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It is shown that steady channel, simple shear and Couette flows of a Bingham fluid come to rest in a finite amount of time, if either the applied pressure falls below a critical value, or the moving boundaries are brought to rest. An explicit formula for a bound on the finite stopping time in each case is derived. This bound depends on the density, the viscosity, the yield stress, a new geometric constant, and the least eigenvalue of the second order linear differential operator for the interval under consideration.

Consideration is given to the influence of elongational properties on flow characteristics in the case of shear-thinning highly elastic fluids in an abrupt contraction. Sufficient data has been published to demonstrate that viscoelasticity can have a significant effect on flow characteristics in abrupt contractions. This paper reports on numerical experiments with four representative test-fluids of Phan-Thien-Tanner models. Furthermore, a new dimensionless number that takes into account elongational properties is proposed. Of major importance is the observation that the vortex enhancement and the energy loss in the entrance region both vary strongly with the elongational properties of Phan-Thien-Tanner models. Numerical results are qualitatively in good agreement with experimental measurements on polymer solutions and melts. Finally, this numerical study provides a fundamental basis, which may be quite useful for the prediction of viscoelastic fluid flows by using numerical modeling, and for the calculation of rheometrical properties of viscoelastic fluids through constitutive equation parameter adjustment.

The flow curves and kinematics of stretch-thickening fluids flowing through an orifice die have been determined under creeping-flow conditions. As shown, the advantage of this particular flow geometry over other contraction flows is that the pressure drop Pg across the orifice is related to energy losses in such a way that experimental data can be readily analysed in terms of pronounced elongational effects. The fluids tested were low concentration solutions of flexible coils (salt-containing solutions of partially hydrolysed polyacrylamide (HPAM) and polyethylene oxide (PEO) solutions) and of semi-rigid rods (unsalted HPAM solutions) in a thick solvent. Flow parameters were varied over the whole range, that is from Newtonian behaviour at low flow conditions to very strong flow conditions capable of producing chain breakup. Three flow regimes, interconnected by smooth transitions, were identified for solutions of flexible coils. The feature of each regime is that Pg varies with flow rate qv independently of polymer concentration. The flow structure over each regime was thoroughly documented. Careful simultaneous visualisations showed that small-scale instabilities do exist under conditions where the upstream flow may seem to possess a mean stable axisymmetric structure. Stress growth in each regime was connected to a distinct structural mechanism. In the initial linear-viscous Newtonian regime, where Pg is linear in qv, chains are deformed slightly and solvent viscous stresses prevail. In the intermediate quadratic regime, where Pg varies with q2v, significant chain unravelling takes place, giving rise to high elastic stresses. In the ultimate linear-viscous regime where Pg is again linear in qv, chains are stretched to their full length and viscous stresses due to hydrodynamic interaction are dominant. The quadratic regime is absent for solutions of semi-rigid rods. However, these solutions show the same quantitative behaviour in the ultimate regime as solutions of flexible coils, indicating that similar structural effects govern stress growth in this regime. This work gives a global view of low concentration polymer solution flow through an orifice die. Moreover, it provides a basis for incorporating realistic structural effects in constitutive models.

A structural constitutive equation, based on the network theory and on a junction creation and destruction mechanism, is presented in this paper. It allows the behaviour of a class of yield stress fluids to be modelled. The problem of initial state is treated. The constitutive equation is then developed on the basis of experimental results and the properties of the model are illustrated for explicit adapted forms of segment evolution laws.

This paper presents a theoretical study of the hydrodynamic lubrication of a circular thread passing along a rotating drum. The effects of hydrodynamic friction and the influence of cavitation upon the bearing characteristics are included in the analysis. Differential equations governing the problem, derived from the Reynolds equation and the thread equilibrium equations, are established. Analytical solutions and numerical solutions are obtained for all the operating characteristics. Influences of friction and cavitation are discussed. Comparisons with the results of previously studied flat thread lubrication are also made. The effects of shape are evaluated. Some numerical examples in the field of sizing (coating) fibres are described.

The lubrication of flat threads passing along a drum is studied taking hydrodynamic friction into account. The tension varies along the thread, and it is shown that it can be much larger at the outlet than at the inlet. Friction is introduced by using a new dimensionless friction parameter . Complete dimensionless analytical solutions and numerical solutions are obtained for various values of so that all the parameters relevant to a practical situation can easily be calculated.