Thomas empirical equation

In special literature many other theoretical or empirical equations were suggested for describing t sp vs cp dependence. Thus Thomas suggested [20] and Metzner cited [21] [21] the following empirical equation as successful ... 

The viscosity of Newtonian suspensions of yeast and bacteria growing as individual cells in a water-like medium can be estimated from the following empirical equation proposed by Thomas. ... 

Another rough estimate of (1 — s) with reference to an empirical equation presented by Thomas on the various kinds of floes of inorganic materials ranging from 100 to 3,000 microns in size [20] gives (1 — e) = 0.13 commensurate to dj = 180 in Fig. 5. 

Thomas [106] proposed a totally empirical equation based on the concept of the mixture rule. According to Thomas... 

The theory of diffusion through the screens in diffusion batteries, as described by a semi-empirical equation derived by Cheng and Yeh (1980) correlating the screen fractional efficiency with experimental parameters, does not strongly differ from that formulated by Thomas and Hinchliffe (1972) as the penetration of particles through the screen (or the screen collection efficiency) is also an exponential function of the above parameters. 

Thomas (1963) proposed the following empirical equation in the range of VJVq of 0.08-1.0 ... 

This argument shows that the locality hypothesis fails for more than two electrons because the assumed Frechet derivative must be generalized to a Gateaux derivative, equivalent in the context of OEL equations to a linear operator that acts on orbital wave functions. The conclusion is that the use by Kohn and Sham of Schrodinger s operator t is variationally correct, but no equivalent Thomas-Fermi theory exists for more than two electrons. Empirical evidence (atomic shell structure, chemical binding) supports the Kohn-Sham choice of the nonlocal kinetic energy operator, in comparison with Thomas-Fermi theory [288]. A further implication is that if an explicit approximate local density functional Exc is postulated, as in the local-density approximation (LDA) [205], the resulting Kohn-Sham theory is variation-ally correct. Typically, for Exc = f exc(p)p d3r, the density functional derivative is a Frechet derivative, the local potential function vxc = exc + p dexc/dp. 

Several authors [Ong and Price, 1978b Alfonso and Russell, 1986, Runt and Martynowicz, 1986 Cimmino et al., 1989] used one of the equations mentioned above to calculate G°, cr, cr and/or (7(7 (see Table 3.6). The following empirical relationship [Thomas and Staveley, 1952 Geil, 1963 Vidotto et al., 1969] was developed ... 

The Wikon-Thomas method was derived from first principles and does not use empirical correction coefficients. It has proved to be correct for many slurries, but it sometimes overpredicts losses for the Carson slurries (described in Equation 3-52). 

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