Shear Viscous Flow

One simple rheological model that is often used to describe the behavior of foams is that of a Bingham plastic. This appHes for flows over length scales sufficiently large that the foam can be reasonably considered as a continuous medium. The Bingham plastic model combines the properties of a yield stress like that of a soHd with the viscous flow of a Hquid. In simple Newtonian fluids, the shear stress T is proportional to the strain rate y, with the constant of proportionaHty being the fluid viscosity. In Bingham plastics, by contrast, the relation between stress and strain rate is r = where is... 

Melt Viscosity. As shown in Tables 2 and 3, the melt viscosity of an acid copolymer increases dramatically as the fraction of neutralization is increased. The relationship for sodium ionomers is shown in Figure 4 (6). Melt viscosities for a series of sodium ionomers derived from an ethylene—3.5 mol % methacrylic acid polymer show that the increase is most pronounced at low shear rates and that the ionomers become increasingly non-Newtonian with increasing neutralization (9). The activation energy for viscous flow has been reported to be somewhat higher in ionomers than in related acidic... 

Rheology. Both PB and PMP melts exhibit strong non-Newtonian behavior thek apparent melt viscosity decreases with an increase in shear stress (27,28). Melt viscosities of both resins depend on temperature (24,27). The activation energy for PB viscous flow is 46 kj /mol (11 kcal/mol) (39), and for PMP, 77 kJ/mol (18.4 kcal/mol) (28). Equipment used for PP processing is usually suitable for PB and PMP processing as well however, adjustments in the processing conditions must be made to account for the differences in melt temperatures and rheology. 

EPDM-ZnO-stearic acid systems could not be extruded even at 190°C. This is not unexpected since the material, in the absence of zinc stearate, shows no transition from the rubbery state to the viscous flow state (Fig. 1). In the presence of 10 phr of zinc stearate, the m-EPDM-ZnO-stearic acid system could be extruded but melt fracture occurred at a lower temperature (150°C) at all shear rates. At 160°C and 170°C, however, the extrudates showed melt fracture only at high shear conditions. At 20 phr loading of zinc stearate, melt fracture of the extrudate occurred at high shear conditions at 150°C, but at higher temperatures no melt fracture occurred and the extrusion was smooth under all shear conditions. At 30 and 40 phr loadings of zinc stearate, the extrudates were smooth under all shear conditions at all temperatures. 

A similar thing takes place when we consider flow curves obtained at different temperatures. As seen from Fig. 7, if we take a region of low shear rates, then due to the absence of the temperature dependence Y, the apparent activation energy vanishes. At sufficiently high shear rates, when a polymer dispersion medium flows, the activation energy becomes equal to the activation energy of the viscous flow of a polymer melt and the presence of the filler in this ratio is of little importance. 

The flow behaviour of a material is described by the relationship between the force acting on the sample of a material, and the effect of this force. The effect may be elastic deformation or viscous flow. For technological and historical reasons, the standard measuring technique has been to force the sample to undergo a predetermined shear rate and measure the force required. 

Although the transport properties, conductivity, and viscosity can be obtained quantitatively from fluctuations in a system at equilibrium in the absence of any driving forces, it is most common to determine the values from experiments in which a flux is induced by an external stress. In the case of viscous flow, the shear viscosity r is the proportionality constant connecting the magnitude of shear stress S to the flux of matter relative to a stationary surface. If the flux is measured as a velocity gradient, then... 

While electrical conductivity, diffusion coefficients, and shear viscosity are determined by weak perturbations of the fundamental diffu-sional motions, thermal conductivity is dominated by the vibrational motions of ions. Heat can be transmitted through material substances without any bulk flow or long-range diffusion occurring, simply by the exchange of momentum via collisions of particles. It is for this reason that in liquids in which the rate constants for viscous flow and electrical conductivity are highly temperature dependent, the thermal conductivity remains essentially the same at lower as at much higher temperatures and more fluid conditions. 

The motion occurring during viscous flow consists of a shear in which different layers of the solution move with different velocities. The large polymer molecule finds it impossible to adjust its motions so as to coincide with the velocities of the different layers of the liquid through which it extends. Its situation is depicted in Fig. 139, where vectors representing the unperturbed velocity of the liquid relative to the position of the center of gravity of the molecule are shown. Let the velocity gradient be 7 ... 

Caustic Waterflooding. In caustic waterflooding, the interfacial rheologic properties of a model crude oil-water system were studied in the presence of sodium hydroxide. The interfacial viscosity, the non-Newtonian flow behavior, and the activation energy of viscous flow were determined as a function of shear rate, alkali concentration, and aging time. The interfacial viscosity drastically... 

Torres, F. E., Russel, W. B., and Schowalter, W. R., Floe structure and growth kinetics for rapid shear coagulation of polystyrene colloids. J. Colloid Interface Sci. 142, 554-574 (1991a). Torres, F. E., Russel, W. B., and Schowalter, W. R., Simulations of coagulation in viscous flows. J. Colloid Interface Sci. 145, 51-73 (1991b). 

For a viscoelastic solid the situation is more complex because the solid component will never flow. As the strain is applied with time the stress will increase continually with time. The sample will show no plateau viscosity, although there may be a low shear viscous contribution. This applies to both a single Maxwell model and one with a spectrum of processes ... 

A plastic material is one which displays a yield stress. As the shear rate is reduced the apparent viscosity progressively increases, diverging and never reaching a constant value. If a stress is applied to a plastic material no flow will be observed until the stress exceeds the yield stress. Expressions describing plastic materials must include at least two terms, a yield stress and a limiting high shear viscous term. Expressions usually describe shear stress in terms of shear rate ... 

When considering a sohd-liquid interface, we begin with the simplest case of steady shear flow parallel to the surface, with D /Dt = 0 and v = V . Equation (1) reduces to Newtonian viscous flow,... 

Fig. 6. The effect of spherical and rod-shaped filler particles on the viscous flow of a polymer melt as a function of shear rate (the concentration of spheres is higher than that of the rods) [4]...

In Eq. (38) the hydrodynamic velocity is that used to evaluate the momentum of the phase. In viscous flow it is the term used in establishing the shear from a knowledge of the viscosity when effects of cross linking of fluxes (01, 02) are neglected. The hydrodynamic velocity and the diffusional velocity are related by... 

Ellis AT, Ting RY, Napolink RH (1970) Some effects of storage and shear history on the friction reducing properties of dilute polymer solutions Prog Astronaut Aeronaut 70 Viscous flow flow drag reduction (AIAA) 532... 

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