A purely elastic instability in Taylor–Couette flow

Abstract

A non-inertial (zero Taylor number) viscoelastic instability is discovered for Taylor–Couette flow of dilute polymer solutions. A linear stability analysis of the inertialess flow of an Oldroyd-B fluid (using both approximate Galerkin analysis and numerical solution of the relevant small-gap eigenvalue problem) show the growth of an overstable (oscillating) mode when the Deborah number exceeds f(S) ε−½, where ε is the ratio of the gap to the inner cylinder radius, and f(S) is a function of the ratio of solvent to polymer contributions to the solution viscosity. Experiments with a solution of 1000 p.p.m. high-molecular-weight polyisobutylene in a viscous solvent show an onset of secondary toroidal cells when the Deborah number De reaches 20, for ε of 0.14, and a Taylor number of 10−6, in excellent agreement with the theoretical value of 21. The critical De was observed to increase as ε decreases, in agreement with the theory. At long times after onset of the instability, the cells become small in wavelength compared to those that occur in the inertial instability, again in agreement with our linear analysis. For this fluid, a similar instability occurs in cone-and-plate flow, as reported earlier. The driving force for these instabilities is the interaction between a velocity fluctuation and the first normal stress difference in the base state. Instabilities of the kind that we report here are likely to occur in many rotational shearing flows of viscoelastic fluids.

Mixing of Non-Newtonian Fluids in Steadily Forced Systems

“…We speculate, but cannot confirm, that this flow oscillation may be directly linked to the longest fluid relaxation time ( ). This analysis is consistent with prior work that also reports oscillatory elastic instabilities in stressed viscoelastic fluids [10,12,20]. We believe that the instabilities observed in our experiments occur in regions where p = s p _ _ = s _ > 1, where p ÿ s p _ _ is the elastic stress and s s _ is the viscous stress.…”

Experimental Evidence for an Intrinsic Route to Polymer Melt Fracture Phenomena: A Nonlinear Instability of Viscoelastic Poiseuille Flow

“…Less well understood are flow instabilities in complex fluids. The unusual non-Newtonian flow properties of complex fluids can not only modify existing instabilities such as viscous fingering [1] but they can also give rise to completely new instabilities and flow behavior [2][3][4][5][6][7][8]. In this Letter we present evidence that a viscoelastic flow instability that is absent for Newtonian fluids underlies an important set of phenomena that occur in the spinning of polymer fibers, and that have plagued the plastic industry ever since the first plastic fibers were produced.…”

Coating flows of non-Newtonian fluids: weakly and strongly elastic limits

“…Grillet et al, 1999;Joo and Shaqfeh, 1992;Graham, 2003) have been studied in single roll coating applications. Furthermore detailed studies in the Taylor-Couette geometry have shown that in addition to purely elastic instabilities arising from streamline curvature (Larson et al, 1990;Muller et al, 1989), weak elastic effects may stabilize or destabilize inertially-driven flow transitions. These competing effects can be represented by stability loci plotted on a diagram of the critical Deborah number versus critical Reynolds number.…”