Although much progress has been made in the computation of Eulerian steady flows with high viscoelasticity, less work has been done for the case of transient flows. Because of their importance in injection moulding, blow moulding and other forming processes, as well as their Intrinsic interest, we believe more attention should be focussed in this area. Hence in this paper we review progress in unsteady flow computations with high elasticity, and show some new results in this area.

A new technique for numerical calculation of viscoelastic flow based on the combination of Neural Net-works (NN) and Brownian Dynamics simulation or Stochastic Simulation Technique (SST) is presented in this paper. This method uses a "universal approximator" based on neural network methodology in combination with the kinetic theory of polymeric liquid in which the stress is computed from the molecular configuration rather than from closed form constitutive equations. Thus the new method obviates not only the need for a rheological constitutive equation to describe the fluid (as in the original Calculation Of Non-Newtonian Flows: Finite Elements St Stochastic Simulation Techniques (CONNFFESSIT) idea) but also any kind of finite element-type discretisation of the domain and its boundary for numerical solution of the governing PDE's. As an illustration of the method, the time development of the planar Couette flow is studied for two molecular kinetic models with finite extensibility, namely the Finitely Extensible Nonlinear Elastic (FENE) and FENE-Peterlin (FENE-P) models.P) models.

We review the modeling and simulation of fiber orientation during injection molding processes of short fiber reinforced thermoplastics. Generally, a group of fibers are described in terms of probability distribution function or orientation tensor. Various closure approximation models to express higher order tensor in terms of Bower order tensors are reviewed. Rheology of fiber suspensions, multiple fiber-fiber interaction and numerical technique for the prediction of fiber orientation are also considered for concentrated situations.

The interaction between hydrophobically modified hydroxyethyl cellulose (hmHEC), containing approximately 1 wt% side-alkyl chains of $C_{16}$, and an anionic sodium dodecyl sulphate (SDS) surfactant was investigated. For a semi-dilute solution of 0.5 wt% hmHEC, the previously observed behaviour of a maximum in solution viscosity at intermediate SDS concentrations, followed by a drop at higher SDS concentrations, until above the cmc of surfactant when the solution resembles that of the unsubstituted polymer, was confirmed. Additionally, a two-phase region containing a hydrogel phase and a water-like supernatant was found at low SDS concentrations up to 0.2 wt%, a concentration which is akin to the critical association concentration, cac, of SDS in the presence of hmHEC. Above this concentration, SDS molecules bind strongly to form mixed micellar aggregates with the polymer alkyl side-chains, thus strengthening the network junctions, resulting in the observed increase in viscosity and elastic modulus of the solution. The shear behaviour of this polymer-surfactant complex during steady and step stress experiments was examined In great detail. Between SDS concentrations of 0.2 and 0.25 wt%, the shear viscosity of the hmHEC-polymer complex network undergoes shear-induced thickening, followed by a two-stage shear-induced fracture or break-up of the network. The thickening is thought to be due to structural rearrangement, causing the network of flexible polymers to expand, enabling some polymer hydrophobic groups to be converted from intra- to inter-chain associations. At higher applied stress, a partial local break-up of the network occurs, while at even higher stress, above the critical or network yield stress, a complete fracture of the network into small microgel-like units, Is believed to occur. This second network rupture is progressive with time of shear and no steady state in viscosity was observed even after 300 s. The structure which was reformed after the cessation of shear is found to be significantly different from the original state.

Particle-particle interaction is of great importance in the study of suspension rheology. In this research we have investigated the hydrodynamic interaction between two identical cylinders in viscoelastic fluids numerically as a model problem for the study of viscoelastic suspension. We confine two neutrally buoyant cylinders between two parallel plates and impose a shear flow. We determine the migration velocity of two cylinders. The result shows that cylinders move toward or away from each other depending upon the initial distance between them and that there is an equilibrium distance between two cylinders in viscoelastic fluids regardless of the initial distance. In the case of Newtonian fluid, there is no relative movement as expected. The results partly explain the chaining phenomena of spherical particles in shear flows of viscoelastic fluids.