Bulk viscosity terms

The normal component of the collisional deviatoric pressure tensor resembles the bulk viscosity term and is thus denoted by pB,d-... 

The pressure inside individual bubbles may vary, but this was assumed to have no relation to the flow of the continuous phase. The volume averaged pressure of the two phases were assumed to be equal, pi = Pg- The dispersed phase approximation neglects internal flow inside the dispersed phases. The viscous terms of the gas equation were thus neglected. The bulk viscosity terms were also neglected since they are generally small, as discussed in chap 2. These assumptions and approximations simplify the momentum equations. 

Shear viscosity is a measure of the ahihty of one layer of molecules to move over an adjacent layer. Bulk viscosity will be mentioned in Section V.2. Since viscosity usually refers to shear viscosity, the term will he used in this way unless otherwise stated. Recommended techniques for measuring the viscosity of high-temperature melt are given below. Experimental data are available from the database mentioned in Section 1.2. Data on viscosities of slags (7 single component systems, 35 two-component... 

Lubricity is a term used to describe the ability of a fluid to minimize friction between, and damage to, surfaces in relative motion under load. Fuel helps to lubricate and prevent wear of high-pressure fuel injection pump components, especially under boundary lubrication conditions. Boundary lubrication is defined as a condition whereby friction and wear between two surfaces in relative motion are determined by the properties of the surfaces and the bulk properties of the contacting fluid. The bulk viscosity of the fuel or oil is not a critical factor under boundary lubrication conditions. 

Here pg and p f are the mass densities of the gel and the solvent, respectively, K is a bulk modulus, c0 is the speed of sound, and i s is the solvent shear viscosity. The solvent bulk viscosity has been neglected. The terms proportional to / arise from an elastic coupling in the free energy between the density deviation of gel and that of solvent The p in Eq. (6.1) coincides with the shear modulus of gels treated so far. We neglect the frequency-dependence of the elastic moduli. It can be important in dynamic light scattering, however, as will be discussed in the next section. 

The dissipation function, also called viscous dissipation, represents the irreversible conversion of kinetic energy into thermal energy. Since the dynamic viscosity p, is positive and all the terms are squared, the first two terms of the dissipation must be always positive. The bulk viscosity can be negative the Stokes hypothesis (Section 2.11) says that k = —2p/3. It turns out that the necessary condition for the dissipation function to be positive is that... 

The dielectric behaviour of proteins in aqueous solutions was first extensively studied by Ondey and co-workers. They interpreted the data in terms of rotational polarization of permanent dipole moments. The latter were found to be in the range of 100—1000 D (1 D = 10- e.s.u.) while the relaxation times came out at ca. 10" s. Despite some ta-itidsm, the preferential-orientation effect must still be considered the prindpal dielectric-polarization mechanism of proteins. - This view is also supported by dieledric dispersion studies of various proteins in solvents of different viscosity. The measured relaxation times were indeed proportional to rj as predided by (29) and (30). Nevertheless, for very large molecules (M, > 10 ) indications of other mechanisms, whose relaxation does not depend on the bulk viscosity of the solvent, have been observed. ... 

Rheology. Bulk Viscosity Properties. The rheological properties of an emulsion are very important. High viscosity may be the reason that an emulsion is troublesome, a resistance to flow that must be dealt with, or a desirable property for which an emulsion is formulated. The simplest description applies to Newtonian behavior in laminar flow. The viscosity, r], is given in terms of the shear stress, t, and shear rate, 7, by ... 

Note the definition of this viscosity term. The viscosity of the film at the wall is related to the viscosity of the bulk of the liquid p. Many authors used the inverse of this term. 

The quantities a, c, f, F, r, and p are the thermal diffusivity, sound speed, heat capacity ratio, bulk viscosity coefficient, shear viscosity coefficient, and density of the sample, respectively and Eo, a, P and Cp are the energy fluence of the laser beam, the optical absorption coefficient, the volume expansion coefficient, and the isobaric heat capacity, respectively, of the fluid. Tlie first and second terms in Eq. 2 describe the time dependences of the thermal and acoustic modes of wave motion, respectively. Since the decays of the acoustic and thermal mode densities back to their ambient values take place on such different time scales (microsecond time scale for acoustic mode and millisecond time scale for thermal mode), they were recorded on the oscilloscope using different time bases. 

In these equations jy, = tiltjQ is the relative bulk viscosity, with t o referring to the pure monomer viscosity at identical p and T. The terms and kp refer to the termination and propagation rate coefficients at very low conversion, respectively. Also from SP-PLP experiments, these two quantities are found to be ... 

Beyond the linear range, it has been shown by Rastogi and Misra [3] that the nonlinear flux equations for mass and heat transport involve non-linear terms containing forces corresponding to the anti-symmetric part of the viscous pressure tensor and the force corresponding to the divergent part of the viscous tensor responsible for bulk viscosity as discussed in Chapter 6. In case of spatially non-uniform systems, a proper expression for Gibbs function should take into account the existence of physical forces as indicated above. 

Here, p d is the relaxation pressure, ij and are the coefficients of shear and bulk viscosity. In the one-temperature approach, the additional terms connected to the bulk viscosity and... 

---