Viscosity relations

Extensional Viscosity. In addition to the shear viscosity Tj, two other rheological constants can be defined for fluids the bulk viscosity, iC, and the extensional or elongational viscosity, Tj (34,49,100—107). The bulk viscosity relates the hydrostatic pressure to the rate of deformation of volume, whereas the extensional viscosity relates the tensile stress to the rate of extensional deformation of the fluid. Extensional viscosity is important in a number of industrial processes and problems (34,100,108—110). Shear properties alone are insufficient for the characterization of many fluids, particularly polymer melts (101,107,111,112). 

Film Thickness Versus Inlet Viscosity Relation... 

A Casson fluid is Theologically identified by two parameters yield value and plastic viscosity. The plastic viscosity relates to the asymmetry of the flow particles and the yield value is connected with the forces of attraction between particles. The... 

H2d, is accordingly proportional to M2 and thus the viscosity increment proportional to M, i.e. eq. (1) is obtained. Staudin-ger s viscosity relation has exerted a great invluence on both experimental and theoretical research. As is well established, eq. (1) is not verified by either for the type of polymers under discussion here. The investigations resulting in this inclusion tend to confirm the basic concepts of macromolecular science mentioned at the beginning and thus may also be regarded as one of the first applications of these concepts. 

Fiber orientation uniformity is also affected by small-scale or timewise variations in polymer viscosity, related to breakage of polymer chains during the extrusion process. The degradation occurs as a result of residual moisture that immediately reacts to break chains, and by thermal degradation that occurs more gradually over time. Different residence times and temperature histories within the laminar flow streamlines lead to different viscosities, and hence different average orientation levels in the different fibers. 

The viscosity relates to the longest relaxation time in a system. If we consider Rouse diffusion along the tube with a Rouse diffusion coefficient DJ l/ NQ) then an initial tube configuration is completely forgotten when the mean-square displacement along the tube fulfils (r (t))tube=(contour length ly. Thus, for the longest relaxation time, we obtain ... 

Generalized Intrinsic Viscosity Relations for Copolymers and Higher Multispecies Polymers... 

Unlike metals, in which momentum transport properties are generally limited to the molten state, and ceramics, in which momentum transport properties are primarily (but not always) described by the solution state, polymers can be found in either the solution or molten state. As a result, many of the principles that have been previously discussed apply to polymers, especially with regard to non-Newtonian behavior. There are, however, a few viscosity-related concepts, exclusive to polymers, that we will describe here. 

Effects of solvent mixtures can be seen in biochemical systems. Ligand binding to myoglobin in aqueous solution involves two kinetic components, one extramolecular and one intramolecular, which have been interpreted in terms of two sequential kinetic barriers. In mixed solvents and subzero temperatures, the outer barrier increases and the inner barrier splits into several components, giving rise to fast intramolecular recombination. Measurements of the corresponding solvent structural relaxation rates by frequency resolved calorimetry allows the discrimination between solvent composition and viscosity-related effects. The inner barrier and its coupling to structural relaxation appear to be independent of viscosity but change with solvent composition (Kleinert et al., 1998). 

It should be emphasized also that the viscosity relation applies to infinitely dilute solution. In a network swollen to equilibrium the segment concentration is far from being infinitely small. 

Since the width of this zone is significantly greater than the length of the molecular mean free path, we should speak not of energy transfer by direct impact, but of heat conduction and other dissipative processes in the gas—diffusion and viscosity—related to the gradients of the temperature, concentration and the velocity along the normal to the wave front. 

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