Mixtures critical value

As an example of the quantitative testing of Eq. (5.47), consider the polymerization of diethylene glycol (BB) with adipic acid (AA) in the presence of 1,2,3-propane tricarboxylic acid (A3). The critical value of the branching coefficient is 0.50 for this system by Eq. (5.46). For an experiment in which r = 0.800 and p = 0.375, p = 0.953 by Eq. (5.47). The critical extent of reaction, determined by titration, in the polymerizing mixture at the point where bubbles fail to rise through it was found experimentally to be 0.9907. Calculating back from Eq. (5.45), the experimental value of p, is consistent with the value =0.578. 

Fig. 1. Phase diagram for mixtures (a) upper critical solution temperature (UCST) (b) lower critical solution temperature (LCST) (c) composition dependence of the free energy of the mixture (on an arbitrary scale) for temperatures above and below the critical value.

Another important concept is that of the critical ignition volume. During the propagation of the combustion wave, the flame volume cannot continually grow beyond a critical value without an additional supply of energy. The condition that controls the critical volume for ignition is reached when the rate of increase of flame volume is less than the rate of increase of volume of the combustion products. In this condition a positive exchange of heat between the flame and the fresh mixture is achieved. 

Variation of the normalized remaining percentage of CH4 fuel (c/Cj) after a run, measured by the gas chromatography, plotted over a very wide range of normalized turbulent intensities (u /Sl 10 100), where the subscript "i" refers to the initial condition. Both very rich (0 = 1.45 Cj = 13.2%) and very lean = 0.6 q = 5.92%) pure methane/air mixtures are investigated, showing critical values of Ka for the transition across which global quench occurs. 

One significant result from the studies of stretched premixed flames is that the flame temperature and the consequent burning intensity are critically affected by the combined effects of nonequidiffusion and aerodynamic stretch of the mixture (e.g.. Refs. [1-7]). These influences can be collectively quantified by a lumped parameter S (Le i-l)x, where Le is the mixture Lewis number and K the stretch rate experienced by the flame. Specifically, the flame temperature is increased if S > 0, and decreased otherwise. Since Le can be greater or smaller than unity, while K can be positive or negative, the flame response can reverse its trend when either Le or v crosses its respective critical value. For instance, in the case of the positively stretched, counterflow flame, with k>0, the burning intensity is increased over the corresponding unstretched, planar, one-dimensional flame for Le < 1 mixtures, but is decreased for Le > 1 mixtures. 

The phenomenon of critical flow is well known for the case of single-phase compressible flow through nozzles or orifices. When the differential pressure over the restriction is increased beyond a certain critical value, the mass flow rate ceases to increase. At that point it has reached its maximum possible value, called the critical flow rate, and the flow is characterized by the attainment of the critical state of the fluid at the throat of the restriction. This state is readily calculable for an isen-tropic expansion from gas dynamics. Since a two-phase gas-liquid mixture is a compressible fluid, a similar phenomenon may be expected to occur for such flows. In fact, two-phase critical flows have been observed, but they are more complicated than single-phase flows because of the liquid flashing as the pressure decreases along the flow path. The phase change may cause the flow pattern transition, and departure from phase equilibrium can be anticipated when the expansion is rapid. Interest in critical two-phase flow arises from the importance of predicting dis-... 

The reliability of multispecies analysis has to be validated according to the usual criteria selectivity, accuracy (trueness) and precision, confidence and prediction intervals and, calculated from these, multivariate critical values and limits of detection. In multivariate calibration collinearities of variables caused by correlated concentrations in calibration samples should be avoided. Therefore, the composition of the calibration mixtures should not be varied randomly but by principles of experimental design (Deming and Morgan [1993] Morgan [1991]). 

Mixtures of amines, for example aniline, with tetranitromethane (19.5%) ignite in 35-55 s, and will proceed to detonation if the depth of liquid is above a critical value. 

The extent to which a detonation will propagate from one experimental configuration into another determines the dynamic parameter called critical tube diameter. It has been found that if a planar detonation wave propagating in a circular tube emerges suddenly into an unconfined volume containing the same mixture, the planar wave will transform into a spherical wave if the tube diameter d exceeds a certain critical value dc (i.e., d > dc). II d < d.. the expansion waves will decouple the reaction zone from the shock, and a spherical deflagration wave results [6],... 

A mixture of ammonia and hydrogen sulphide does not unite if the press, is less than a certain critical value, which depends on the temp. If the press, is at or above this value crystals of ammonium hydrosulphide are formed if the press, be increased,more crystals will form and if the press, be reduced, crystals will decompose. When the two gases are present in eq. amounts this press, is called the dissociation pressure of the solid. In the present case, if the vapour phase has the same composition as the solid with which it is in equilibrium, the system is univariant, and there is a definite dissociation press, for each temp. F. Isambert found the dissociation press, of ammonium hydrosulphide, in mm. of mercury, increases rapidly with a rise of tomp. ... 

In connection with this disaster, tests conducted at Pic Arsn and Aberdeen PG showed that transformation of the combustion of a mixture of FGAN and bagging paper into detonation required the building up of a gas pressure greater than a certain critical value. This was calcd to be about 100 psi (abs) or perhaps less... 

Three conditions must be fulfilled obtain complete conversion of the reactants, H2 and CI2. The first condition is that thermal equilibrium of the system be favorable. This condition is fulfilled at low and intermediate temperatures, where formation of the product HC1 is thermodynamically favored. At very high temperatures, equilibrium favors the reactants, and thereby serves to limit the fractional conversion. The second requirement is that the overall reaction rate be nonnegligible. There are numerous examples of chemical systems where a reaction does not occur within reasonable time scales, even though it is thermodynamically favored. To initiate reaction, the temperature of the H2-CI2 mixture must be above some critical value. The third condition for full conversion is that the chain terminating reaction steps not become dominant. In a chain reaction system, as opposed to a chain-branching system discussed below, the reaction progress is very sensitive to the competition between chain initiation and chain termination. This competition determines the amount of chain carriers (batons) in the system and thereby the rate of conversion of reactants. 

Levedahl (106) noted that aliphatics from acetylene to octane all gave hot flames at 600° C. He suggested that some reaction, such as thermal decomposition, which was common to all aliphatics, became important. Benzene showed a very high, inconsistent hot flame limit, while cyclohexane was low and variable. Levedahl believed the cool flame and subsequent reaction, along with compression, served to raise the mixture temperature to the critical value. Acetylene was believed to play a major role in the ignition reaction. 

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