rallison fluids is stabilized at a critical wall velocity approximately 0.7 times the maximal velocity of the plane Poiseuille flow, independent of the elastic parameters investigated. This value is surprisingly close to the Newtonian critical value. A long wavelength analysis, following the distinguished limit method of Cowley and Smith [8], confirms that at leading order this stabilizing wall velocity is indeed independent of the elasticity number of the flow.