Roger E. Khayat

A three-dimensional boundary-element approach to gas-assisted injection molding

An Eulerian boundary-element approach is implemented for the three-dimensional simulation of the primary gas penetration stage of the gas-assisted injection molding process. The fluid is assumed to be viscous, Newtonian and incompressible. The formation of a solid skin layer due to cooling is neglected. The evolution of the melt front and gas/melt interface is obtained on the basis of mass conservation as the melt flows through a fixed (three-dimensional) mesh of the cavity. At each time step, the boundary integral equations are solved over the two front surfaces and part of the cavity walls surrounding the melt region. The front tracking technique combined with an effective boundary-element scheme appears to be quite efficient for handling complex three-dimensional geometries. The method and its potential are illustrated through examples from two- and three-dimensional simple flows.

Inflation of an elastic cylindrical membrane: Non-linear deformation and instability

Abstract The axisymmetric free inflation of an initially cylindrical membrane is examined in this study. The initial thickness and radius distributions are in general non-uniform. The neo-Hookean constitutive model is used. Special attention is focused on the non-linear buckling instability under various innation and geometrical conditions. It is found that for a given inflation pressure and aspect ratio S the thicker the cylinder ends are the more unstable the deformation becomes. The study also shows that for a given aspect ratio there are in general two solutions and that beyond a maximum S value no solution exists. In some cases of pressure and thickness values the number of bulges increases from one in the unstable cylinder profile as S is increased beyond a certain critical value. A similar phenomenon is observed for a long cylinder when the pressure is increased. Although the problem is formulated to account for non-uniform original thickness and radius distributions, only results based on linear thickness and radius variations arc presented.

Finite-amplitude Rayleigh–Bénard convection and pattern selection for viscoelastic fluids

The influence of inertia and elasticity on the onset and stability of Rayleigh–Benard thermal convection is examined for highly elastic polymeric solutions with constant viscosity. These solutions are known as Boger fluids, and their rheology is approximated by the Oldroyd-B constitutive equation. The Galerkin projection method is used to obtain the departure from the conduction state. The solution is capable of displaying complex dynamical behaviour for viscoelastic fluids in the elastic and inertio-elastic ranges, which correspond to

Dynamic inflation of hyperelastic spherical membranes

{\it Ra} \,{ and

Influence of shear and elongation on drop deformation in convergent–divergent flows

{\it Ra} \,{>}\, {\it Ra}_c^s

Chaos and overstability in the thermal convection of viscoelastic fluids

, respectively,

INERTIA EFFECTS ON THE MOTION OF LONG SLENDER BODIES

{\it Ra}_c^s

Boundary-element analysis of planar drop deformation in confined flow. Part 1. Newtonian fluids

being the critical Rayleigh number at which stationary thermal convection emerges. This behaviour is reminiscent of that observed experimentally for viscoelastic Taylor–Couette flow. For a given

Finite-amplitude Taylor-vortex flow of viscoelastic fluids

{\it Ra}

Non-linear overstability in the thermal convection of viscoelastic fluids

in the pre-critical range, finite-amplitude periodic oscillatory convection emerges when the elasticity number,