Compressional modulus

The effect of protein and other monolayers on mass-transfer rates depends quantitatively 50) on the surface compressional modulus, Cr this is defined as the reciprocal of the compressibility of the contaminating surface film, i.e., Cr = —A dU/dA. For films at the oil-water interface Cr is often close to II, the surface pressure, which is equal to the lowering of the interfacial tension by the film. 

Solubility of the film will short-circuit the compressional modulus a minimum in the transfer coefficient is often observed 50, 57, 58) (Fig. 13). From this figure it is also clear that, whereas monolayers affect greatly the stirring near the surface (and so reduce 2 and the transfer... 

In practice one cannot measure n on the moving drop, and it is preferable to use the mean compressional modulus of the surface film, defined hy Cr = —A dU/dA. lor the drop as a whole this becomes... 

Nevertheless, some conclusions may be drawn from the set of results presented here. First, with the notable exception of InN, the group III nitrides form a family of hard and incompressible materials. Their elastic moduli and bulk modulus are of the same order of magnitude as those of diamond. In diamond, the elastic constants are [49] Cu = 1076 GPa, Cn = 125 GPa and Cm = 577 GPa, and therefore, B = (Cn + 2Ci2)/3 = 442 GPa. In order to make the comparison with the wurtzite structured compounds, we will use the average compressional modulus as Cp = (Cu + C33)/2 and the average shear modulus as Cs = (Cu + Ci3)/2. The result of this comparison is shown in TABLE 8. 

Within an optics-type approach, one considers the resonator as an acoustic cavity. The term acoustic in this context always pertains to shear waves, never to longitudinal waves. This distinction is important in hquids, shear waves rapidly decay because the elastic part of the shear modulus is zero. Shear waves therefore provide for surface specificity. Longitudinal waves, on the contrary, propagate because the elastic component of the compressional modulus is nonzero. 

Film Elasticity The differential change in surface tension of a surface film with relative change in area. Also termed surface elasticity, dilata-tional elasticity, areal elasticity, compressional modulus, surface dilata-tional modulus, or modulus of surface elasticity. For fluid films, the surface tension of one surface is used. The Gibbs film (surface) elasticity is the equilibrium value. If the surface tension is dynamic (time-dependent) in character, then for nonequilibrium values, the term Marangoni film... 

If the rate of desorption of surfactants is very much greater than the rate at which the drop traverses through a distance equivalent to its diameter (about 0.02 sec), one may expect (D6) no accumulation of surfactants at the rear end. A quantitative semiempirical expression for the degree of drop circulation as a function of the viscous forces, drop diameter, densities and the compressional modulus of the surface film (surface-tension gradient), as well as the empirical fraction of liquid circulating, has been suggested by Davies (D6). 

Where K, is the modulus of the solid grain, is porosity, and c is a consolidation parameter that represents the sediments and fluid inside the vugs (unconsolidated material). We use c = 200. The effective compressional modulus (harmonic average of the Ki and /fj drained moduli) and the shear bulk modulus, G, of the double porosity medium can be obtained, respectively, from... 

Mohammed et al. [55] published a series of papers in which they probed the rheology, interfacial tension, surface pressure, and compressional modulus of crude oil-water interfaces with and without added demulsifiers under thermal and electrical fields. They observed that with short aging times of the crude oil-water interface, the interface rheology could be characterized as substantially viscous, but with very little elastic character. They demonstrated that thick viscoelastic films tended to accumulate in aged films and that some demulsifiers prevented such accumulations. 

At the same time, the compressional modulus K of polymer networks is of the same order of magnitude than that of water (Treloar, 1970). This is associated with the fact that compressibility is due to the manifestation of intermolccular forces which are not specific for polymers compressibility is by no means related to the network properties which manifest themselves under deformation. 

Geissler, E., Hecht, A.-M., Horkay, F. and Zrinyi, M. (1998) Compressional Modulus of Swollen Polyacrylamide Networks, Macromolecules, 21, 2594-9. 

The Goe values together with Ma and KO0, the compressional modulus (-M00 -4/3Geo) are reported in Fig. 2 at P = 0.1 GPa as a function of the temperature. The moduli values obtain d as a function of the pressure at various temperatures are reported in Fig. 3, 4 and 5 for Got, Moe and, respectively. The H modulus, not reported here, has been obtained from high temperature longitudinal velocity measurements. 

From the free energy per unit surface, we readily calculate the layer compressional modulus B and 17 as a function of d. Indeed, B is related to the second derivative of the free energy per unit volxme ... 

For compressional wave velocities is Fp,minerals > kp, water, oil > Fp, gas and for the corresponding compressional modulus is minerals > water, oil > gas-... 

TABLE 6.4 Some Values for Hydrocarbon Gas Density and Compressional Modulus... 

TABLE 6.6 Some Values for Brine Density and Compressional Modulus Concentration (Salinity),... 

The ratio of compressional wave velocities of water saturated to dry rock increases with porosity, as shown in Fig. 6.15b. This ratio is strrMigly controlled by the contribution of the high compressional modulus of water compared with that of air therefore, the effect increases with porosity. 

Figure 6.26 gives an example for compressional modulus calculation. 

The bulk compressional modulus is strongly controlled by porosity. For an estimate based on the critical porosity concept, the following equation is recommended (Mavko and Mukerji, 1995 Nur, 1992) ... 

Figure 6.40 shows the normalized dry compressional modulus k rylk as a function of the porosity experimental data from Russell (2013), determined at clean... 

Voigt and Reuss equations in general describe the upper and lower limit of the compressional modulus for a mixture. Domenico (1976) notes that Voigt s averaging gives the best estimate when patch sizes are large with respect to the seismic wavelength. 

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