Newman solution

Figure 3.12 shows the variation of F with Xp when FT = 1. As decreases, the curves approach a limiting case solved much earlier, (Nl), often called the Newman solution. This corresponds to negligible external resistance, and Eqs. 

Solutions have been obtained for a rigid sphere with Pep = 0 (G8), and the results are shown in Fig. 3.21. We have complemented these with solutions for a sphere circulating with the Hadamard-Rybczynski velocities at PCp/(l + k) 00, assuming Shi proportional to sin 0 and with the overall mean Sh used to define Bi. These results are shown in Fig. 3.22. For Bi oo (i.e., negligible external resistance), the limiting curves are the Newman solution in Fig. 3.21 and the Kronig-Brink solution in Fig. 3.22. For Bi < 0.2 the internal resistance... 

Figure 18.4 The hanging-drop method of protein crystallization, (a) About 10 pi of a 10 mg/ml protein solution in a buffer with added precipitant—such as ammonium sulfate, at a concentration below that at which it causes the protein to precipitate—is put on a thin glass plate that is sealed upside down on the top of a small container. In the container there is about 1 ml of concentrated precipitant solution. Equilibrium between the drop and the container is slowly reached through vapor diffusion, the precipitant concentration in the drop is increased by loss of water to the reservoir, and once the saturation point is reached the protein slowly comes out of solution. If other conditions such as pH and temperature are right, protein crystals will occur in the drop, (b) Crystals of recombinant enzyme RuBisCo from Anacystis nidulans formed by the hanging-drop method. (Courtesy of Janet Newman, Uppsala, who produced these crystals.)...

An evaluation of the retardation effects of surfactants on the steady velocity of a single drop (or bubble) under the influence of gravity has been made by Levich (L3) and extended recently by Newman (Nl). A further generalization to the domain of flow around an ensemble of many drops or bubbles in the presence of surfactants has been completed most recently by Waslo and Gal-Or (Wl). The terminal velocity of the ensemble is expressed in terms of the dispersed-phase holdup fraction and reduces to Levich s solution for a single particle when approaches zero. The basic theoretical principles governing these retardation effects will be demonstrated here for the case of a single drop or bubble. Thermodynamically, this is a case where coupling effects between the diffusion of surfactants (first-order tensorial transfer) and viscous flow (second-order tensorial transfer) takes place. Subject to the Curie principle, it demonstrates that this retardation effect occurs on a nonisotropic interface. Therefore, it is necessary to express the concentration of surfactants T, as it varies from point to point on the interface, in terms of the coordinates of the interface, i.e.,... 

NMR Studies of the Structure of Electrolyte Solutions Covington, A. K. Newman, K. E 12... 

Eqs. (40H41) are obtained from the analytical solution using the first two terms in the 0-series expansion of the concentration profile. As a result, they are accurate only for small values of meridional angle, 8. To correct for large values of 6, Newman [45] used Lighthill s transformation and Eq. (15) for the meridional velocity gradient to calculate the local mass transfer rate as Sc - oo. His numerical result is plotted in Fig. 5 in the form of Shloc/Re1/2 Sc1/3 vs. 8 as the thin solid line. The dashed line is... 

Edwards, T. J., John Newman and J. M. Prausnitz, "Thermodynamics of Aqueous Solutions Containing Volatile Weak Electrolytes," AIChE J., 1975, 21, 248. 

This contribution describes and compares three procedures for representing vapor-liquid equilibria in multicomponent aqueous solutions of volatile weak electrolytes. Starting from the basic thermodynamic relations, the approximations and simplifications applied by van Krevelen, Hoftijzer and Huntjens ( ), Beutier and Renon (2) and Edwards, Maurer, Newman and Prausnitz (3) are discussed the necessary information for using these correlations is compiled. Results calculated with these procedures are discussed and compared with literature data. 

A number of 1,1 -disubstituted 9,9 -bisfluoronylidenes (23) have been studied by variable-temperature (dynamic) NMR of their solutions, either immediately after dissolution of the solids at low temperature or after equilibration (65). It appears that the dominant configuration in equilibrated solutions is a twisted trans one (Newman projection along C=C shown on the right). In the solid, compounds 23b and 23c retain this configuration [as shown for 23b by X-ray analysis also (66)], whereas 23a possesses a cis configuration. 

Sherwood(12) and Newman i3 have presented the following solution assuming an initially uniform water distribution and zero water-concentration at the surface once drying... 

Johnson CM, Skulan JL, Beard BL, Sun H, Nealson KH, Braterman PS (2002) Isotopic fractionation between Fe(lll) and Fe(ll) in aqueous solutions. Earth Planet Sci Lett 195 141-153 Johnson CM, Beard BL, Roden EE, Newman DK, Nealson KH (2004) Isotopic constraints on biogeochemical cycling of Fe. Rev Mineral Geochem 55 59-408... 

Using this method, it takes many days to determine a single reliable CPT value. Salinas-Bravo and Newman published in 1994 what they called An alternative Method to Determine Critical Pitting Temperature of Stainless Steels in Ferric Chloride solution. ... 

Instead of the dilute solution approach above, concentrated solution theory can also be used to model liquid-equilibrated membranes. As done by Weber and Newman, the equations for concentrated solution theory are the same for both the one-phase and two-phase cases (eqs 32 and 33) except that chemical potential is replaced by hydraulic pressure and the transport coefficient is related to the permeability through comparison to Darcy s law. Thus, eq 33 becomes... 

Porous-Electrode Models. The porous-electrode models are based on the single-pore models above, except that, instead of a single pore, the exact geometric details are not considered. Euler and Nonnenmacher and Newman and Tobias were some of the first to describe porous-electrode theory. Newman and Tiedemann review porous-electrode theory for battery applications, wherein they had only solid and solution phases. The equations for when a gas phase also exists have been reviewed by Bockris and Srinivasan and DeVidts and White,and porous-electrode theory is also discussed by New-man in more detail. 

Stagnant cap, o- Results lie between the solutions of Newman and Kronig and Brink. This model can easily be extended to include changes of cap angle with time. 

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