Viscoelastic Shear Flow Research Articles

Effect of wall slip on the stability of viscoelastic plane shear flow

We show that for shear flow of an upper convected Maxwell fluid with small but nonzero slip velocity, an increasing dependence of the slip velocity on the elastic normal stress in the flow direction leads to short wavelength flow instability at sufficiently high Weissenberg number (≳10). Pressure-dependent slip can also lead to instability, but only at unrealistically large Weissenberg number. If the slip velocity depends only on shear stress, then the flow is always stable. These analytical results are valid in a specific asymptotic limit, but are independent of the specific form of the model for slip. Numerical results for specific, phenomenological slip models and the Phan-Thien–Tanner bulk constitutive model show that the results are robust in the presence of nonlinear viscoelasticity. The scaling of the critical shear stress for instability with modulus and molecular weight and of the distortion period with polymer relaxation time are qualitatively consistent with experimental observations of the sharkskin instability in linear polyethylenes. The results may also have some relationship to the recent experimental observation of short wavelength instability in plane Couette flow of an entangled solution with wall slip.

The sharkskin instability of polymer melt flows.

Flows of polymeric liquids undergo instabilities whose origins are quite different from those of Newtonian flows, due to their elastic character and the complexity of the fluid/solid boundary condition. This article reviews recent studies of one such instability, the sharkskin phenomenon observed during extrusion of many linear polymers. Key experimental observations are summarized; one important fact that has become clear is the importance of the interaction between the molten polymer and the solid walls of the flow channel, especially near the contact line at the exit of the channel. Recent developments in understanding the relationship between wall slip and disentanglement of wall-adsorbed polymers from the bulk flow are briefly described, and putative heuristic mechanisms relating the instability to slip and contact line motion are presented. Finally, we review mathematical analyses of the stability of viscoelastic shear flows with slip boundary conditions. Some recent analyses yield instability predictions that are consistent with experiments, but further work is required to discriminate between the various mechanisms that have been proposed. (c) 1999 American Institute of Physics.

Stability of viscoelastic shear flows subjected to steady or oscillatory transverse flow

Experiments and theory show that hydrodynamic instabilities can arise during flow of viscoelastic liquids in curved geometries. A recent study has found that a relatively weak steady transverse flow can delay the onset of instability in the circular Couette geometry until the azimuthal Weissenberg number Weθ is significantly higher than without axial flow. In this work we investigate the effect of superposition of a time-periodic axial Couette flow on the viscoelastic circular Couette and Dean flow instabilities. The analysis, carried out for the upper-convected Maxwell and Oldroyd-B fluids, generally shows increased stability compared to when there is no axial flow. However, we also find that the system shows instability – synchronous resonance – for some values of the axial Weissenberg number, Wez and forcing frequency ω. In particular, instability can be induced not only when ω is of the order of the inverse relaxation time of the fluid but also when it is much smaller. Scaling arguments and numerical results indicate that the high-ω, low-Wez regime is essentially equivalent to Wez=0 in the steady case, implying no stabilization. At high values of ω and Wez, scaling analysis shows that the flow will always be stable. Numerical results are in agreement with these conclusions. Consistent with previous results on parametrically forced systems, we find that the zero-frequency limit is singular. In this limit, the disturbances display quiescent intervals punctuated by periods of large transient growth and subsequent decay.This study also presents linear and nonlinear stability results for the addition of steady axial Couette and Poiseuille flows to viscoelastic instabilities in azimuthal Dean flows. It is shown that, for high Wez, the qualitative effect of adding a steady axial flow is similar to that in the circular Couette geometry, with a linear relationship between the critical Weθ and Wez. For low Wez, we find that the flow is stabilized, unlike in the circular Couette flow where the critical value of Weθ decreases at low Wez. Further, weakly nonlinear analysis shows that the criticality of the bifurcation depends on the value of Wez and the solvent viscosity, S. Finally, we also show the presence of a codimension-2 Takens–Bogdanov bifurcation point in the linear stability curve of Dean flow. This point represents a transition from one mechanism of instability to another.

Stability of vorticity defects in viscoelastic shear flow

We analyze the stability of certain kinds of two-dimensional, incompressible, viscoelastic shear flows at high Reynolds number. These particular flows consist of a strong background linear shear, with a superposed ‘defect’; i.e. a localized region over which the vorticity varies rapidly. A matched asymptotic expansion recasts the problem in a simpler form for which one can derive explicit dispersion relations for the normal modes. This provides an analytic method for investigating stability in regimes when numerical approaches are cumbersome. This technique is used to explore the stability properties of some constitutive models including the Oldroyd-B, Johnson-Segalman and Phan-Thien-Tanner models. Finally, for large Weissenberg number, the defect approximation allows us to study the continuous spectrum associated with the elasticity of the constitutive models. The dynamics associated with this continuous spectrum contains features such as transient amplification and ultimate decay, phenomena familiar for Newtonian fluids in the inviscid limit. However, our calculations indicate that this continuous spectrum decays less quickly than in the Newtonian problem, suggesting that these features of the linear dynamics are even more pronounced.

Wall-Slip and Polymer-Melt Flow Instability.

Instabilities and complex time dependence are often associated with wall slip in polymer-melt flows. We present here a phenomenological slip model that takes into account the unsteady-state kinetics of the wall-polymer interactions. In this model, both the shear and normal stresses arise, in contrast to other models used in stability analyses of shear flow, which incorporate only shear stresses and yield only stable flow. Asymptotic analysis of viscoelastic shear flow with this slip model predicts instability with respect to short wavelength fluctuations at sufficiently high shear rates, showing that slip can lead to instability in viscoelastic shear flow.

Transient processes in shear flows of a viscoelastic fluid. III. Elastic recovery

A mathematical description of the elastic recovery effect associated with viscoelastic shear flow is given.