Lucas equation

Figure 3.20 Dynamic viscosity of liquid R134a (l,lJ,2-tetrafluoroethane) as a function of pressure at various temperatures with the Lucas equation. (Data from Comunas et af. [74].)...

The limitations of the Washbum-Lucas equation are frequently overlooked. The equation assumes incorrectly a constant advancing contact angle 6U for the moving meniscus [42,43]. The Washburn-Lucas equation (19) does not take in account the inertia of the flow [25], and implies that at time t = 0 and / = 0, the flow rate is infinite. In spite of these limitations, a variety of liquids have obeyed the Washbum-Lucas wicking kinetics [44]. Other forms of the Washbum-Lucas equation have been suggested [45-51]. 

Siddiqi-Lucas In an impressive empirical study, these authors examined 1275 organic liquid mixtures. Their equation yielded an average absolute deviation of 13.1 percent, which was less than that for the Wilke-Chang equation (17.8 percent). Note that this correlation does not encompass aqueous solutions those were examined and a separate correlation was proposed, which is discussed later. 

Siddiqi-Lucas These authors examined 658 aqueous liqiiid mixtures in an empirical study. They found an average absolute deviation of 19.7 percent. In contrast, the Wilke-Chang equation gave 35.0 percent and the Hayduk-Laudie correlation gave 30.4 percent. 

A modification of the Lucas-Moore-Spurr equation to account for the effect of the physical stack. 

Dillon, Young, and Lucas (5) described a method for determining dibromobutanes in 99% methanol. Dillon ( ) expanded this work to include a procedure for determining ethylene dibromide. Brenner and Poland (1) described a procedure in which they determined 1.000 mg. of ethylene dibromide with a recovery of 65.8%. Equations 1 and 2 show the main reactions that occur. 

The left-hand side of the latter equation is related to the liquid inertia, whereas both terms in the right-hand side are related to capillarity (the driving force), and viscous resistance, respectively. Under steady conditions, capillarity is balanced by the viscous drag of the liquid, and the famous Lucas-Washbum s equation can be derived (De Geimes et al., 2002) ... 

Figure 9 shows the temperature dependence of the recovered kinetic rate coefficients for the formation (k bimolecular) and dissociation (k unimolecular) of pyrene excimers in supercritical CO2 at a reduced density of 1.17. Also, shown is the bimolecular rate coefficient expected based on a simple diffusion-controlled argument (11). The value for the theoretical rate constant was obtained through use of the Smoluchowski equation (26). As previously mentioned, the viscosities utilized in the equation were calculated using the Lucas and Reichenberg formulations (16). From these experiments we obtain two key results. First, the reverse rate, k, is very temperature sensitive and increases with temperature. Second, the forward rate, kDM, 1S diffusion controlled. Further discussion will be deferred until further experiments are performed nearer the critical point where we will investigate the rate parameters as a function of density. 

The Lucas test is used to check for the presence of an alcohol functional group in an unknown compound. The test reaction is shown in the following equation ... 

Rathbun and Babb [20] suggested that Darkens equation could be improved by raising the thermodynamic correction factor PA to a power, n, less than unity. They looked at systems exhibiting negative deviations from Raoult s law and found n = 0.3. Furthermore, for polar-nonpolar mixtures, they found n = 0.6. In a separate study, Siddiqi and Lucas [22] followed those suggestions and found an average absolute error of 3.3 percent for nonpolar-nonpolar mixtures, 11.0 percent for polar-nonpolar mixtures, and 14.6 percent for polar-polar mixtures. Siddiqi, Krahn, and Lucas (ibid.) examined a few other mixtures and... 

The above equation (1) was used for calculating diffusivities at pressures higher than critical pressure in this study. The viscosity of the system is approximated as that of pure C02> using experimental data of Stephan and Lucas (7). In addition, the density of the CO 2 -naphthalene mixture is needed at different mixture compositions. These values are obtained from the modified Peng-Robinson equation of state (8,9). The standard form of P-R EOS (9) can be written as... 

Other analysis equations, some more complex than Eq. (15-4), are also in use, namely, those developed by Lucas-Tooth and Pyne [15.4, 15.5], Lachance and Traill [15.6], Claisse and Quintin [15.7], and Rasberry and Heinrich [15.8, 15.9]. 

Fortin M, Peyert R, Temam R (1971) R olution numerique des equations de Navier-Stokes pour un fluide incompressible. J Mec 10 357-390 Prank T, Zwart PJ, Shi J-M, Krepper E, Lucas D, Rohde U (2005) Inhomogeneous MUSIG Model - a Population Balance Approach for Polydispersed Bubbly Flows. Int Conf Nuclear Energy for New Europe 2005, Bled, Slovenia, September 5-8... 

Penetration of a liquid flowing under its own capillary pressure in a horizontal capillary, or in general, where gravity can be neglected, is theoretically described (4) by the Lucas-Washbum equation... 

The Lucas-Washbum equation is the simplest equation to model the rate of capillary penetration into a porous material. It is derived from Poiseuille s iaw (4) for laminar flow of a Newtonian liquid through capillaries of circular cross-section by assuming that the pressure drop (AP) across the liquid-vapor interface is given by the Laplace-Young (6) equation. In practice, depending... 

Gillespie (8) on the other hand developed an equation of the Lucas-Washburn type without specific reference to an explicit pore model on the basis of D Arcy s law (6). Assuming that AP was constant Gillespie derived the following equation for two dimensional radial spreading of a liquid drop... 

Polar and quantum effects (in H2, D2, and He) can be taken into account by multiplying equation (2-51) by factors given by Lucas (1980). The data needed to apply the Lucas method are tabulated next (Reid et al., 1987). 

Equations similar to (3.63)-(3.63) were obtained by Knobloch and De Luca... 

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