The onset of purely elastic and thermo-elastic instabilities in the Taylor-Couette flow: Influence of gap ratio and fluid thermal sensitivity

Linear stability analysis of Taylor-Couette flow of dilute polymeric solutions has been performed by using two prototypical constitutive equations for polymeric solutions namely, the Oldroyd-B and the FENE-P models. The hydrodynamic stability characteristics of the flow in presence and absence of thermal effects and in the limit of vanishing fluid inertia have been determined using an eigenvalue analysis. Particular attention has been paid to accurate determination of the instability onset conditions as a function of fluid thermal sensitivity and gap ratio. We observe a reduction in the critical Deborah, Dec for the instability onset as the gap ratio and fluid thermal sensitivity is enhanced. In particular, under non-isothermal conditions, Dec is reduced by almost an order of magnitude for all gap ratios. Our results suggest that recent experiments leading to observations of “purely elastic turbulence” in the Taylor-Couette flow at order (1) De by Steinberg and Groisman (reference 17) were not performed under isothermal conditions. Hence, this new flow state should be labeled as “thermo-elastic turbulence”.