In flows with deformation rates larger than the inverse Rouse time of the polymer chain, chains are stretched and their confining tubes become increasingly anisotropic. The pressures exerted by a polymer chain on the walls of an anisotropic confinement are anisotropic and limit chain stretch. In the Molecular Stress Function (MSF) model, chain stretch is balanced by an interchain pressure term, which is inverse proportional to the $3^{rd}$ power of the tube diameter and is characterized by a tube diameter relaxation time. We show that the tube diameter relaxation time is equal to 3 times the Rouse time in the limit of small chain stretch. At larger deformations, we argue that chain stretch is balanced by two restoring tensions with weights of 1/3 in the longitudinal direction of the tube (due to a linear spring force) and 2/3 in the lateral direction (due to the nonlinear interchain pressure), both of which are characterized by the Rouse time. This approach is shown to be in quantitative agreement with transient and steady-state elongational viscosity data of two monodisperse polystyrene melts without using any nonlinear parameter, i.e. solely based on the linear-viscoelastic characterization of the melts. The same approach is extended to model experimental data of four styrene-butadiene random copolymer melts in shear flow. Thus for monodisperse linear polymer melts, for the first time a constitutive equation is presented which allows quantitative modeling of nonlinear extension and shear rheology on the basis of linear-viscoelastic data alone.

Taylor-Couette flow (i.e., flow between concentric, rotating cylinders) has long served as a paradigm for studies of hydrodynamic stability. For Newtonian fluids, the rich cascade of transitions from laminar, Couette flow to turbulent flow occurs through a set of well-characterized flow states (Taylor Vortex Flow, wavy Taylor vortices, modulated wavy vortices, etc.) that depend on the Reynolds numbers of both the inner and outer cylinders ($Re_i$ and $Re_o$). While extensive work has been done on (a) the effects of weak viscoelasticity on the first few transitions for $Re_o=0$ and (b) the effects of strong viscoelasticity in the limit of vanishing inertia ($Re_i$ and $Re_o$ both vanishing), the viscoelastic Taylor-Couette problem presents an enormous parameter space, much of which remains completely unexplored. Here we describe our recent experimental efforts to examine the effects of drag reducing polymers on the complete range of flow states observed in the Taylor-Couette problem. Of particular importance in the present work is 1) the rheological characterization of the test solutions via both shear and extensional (CaBER) rheometry, 2) the wide range of parameters examined, including $Re_i$, $Re_o$ and Elasticity number E1, and 3) the use of a consistent, conservative protocol for accessing flow states. We hope that by examining the stability changes for each flow state, we may gain insights into the importance of particular coherent structures in drag reduction, identify simple ways of screening new drag reducing additives, and improve our understanding of the mechanism of drag reduction.

In various attempts to relate the behaviour of highly-elastic liquids in complex flows to their rheometrical behaviour, obvious candidates for study have been the variation of shear viscosity with shear rate, the two normal stress differences $N_1$ and $N_2$, especially $N_1$, and the extensional viscosity $\eta_E$. In this paper, we shall be mainly interested in 'constant-viscosity' Boger fluids, and, accordingly, we shall limit attention to $N_1$ and $\eta_E$. We shall concentrate on two important flows - axisymmetric contraction flow and "splashing" (particularly that which arises when a liquid drop falls onto the tree surface of the same liquid). Modern numerical techniques are employed to provide the theoretical predictions. It is shown that the two obvious manifestations of viscoelastic rheometrical behaviour can sometimes be opposing influences in determining flow characteristics. Specifically, in an axisymmetric contraction flow, high $\eta_E$ can retard the flow, whereas high $N_1$ can have the opposite effect. In the splashing experiment, high $\eta_E$ can certainly reduce the height of the so-called Worthington jet, thus confirming some early suggestions, but, again, other rheometrical influences can also have a role to play and the overall picture may not be as clear as it was once envisaged.

Miscible polymer blends still have heterogeneity in their component chain concentration in the segmental length scale because of the chain connectivity (that results in the self-concentration of the segments of respective chains) as well as the dynamic fluctuation over various length scales. As a result, the blend components feel different dynamic environments to exhibit different temperature dependence in their segmental relaxation rates. This type of dynamic heterogeneity often results in a broad glass transition (sometimes seen as two separate transitions), a broad distribution of the local (segmental) relaxation modes, and the thermo-rheological complexity of this distribution. Furthermore, the dynamic heterogeneity also affects the global dynamics in the miscible blends if the component chains therein have a large dynamic asymmetry. Thus, the superficially simple miscible blends exhibit interesting dynamic behavior. This article gives a brief summary of the features of the segmental and global dynamics in those blends.

Recent developments in dilute polymer solution rheology are reviewed, and placed within the context of the general goals of predicting the complex flow of complex fluids. In particular, the interplay between the use of polymer kinetic theory and continuum mechanics to advance the microscopic and the macroscopic description, respectively, of dilute polymer solution rheology is delineated. The insight that can be gained into the origins of the high Weissenberg number problem through an analysis of the configurational changes undergone by a single molecule at various locations in the flow domain is discussed in the context of flow around a cylinder confined between flat plates. The significant role played by hydrodynamic interactions as the source of much of the richness of the observed rheological behaviour of dilute polymer solutions is highlighted, and the methods by which this phenomenon can be incorporated into a macroscopic description through the use of closure approximations and multi scale simulations is discussed.

The drop formation dynamics of a shear thinning, elastic, yield stress ($\tau_o$) fluid (Carbopol 980 (poly(acrylic acid)) dispersions) in silicone oil has been investigated in a flow-focusing microfluidic channel. The rheological character of each solution investigated varied from Netwonian-like through to highly non-Newtonian and was varied by changing the degree of neutralization along the poly (acrylic acid) backbone. We have observed that the drop size of these non-Newtonian fluids (regardless of the degree of neutralisation) showed bimodal behaviour. At first we observed increases in drop size with increasing viscosity ratio (viscosity ratio=viscosity of dispersed phase (DP)/viscosity of continuous phase (CP)) at low flowrates of the continuous phases, and thereafter, decreasing drop sizes as the flow rate of the CP increases past a critical value. Only at the onset of pinching and during the high extensional deformation during pinch-off of a drop are any differences in the non-Newtonian characteristics of these fluids, that is extents of shear thinning, elasticity and yield stress ($\tau_o$), apparent. Changes in these break-off dynamics resulted in the observed differences in the number and size distribution of secondary drops during pinch-off for both fluid classes, Newtonian-like and non-Newtonian fluids. In the case of the Newtonian-like drops, a secondary drop was generated by the onset of necking and breakup at both ends of the filament, akin to end-pinching behavior. This pinch-off behavior was observed to be unaffected by changes in viscosity ratio, over the range explored. Meanwhile, in the case of the non-Newtonian solutions, discrete differences in behaviour were observed, believed to be attributable to each of the non-Newtonian properties of shear thinning, elasticity and yield stress. The presence of a yield stress ($\tau_o$), when coupled with slow flow rates or low viscosities of the CP, reduced the drop size compared to the Newtonian-like Carbopol dispersions of much lower viscosity. The presence of shear thinning resulted in a rapid necking event post onset, a decrease in primary droplet size and, in some cases, an increase in the rate of drop production. The presence of elasticity during the extensional flow imposed by the necking event allowed for the extended maintenance of the filament, as observed previously for dilute solutions of linear polymers during drop break-up.

Numerical investigations have been conducted on the assessment of the performance of drug-eluting stent. Computational fluid dynamics is applied to investigate the flow disturbances and drug distributions released from the stent in the immediate vicinity of the given idealized stent in the protrusion into the flow domain. Our simulations have revealed the drug concentration in the flow field due to the presence of a drug-eluting stent within an arterial segment. Wall shear stress increases with Reynolds number for a given stent diameter, while it increases with stent diameter for a given Reynolds number. The drug concentration is dependent on both Reynolds number and stent geometry. In pulsatile flow, the minimum drug concentration in the zone of inter-wire spacing occurs at the maximum acceleration of the inlet flow while the maximum drug concentration gains at the maximum deceleration of the inlet flow. These results provide an understanding of the flow physics in the vicinity of drug-eluting stents and suggest strategies for optimal performance of drug-eluting stent to minimize flow disturbance.

We numerically analyzed flow characteristics of the polymer melt in the screw equipment using a proper modeling and investigated design parameters which have influence on the mixing performance as the capability of the screw equipment. We considered the non-Newtonian and non-isothermal flow in a single rotor equipment to investigate the mixing performance with respect to screw dimensions as shape parameter of the single rotor equipment and screw speed as process parameter. We used Bird-Carreau-Yasuda model as a viscous model of the polymer melt and the particle tracking method to investigate the mixing performance in the screw equipment and considered four mixing performance indexes: residence time distribution, deformation rate, total strain and particle standard deviation as a new mixing performance index. We compared these indexes to determine design parameters and object function. On basis of the analysis results, we carried out the optimal design by using the response surface method and design of experiments. In conclusion, the differences of results between the optimal value and numerical analysis are about 5.0%.