Viscosity defined

The elongation viscosity defined by Equation (1.19) represents a uni-axial extension. Elongational flows based on biaxial extensions can also be considered. In an equi-biaxial extension the rate of deformation tensor is defined as... 

The apparent viscosity, defined as du/dj) drops with increased rate of strain. Dilatant fluids foUow a constitutive relation similar to that for pseudoplastics except that the viscosities increase with increased rate of strain, ie, n > 1 in equation 22. Dilatancy is observed in highly concentrated suspensions of very small particles such as titanium oxide in a sucrose solution. Bingham fluids display a linear stress—strain curve similar to Newtonian fluids, but have a nonzero intercept termed the yield stress (eq. 23) ... 

All fluids for which the viscosity varies with shear rate are non-Newtonian fluids. For uou-Newtouiau fluids the viscosity, defined as the ratio of shear stress to shear rate, is often called the apparent viscosity to emphasize the distiuc tiou from Newtonian behavior. Purely viscous, time-independent fluids, for which the apparent viscosity may be expressed as a function of shear rate, are called generalized Newtonian fluids. 

Viscosity, defined as the resistance of a liquid to flow under an applied stress, is not only a property of bulk liquids but of interfacial systems as well. The viscosity of an insoluble monolayer in a fluid-like state may be measured quantitatively by the viscous traction method (Manheimer and Schechter, 1970), wave-damping (Langmuir and Schaefer, 1937), dynamic light scattering (Sauer et al, 1988) or surface canal viscometry (Harkins and Kirkwood, 1938 Washburn and Wakeham, 1938). Of these, the last is the most sensitive and experimentally feasible, and allows for the determination of Newtonian versus non-Newtonian shear flow. 

The transport equations for the turbulent kinetic energy, k, and the turbulence dissipation, e, in the RNG k-s model are again defined similar to the standard k-s model, now utilizing the effective viscosity defined through the RNG theory. The major difference in the RNG k-s model from the standard k-s model can be found in the e balance where a new source term appears, which is a function of both k and s. The new term in the RNG k- s model makes the turbulence in this model sensitive to the mean rate of strain. The result is a model that responds to the effect of strain and the effect of streamline curvature,... 

The pipe flow apparent viscosity, defined by equation 3.31, is given by... 

The turbulent diffusivity defined by (4.74) is proportional to the turbulent viscosity defined by (4.46). Turbulent-diffusivity-based models for the scalar flux extend this idea to arbitrary mean scalar gradients. The standard gradient-diffusion model has the form... 

The relative viscosity (a misnomer since it is a unitless ratio) is larger than unity since the dissolved polymer molecules impede the flow of solvent. The specific viscosity, defined by... 

For a non-draining coil, the characteristic viscosity defined by equation (6.23) can be expressed in the form... 

The initial characteristic viscosity defined by equation (6.23) is seen to be independent of the characteristics of intramolecular friction, but this is a consequence of the simplifying assumptions. It has been shown for a dumbbell (Altukhov 1986) that, when account of the internal viscosity and the anisotropy of the hydrodynamic interaction is taken simultaneously, the characteristics of these quantities enter into the expression for a viscosity of type (6.23). This result must be revealed also by the subchain model when account is taken of the anisotropy of the hydrodynamic interaction. 

Pc Viscosity of the continuous phase Pd Viscosity of the dispersed phase p. Effective mean viscosity defined by Eq. (35)... 

Brenner (1974) has presented numerical results for the suspension stresses in various flows. Figure 6-14 plots the intrinsic viscosity [defined in Eq. (6-6)] for oblate and prolate spheroids of various aspect ratios as functions of the Peclet number. Note that as the aspect ratio of the spheroid increases, the zero-shear viscosity increases, and the suspension shows more shear thinning. The suspension also becomes more elastic when the aspect ratio p for prolate or 1/ for oblate spheroids) is large see Fig. 6-15, which plots Ni N2 versus Pe for prolate spheroids of various aspect ratios p. Typically, N2 is roughly an order of magnitude less than Ni, so this plot of Nj, mainly reflects the behavior of V,. 

The flow of liquids or semisolids is described by viscosity, or, more precisely, by shear viscosity (unit Pa sec). The viscosity defines the resistance of the material against flow. Viscosity is not a coefficient, because it is a function of the shear strain rate y [ti = /(y)]. In the classical fluid mechanics, the dynamic viscosity is obtained using a viscometer. (A viscometer is a rheometer, i.e., an instrument for the measurement of rheological properties, limited to... 

The viscosity of solutions of macromolecules is conveniently expressed by the relative viscosity, defined as the ratio of the viscosity of the solution, t], to the viscosity of the pure solvent t]Q ... 

Liquid viscosity Chemical potential of component t in phase I Mixture mean viscosity defined in Eq. (15-180) Reference viscosity (of water) MOSCED asymmetry factor Efficiency of a batch e3q)eriment [Eq. (15-175)] Efficiency of a continuous process [Eq. (15-176)] Murphree stage efficiency Murphree stage efficiency based on dispersed phase Overall stage efficiency Solvatochromic polarity parameter... 

---