Similarity solutions sufficient

Actually, a similar approach was used in studying the oxidative addition of methane to an iridium complex. Hydrocarbon solvents would have reacted faster than methane with the photochemically produced unsaturated iridium species, therefore J.K. Hoyano et al chose perfluorinated hexane as being an inert solvent. The elevated pressure was necessary in order to increase the concentration of the methane in the solution sufficiently to shift equilibrium (15) to the right /20/. 

The choice of salt or alkali depends on factors similar to those considered for single oxide precipitations, the most important being the possible harmful effects on the final catalyst. Powders or particles are slurred with an amount of salt solution sufficient to give the required loading. It is helpful to carry out preliminary heating or evacuation to ensure that the pores are properly filled with solution. The sequence of events is. shown in Fig. 6.12. 

Necessary conditions for the existence of a self-similar solution are that (1) the governing PDE must reduce to an ODE for F as a function ot// alone, and (2) the original boundary and initial conditions must reduce to a number of equivalent conditions for F that are consistent with the order of the ODE. Of course, a proof of sufficient conditions for existence of a selfsimilar solution would require a proof of existence of a solution to the ODE and boundary conditions that are derived for F. In general, however, the problems of interest will be nonlinear, and we shall be content to derive a self-consistent set of equations and boundary conditions and attempt to solve this latter problem numerically rather than seeking a rigorous existence proof. Let us see how the systematic solution scheme based on the general form (3-135) works for the Rayleigh problem. 

This is precisely the self-similar solution of the Rayleigh problem, (3-134), which was obtained in the previous section. Notice that the length scale d drops completely out of this limiting form of the solution (3-158). This is consistent with our earlier observation that the presence of the upper boundary should have no influence on the velocity field for sufficiently small times 7 <[Pg.151]

Thus a necessary condition for the existence of similarity solutions for a, p 0 is that ue = xm. The sufficient condition is that ue = xm and a solution /(>]) exists that satisfies (10-95) in the form... 

Similarly, solutions of CH2X2/CH3CN (X = Cl, Br, 1) give Ep = 1.0 mol F , and in the case of X = Br or I, the products are derivatives of InCH2X InCl disproportionates in these systems to give In + 10X3. The oxidative reactions of InX have been sufficiently well studied in non-electrochemical work for the chemical processes (9) and (10), and the disproportionation, to be well understood [67]. 

What will be of interest to us in this chapter is whether a similarity solution is feasible for a population balance equation. In other words, can the population balance equation admit a self-similar solution Feasibility is of course necessary (but far from sufficient ) for the existence of a self-similar... 

Half-reaction (i) means that Co(II) in aqueous solution cannot be oxidised to Co(III) by adding ammonia to obtain the complexes in (ii), oxidation is readily achieved by, for example, air. Similarly, by adding cyanide, the hexacyanocobaltate(II) complex becomes a sufficiently strong reducing agent to produce hydrogen from water ... 

Chromatographic separations are accomplished by continuously passing one sample-free phase, called a mobile phase, over a second sample-free phase that remains fixed, or stationary. The sample is injected, or placed, into the mobile phase. As it moves with the mobile phase, the sample s components partition themselves between the mobile and stationary phases. Those components whose distribution ratio favors the stationary phase require a longer time to pass through the system. Given sufficient time, and sufficient stationary and mobile phase, solutes with similar distribution ratios can be separated. 

Pentaerythritol may be nitrated by a batch process at 15.25°C using concentrated nitric acid in a stainless steel vessel equipped with an agitator and cooling coils to keep the reaction temperature at 15—25°C. The PETN is precipitated in a jacketed diluter by adding sufficient water to the solution to reduce the acid concentration to about 30%. The crystals are vacuum filtered and washed with water followed by washes with water containing a small amount of sodium carbonate and then cold water. The water-wet PETN is dissolved in acetone containing a small amount of sodium carbonate at 50°C and reprecipitated with water the yield is about 95%. Impurities include pentaerythritol trinitrate, dipentaerythritol hexanitrate, and tripentaerythritol acetonitrate. Pentaerythritol tetranitrate is shipped wet in water—alcohol in packing similar to that used for primary explosives. 

---