Role of elasticity and solvent viscosity on the center mode instability in pipe Poiseuille flow of Oldroyd-B fluids.

A linear stability analysis of pipe Poiseuille flow of an Oldroyd-B fluid has been carried out to investigate the interplay among fluid inertia, elasticity and the ratio of solvent to the total viscosity. The stability has been analyzed for axisymmetric perturbations using pseudospectral and shooting methods. The system is found to be linearly unstable at the Reynolds numbers relatively lower than the values for which the transition to turbulence is typically observed for the Newtonian pipe flows. The system has been analyzed for the vast ranges of the wavelength, Reynolds number, elasticity number and the ratio of solvent to the total viscosity. In the limit of low elasticity, the fluctuations are found to be near the axis in the flow domain; hence we refer to this unstable mode as ‘centre mode’. This unstable mode stabilizes in the UCM limit (absence of solvent). Various scalings among the threshold and critical parameters have been established. Comparisons of the present results with those from the experimental studies in the existing literature have been made to establish theoretical evidence for the instability in viscoelastic flows which can potentially turn the steady laminar base flow into a turbulent one.