Models, xiii

The Washburn model is consistent with recent studies by Rye and co-workers of liquid flow in V-shaped grooves [49] however, the experiments are unable to distinguish between this and more sophisticated models. Equation XIII-8 is also used in studies of wicking. Wicking is the measurement of the rate of capillary rise in a porous medium to determine the average pore radius [50], surface area [51] or contact angle [52]. 

Micellar structure has been a subject of much discussion [104]. Early proposals for spherical [159] and lamellar [160] micelles may both have merit. A schematic of a spherical micelle and a unilamellar vesicle is shown in Fig. Xni-11. In addition to the most common spherical micelles, scattering and microscopy experiments have shown the existence of rodlike [161, 162], disklike [163], threadlike [132] and even quadmple-helix [164] structures. Lattice models (see Fig. XIII-12) by Leermakers and Scheutjens have confirmed and characterized the properties of spherical and membrane like micelles [165]. Similar analyses exist for micelles formed by diblock copolymers in a selective solvent [166]. Other shapes proposed include ellipsoidal [167] and a sphere-to-cylinder transition [168]. Fluorescence depolarization and NMR studies both point to a rather fluid micellar core consistent with the disorder implied by Fig. Xm-12. 

Fig. XIII-12. Lattice model of a spherical micelle. (From Ref. 160a.)...

Very recently, a very bold chemical model for histamine H2-receptors has been proposed using [18]aneN6-3H+ 84), which can chemically recognize histamine, histamine H2-agonists, and histamine H2-antagonists such as cimetidine XII or ranitidine XIII that are currently in world-wide use for treatment of peptic ulcers 85). 

The quantitative comparison of measured. To values and 5 values calculated for models A for mesitylene and hexamethylbenzene is given in Tables XII and XIII. With omission of the innermost maximum and minimum, the unreliable third minimum, and the very weak fifth maximum for each substance, the average values sa/s0 = 1.000 and 1.002, respectively, are found. These correspond to the interatomic distances C — = 1.54 0.01 A. and Car-Car = 1.39 A. in both substances, the 0 —Qa distance being equal to the single-bond distance in aliphatic compounds and the Car—distance to that in benzene to within the probable error of the determination. 

R. F. Kudritsky and D. G. Hummer, Quantitative Spectroscopy of Hot Stars , Ann. Rev. Astr. Astrophys., 28, 303, 1990 W. Schmutz, C. Leitherer and R. B. Gru-enwald, Theoretical Energy Distributions of Wolf-Rayet Stars , Pub. Astr. Soc. Pacific, 104, 1164, 1992 A.W. A. Pauldrach, T.L. Hoffmann and M. Lennon, Radiation-driven winds of hot luminous stars. XIII A description of NLTE line blocking and blanketing towards realistic models for expanding atmospheres , A ... 

To obtain the results in Table 20.2, equations (xii) and (xiii) are solved numerically using E-Z Solve (file ex20-5.msp) and die initial conditions above for cA and cD. For N = 1, equation 13.4-2 is used for Ex(t) and is integrated to obtain W,(t), and similarly for N = 2 and equation 17.2-4. Note that most software for numerical integration cannot directly handle the negative step sizes required to solve the maximum-mixedness model... 

These equations might be thought to apply for a high concentration of reactant A, at a given concentration of catalyst C, and at isothermal conditions. To describe measurements on the concentration of F as a function of time at each of the initial conditions of the 24 factorial design of Table XIII, we might tentatively entertain the integrated model ... 

Brown, Berni and Mitcham (17) report ash, aluminum, silicon and silica contents of four samples taken from an electrostatic precipitator in a model card room. The silica determinations were made using X-ray diffraction and IR spectroscopy. The results are shown in Table XIII. Based on these data, only a small fraction of the silicon can be attributed to silica. 

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