Viscoelastic instabilities are of practical importance, and are the subject of growing interest. Reviewed here are the fresh developments as well as earlier work in this area, organized into the following categories: instabilities in Taylor-Couette flows, instabilities in cone-and-plate and plate-and-plate flows, instabilities in parallel shear flows, extrudate distortions and fracture, instabilities in shear flows with interfaces, instabilities in extensional flows, instabilities in multidimensional flows, and thermohydrodynamic instabilities. Emphasized in the review are comparisons between theory and experiment and suggested directions for future work.

Instabilities in viscoelastic flows

A new mixed finite element has allowed us to calculate flows of Maxwell-B and Oldroyd-B fluids at very high values of the Deborah number, De . The element is divided into several bilinear sub-elements for the stresses, while streamline-upwinding is used for discretizing the constitutive equation. The method is applied to the stick-slip problem, the flow through a tapered contraction and the flow through four-to-one abrupt plane and circular contractions. Important corner vortices develop at high values of De in the circular contraction. We have not encountered upper limits for the Deborah number in our calculations with Oldroyd-B fluids.

A new mixed finite element for calculating viscoelastic flow

Viscoelastic Flows Through Contractions

The non-Newtonian flow of dilute aqueous polyethylene oxide (PEO) solutions through micro-fabricated planar abrupt contraction-expansions is investigated. The small lengthscales and high deformation rates in the contraction throat lead to significant extensional flow effects even with dilute polymer solutions having time constants on the order of milliseconds. By considering the definition of the elasticity number, El = Wi/Re, we show that the lengthscale of the geometry is key to the generation of strong viscoelastic effects, such that the same flow behaviour cannot be reproduced using the equivalent macro-scale geometry using the same fluid. We observe significant vortex growth upstream of the contraction plane, which is accompanied by an increase of more than 200% in the dimensionless extra pressure drop across the contraction. Streak photography and video-microscopy using epifluorescent particles shows that the flow ultimately becomes unstable and three-dimensional. The moderate Reynolds numbers (0.44 ≤ Re ≤ 64) associated with these high Weissenberg number (0 ≤ Wi ≤ 548) micro-fluidic flows results in the exploration of new regions of the Re-Wi parameter space in which the effects of both elasticity and inertia can be observed. Understanding such interactions will be increasingly important in micro-fluidic applications involving complex fluids and can best be interpreted in terms of the elasticity number, El = Wi/Re, which is independent of the flow kinematics and depends only on the fluid rheology and the characteristic size of the device.

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The inertio-elastic planar entry flow of low-viscosity elastic fluids in micro-fabricated geometries

An approximate analysis is presented for the flow of fluids through planar and axisymmetric contractions. Energy principles are employed to relate the entry pressure drop to flow rate and fundamental rheometric properties. One of the aims of the analysis is to investigate the influence of extensional viscosity on such flows, particularly with regard to the occurrence and enhancement of vortex motion in the entry corners. For the sake of mathematical simplicity, independent power-law models are used to represent the shear and extensional viscosity functions. The analysis indicates that, once significant vortex motion is present, enhancement occurs whenever the Trouton ratio is an increasing function of shearrate (or stretch-rate). It is readily seen how the occurrence of vortices serves as a stress relief mechanism. Indeed, for highly stretch-thickening materials, the entry pressure drop is seen to be dominated by shear properties. The power-law parameters of the extensional viscosity function may be obtained in a straight-forward way from entry pressure drop versus flow rate data. Finally, the extension and application of the analysis to other similar flows, such as through converging nozzles, is briefly discussed.

An approximate analysis for contraction and converging flows

Consideration is given to the influence of small changes in corner geometry on flow characteristics in the case of elastic liquids flowing in various contraction geometries. Both Boger fluids and aqueous solutions of polyacrylamide are used to show that it is very difficult to make generalizations from one geometry to another or from one type of non-Newtonian fluid to another.

Of major importance is the observation that the precise mechanism of vortex enhancement varies with the contraction ratio. For large contraction ratios, a re-entrant corner vortex (not present in a 4:1 contraction) is shown to have an important influence on the development of vortex enhancement.

Flow characteristics associated with abrupt changes in geometry in the case of highly elastic liquids

Aqueous solutions of polyacrylamide are investigated in various planar-contraction flows in an attempt to answer some unresolved questions from an earlier paper of the present authors. It is concluded that a lip-vortex mechanism can be responsible for vortex enhancement for any planar-contraction ratio, provided the polymer concentration is chosen carefully or, alternatively, the contraction angle is varied.

R.E. Evans

Papers

Flow characteristics associated with abrupt changes in geometry in the case of highly elastic liquids

Further remarks on the lip-vortex mechanism of vortex enhancement in planar-contraction flows