Thomas equation

As mentioned above, critical size (r ) at a given equilibrium stage is an important factor for determining the size of resultant nanoparticles. This critical size can be further derived from Gibbs-Thomas equation [12] ... 

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The Thomas model is also applicable to the design of ion-exchange columns (Kapoor and Viraraghavan, 1998). The Thomas equation constants qmm and values can be obtained from the column data and can be used in the design of a full-scale adsorption bed. This equation is simple since it can be used in its linear form ... 

This simplifies to the regular Fermi-Thomas equation for infinitely large values of c and reduces to a well-known difficult form when the term in Z(0) is neglected(lO). 

Where a, b, c, Ax, and BTare constants. Values for the constants in the more general form of the Thomas equation are tabulated in Ref. [215]. 

Within the framework of the method of Gaines and Thomas, Equation 7.10 is differentiated, and then the Gibbs-Duhem equation is applied to obtain the equilibrium constant ... 

The thermodynamic equilibrium constant can be evaluated by using the simplified form of the Gaines-Thomas equation [201], assuming that the change in water content in the exchanger is negligible. The equation, with defined as the corrected selectivity coefficient by Eq. (4), follows-. 

In the Gaines-Thomas equation (22), equivalent fractions are employed to represent the activities of ions in the exchanger phase, that is,... 

In the writer s view, the Thomas equation is the most important single result in the entire theory of adsorption-column performance. By reference to this result, all other solutions are found to be classifiable in terms of their r and N values. 

Such a normalization assumes that the residual Na+ ions are inaccessible for exchange and have no influence on the selectivity coefficient. That this assumption is incorrect results from the fact that the maximum limit to exchange is influenced by the nature of the outgoing and ingoing ions, and also by the Al/Si ratios of the zeolites. In order to obtain comparable values of the equilibrium constant, we modified the Gaines and Thomas equation. The corrected and normalized selectivity coefficient is defined as... 

Figure 12.31. Coefficient of thermal expansion of particulate composites as predicted by (A) ideal rule of mixtures, (B) Kerner s equation, (C) Thomas equation, (D) Turner s equation. The assumed material constants of the components are listed in the text. (From Nielsen, L. E., 1967, J. Compos. Mater. 1,100 courtesy Technomic Publishing Co.)...

The volume coefficients of thermal expansion of the composite, polymer, and filler are a, i, and 2 respectively. The bulk moduli of the components are Bi and B2, respectively. The parameter G is the shear modulus of the polymer. The more the filler particles deviate from spherical, the greater the divergence of the thermal expansion coefficient from this equation. In such cases, the Thomas equation (41), or the logarithmic rule of mixtiu es, provides a better estimate. 

As can be seen in Figure 5.8, the concentration dependence of viscosity for the 0I/Zr02 nanocomposite was found to be consistent with that predicted by the classical Thomas equation [40]... 

FIGURE 1-9 Ratio of viscosity of mixture versus viscosity of carrier in accordance with the Thomas equation for coarse slurries. 

The free settling speed of solid particles is 22 mm/s at a volumetric concentration of 1%. Using the Thomas equation 3-20, determine the settling speed at 25% volumetric concentration. 

The dynamic viscosity is corrected to take in account the presence of fines at a volumetric concentration of 0.089. The dynamic viscosity of water is 1.2 cP, the Einstein-Thomas equation is applied ... 

In Chapter 1, the increase in dynamic viscosity due to the volumetric concentration of solids was discussed it can be expressed as the Einstein Thomas equation ... 

By the Einstein-Thomas equation, the dynamic viscosity of the carrier liquid needs to be corrected for a concentration of 0.0405 in the upper layer ... 

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