Viscous fingering in non-Newtonian fluids in a rectangular Hele-Shaw cell was numerically simulated using the finite element method together with the volume of fluid (VOF) method for the representation of an interface between two viscous fluids. Interfacial tension was treated as a volumeric force using the continuum surface force (CSF) model. The Carreau model was applied for describing the shear-thinning viscosity. In addition, the viscous fingering in a Newtonian fluid was also calculated for comparison. The computation was performed under various conditions of initial finger shape, interfacial tension, and mean velocity. The typical patterns such as `shielding', `spreading', and `splitting' were simulated and the numerical results predicted that the shear-thinning viscosity increased the shielding effect. The present results indicated the numerical approach was effective.
Stress relaxation of multi-arm star polystyrenes were investigated in the molten state. The relaxation modulus was measured over a wide range of strain. The plots of relaxation modulus against time for the multi-arm stars showed a new mechanical relaxation at long times. For entangled systems, although the strain dependence of the damping function for entanglement relaxation was almost identical to that for linear and regular star polymers, the strain dependence for the long-time relaxation was weak. On the other hand, the damping function for the non-entangled systems showed the stronger dependence than the entangled systems. The damping at large strains became weaker with increasing weight-average molecular weight of the arm but appeared to be independent of number of arms.
One-dimensional flow model for non-Newtonian fluids in the inside of a slot die is presented. The viscosity of non-Newtonian liquids is given by the Ellis model. The conservation equations of mass and momentum in the slot die are treated one-dimensionally by assuming an appropriate mean flow over the cross section of the flow. The flow field in the slot is assumed to be fully developed. The equations of flows for the cavity and the slot are derived separately and then coupled. We use a finite difference method to solve these governing equations. It is concluded that a flow model using the Ellis model for liquid viscosity is useful to predict the distribution of flow rate from the die.
Segmented-polyurethanes (SPUs) having different soft segment length (Mn=530-3,000) and their blends were characterized by NMR, DSC and dynamic viscoelastic analyses. The SPUs were prepared from the reaction of 4,4'-diphenylmethane diisocyanate, 1,4-butanediol and polycaprolactone diol. It has been found from the DSC analysis that the long soft segment SPUs with the long hard segment have two melting points due to the hard segment while the short soft segment SPU with the short hard segment has one melting point. The dynamic viscoelastic analysis reveals that the short soft segment SPU forms a glass-like structure more easily than the long soft segment SPUs. The blends of SPUs with various composition ratios were made from the two SPUs which were different in soft segment length (Mn=530 and 2,000). DSC and viscoelastic analyses of the blends show that the short hard segment strongly affects the formation of the crystalline structure. The short segment in the blend seems to prevent the long segment from forming the long-segment-based crystalline structure, and both the segments apparently form the short-segment-based crystalline structure.
Fatigue behavior of HDPE extrudates was investigated on the basis of nonlinear dynamic viscoelastic analyses. The HDPE extrudate was prepared by a solid-state extrusion at an extrusion temperature of 353 K with an extrusion ratio of 11.1. Fatigue tests were carried out under the conditions of strain-controlled frequency of 11 Hz and environmental temperature of 303 K. Three deformation conditions were applied to fatigue tests: tension-tension, tension-compression and compression-compression deformation. Relationship between stress and strain amplitudes during fatigue process indicated that in the cases of tension-compression and compression-compression deformations, fatigue lifetime remarkably decreased with increasing dynamic strain amplitude. Nonlinear viscoelasticity during fatigue process was evaluated quantitatively by nonlinear viscoelastic parameter NVP. With increasing imposed strain amplitude, nonlinear viscoelasticity under compression-compression deformation became more remarkable because kink-bands were formed and stress distribution became inhomogeneous. Analyses of hysteresis loss during fatigue process indicated that nonlinear viscoelasticity was closely related to hysteresis loss consumed for irreversible structural change. In particular, in the case of compression-compression deformation, nonlinearity of viscoelasticity increased remarkably with hysteresis loss consumed for structural change due to kink-band formation.