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

1. Introduction to colloid science and rheology 2. Hydrodynamic effects 3. Brownian hard spheres 4. Stable colloidal suspensions 5. Non-spherical particles 6. Weakly flocculated suspensions 7. Thixotropy 8. Shear thickening 9. Rheometry of suspensions 10. Suspensions in viscoelastic media 11. Advanced topics.

Colloidal Suspension Rheology

We identify the physical mechanism through which newly developed quaternary ammonium salt (QAS) deposit control additives (DCAs) affect the rheological properties of cavitating turbulent flows, resulting in an increase in the volumetric efficiency of clean injectors fuelled with diesel or biodiesel fuels. Quaternary ammonium surfactants with appropriate counterions can be very effective in reducing the turbulent drag in aqueous solutions, however, less is known about the effect of such surfactants in oil-based solvents or in cavitating flow conditions. Small-angle neutron scattering (SANS) investigations show that in traditional DCA fuel compositions only reverse spherical micelles form, whereas reverse cylindrical micelles are detected by blending the fuel with the QAS additive. Moreover, experiments utilising X-ray micro computed tomography (micro-CT) in nozzle replicas, quantify that in cavitation regions the liquid fraction is increased in the presence of the QAS additive. Furthermore, high-flux X-ray phase contrast imaging (XPCI) measurements identify a flow stabilization effect in the region of vortex cavitation by the QAS additive. The effect of the formation of cylindrical micelles is reproduced with computational fluid dynamics (CFD) simulations by including viscoelastic characteristics for the flow. It is demonstrated that viscoelasticity can reduce turbulence and suppress cavitation, and subsequently increase the injector’s volumetric efficiency.

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Turbulence and Cavitation Suppression by Quaternary Ammonium Salt Additives.

A new mixed finite element method for computing viscoelastic flows is presented. The mixed formulation is based on the introduction of the rate of deformation tensor as an additional unknown. Contrary to the popular EVSS method [D. Rajagopalan, R.A. Brown and R.C. Armstrong, J. Non-Newtonian Fluid Mech., 36 (1990) 159], no change of variable is performed into the constitutive equation. Hence, the described method can be used to compute solutions of rheological models where the EVSS method does not apply. The numerical strategy uses a decoupled iterative scheme as a preconditioner for the GMRES algorithm. The stability and the robustness of the method are investigated on two benchmark problems: the 4:1 contraction flow problem and the stick-slip flow problem. Numerical results for the PTT [N. Phan-Thien and R.I. Tanner, J. Non-Newtonian Fluid Mech., 2 (1977) 353] and the Grmela [J. Grmela, J. Rheology, 33 (1989) 207] models show that our method is remarkably stable and cheap in computer time and memory.

A new mixed finite element method for computing viscoelastic flows

A complete rheological equation of state for dilute polymer solutions is obtained by modelling the polymer molecules as bead—spring chains, in which the springs are finitely extensible. Hydrodynamic interactions among the beads are accounted for approximately by using the equilibrium-averaged Oseen tensor as in the Zimm theory. The rheological equation of state thus obtained may be regarded as an extension of the Lodge—Wu equation. Consequently, it incorporates all the good features of the Zimm theory, but it can describe nonlinear viscoelastic phenomena as well, such as monotone decreasing shear-rate-dependent viscosity. Comparisons with experimental data on shear flows are encouraging.

Polymer solution rheology based on a finitely extensible bead—spring chain model

A constitutive equation is derived from a Lodge—Yamamoto type of network theory for polymeric fluids. The network junctions are not assumed to move strictly as points of the continuum but allowed a certain “effective slip”. The rates of creation and destruction of junctions are assumed to depend on the instantaneous elastic energy of the network, or equivalently, the average extension of the network strand, in a simple manner. Agreement between model predictions and the I.U.P.A.C. data on L.D.P.E. is good.

Nhan Phan Thien

Papers

A new constitutive equation derived from network theory