Bulk viscosity, coefficient

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. 

The quantity X + (2/3)(i is commonly called the bulk viscosity coefficient. Besides the inequalities (2 84), no further information appears to be attainable for a Newtonian fluid... 

During the 1960s, the classical view of dynamics described above was seen to be incorrect both long-time and critical-point effects were observed in To a good approximation, the sound absorption coefficient in a fluid is determined by the shear and bulk viscosity coefficients. According to the classical theory, the viscosities should contain no critical anomalies at a binary critical point. However, it was observed that sound absorption shows an anomalous increase at a binary critical point, which indicates that the appropriate elements of must also possess a critical anomaly. Critical sound... 

The second viscosity coefficient X is related to the shear viscosity l (first viscosity coefficient) by A, = 2/3 t if the bulk viscosity coefficient defined by K = A, + 2/3 p is zero. Otherwise, X is given by... 

Hanley, H. J. M. Cohen, E. G. D. (1976). Analysis of the transport coefficients for simple dense fluids The diffusion and bulk viscosity coefficients. Physica, A 83,215-232. 

Fig. 9.1. Decay of the normalized Green-Kubo integrands for the self-diffusion coefficient D, the shear and bulk viscosity coefficients, rj and as well as the thermal conductivity coefficient X for LJ argon near the triple point.

The identity tensor by is zero for i J and unity for i =J. The coefficient X is a material property related to the bulk viscosity, K = X + 2 l/3. There is considerable uncertainty about the value of K. Traditionally, Stokes hypothesis, K = 0, has been invoked, but the vahdity of this hypothesis is doubtful (Slattery, ibid.). For incompressible flow, the value of bulk viscosity is immaterial as Eq. (6-23) reduces to... 

Figure 5-37 presents a typical heating and cooling chart for the changes in process side film coefficients, hg, as a function of bulk viscosity for organic chemicals. 

Bulk viscosity, rj, is evaluated from the ultrasonic absorption coefficient a and shear viscosity ri by "... 

Although these examples demonstrate the feasibility of using calculated values as estimates, several constraints and assumptions must be kept in mind. First, the diffusant molecules are assumed to be in the dilute range where Henry s law applies. Thus, the diffusant molecules are presumed to be in the unassociated form. Furthermore, it is assumed that other materials, such as surfactants, are not present. Self-association or interaction with other molecules will tend to lower the diffusion coefficient. There may be differences in the diffusion coefficient for molecules in the neutral or charged state, which these equations do not account for. Finally, these equations only relate diffusion to the bulk viscosity. Therefore, they do not apply to polymer solutions where microenvironmental viscosity plays a role in diffusion. 

The coefficient of bulk viscosity is of importance only in compressible flow, as may be seen from Eq. (7). This transport coefficient has been studied only slightly and is not further considered here the subject has been reviewed by Karim and Rosenhead (Kl) and has been considered further in a recent symposium under the leadership of Rosenhead (R5). 

On the other hand, if the rate constant for the quenching step exceeds that expected for a diffusion-controlled process, a modification of the parameters in the Debye equation is indicated. Either the diffusion coefficient D as given by the Stokes-Einstein equation is not applicable because the bulk viscosity is different from the microviscosity experienced, by the quencher (e.g. quenching of aromatic hydrocarbons by O, in paraffin solvents) or the encounter radius RAb is much greater than the gas-kinetic collision radius. In the latter case a long-range quenching... 

Some care has been taken to write these expressions in such a way that the bulk viscosity appears only as the coefficient of V-V. Recall from the discussion in Section 2.7, that the... 

To procure a full-scale hydrodynamic model, we may need microrheological data [85-89] (especially for PFPEs with polar endgroups, i.e., Zdol). When the microrheological data are not available, one could use a simplified form of q(z) = pg/( -j to develop the improved hydrodynamic model. Here p/ is the bulk viscosity and / is a function of z to be determined experimentally. A partial justification for the abovementioned functional form can be drawn from the temperature dependence of the surface diffusion coefficient and the bulk viscosity [10], or the fly stiction correlation with the bulk viscosity [9]. We examine the rheological properties of PFPE separately in Section II.C. 

Bueche et al. (1952) derived that the coefficient for self-diffusion of poly(n-butyl acrylate) is inversely proportional to the bulk viscosity of this polymer. Also in the natural rubber (polyisoprene) diffusion system a clear connection appears to exist between diffusion coefficient and bulk viscosity. In general the following expression may be used as a good approximation ... 

Nicolis, G., and G. Severne Nonstationary Contributions to the Bulk Viscosity and other Transport Coefficients. J. Chem. Phys. 44, 1477—1486 (1966). 

One difficulty of connecting theory and experiment arises from the fact that the relation between the microscopic coupling parameter between the reaction coordinate and the medium (the friction coefficient) and the macroscopic observables is not well understood. The usual rule of thumb follows Stokes s law and states that the friction is proportional to the macroscopic bulk viscosity however, this may be grossly incorrect. It would be advantageous to use a local viscosity obtained from the measurement of some sort of molecular relaxation phenomenon, but this is not always available. 

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