Binary process

The recombination of He is a special case. We include it here because of the similarities with H3 and because it is the only known example where three-body recombination of a diatomic molecular ion dominates over the binary process. The literature on the helium afterglow is quite large and we will not be able to do justice to all aspects of this problem. Mulliken71 had predicted that fast dissociative recombination of Hej should not occur due to a lack of a suitable curve crossing between the ionic potential curve and repulsive curves of He. Afterglow experiments in pure helium, at sufficient pressure to enable formation of Hej ions, have confirmed this expectation. It does not appear that the true binary recombination... 

This breakdown of the linear relationship between the absorption coefficient a and the product of densities, Q1Q2, indicates that the observed absorption is not a binary process. Specifically, for the case at hand, one can no longer assume that the measured absorption consists of an incoherent superposition of the pair contributions. Rather, the correlations of the dipoles that are induced in subsequent binary collisions lead to a partially destructive interference, an absorption defect that occurs if the product of the time T12 between Ne-Xe collisions, and microwave frequency, /, approaches unity [404], We note that for the spectra shown above, Figs. 3.1 and 3.2, the product fx 2 is substantially greater than unity at all frequencies where experimental data are shown and, consequently, incoherent superpositions of the waves arising from different induced dipoles occur. The intercollisional absorption defect is limited to low frequencies (Lewis 1980). 

The rate of coagulation is considered to be dominated by a binary process involving collisions between two particles. The rate is given by bn,nj, where nl is the number of particles of z th size and b a collision parameter. For collision between i - and / -sized particles during Brownian motion, the physicist M. Smoluchowski derived the relation ... 

In a multicomponent ion exchange system, the reactions between exchanging ions still can be expressed as in Eqs. 5.1 and 5.2, which are binary processes, but the description of exchanger composition in terms of mole or charge fractions requires a generalization of expressions like Eq. 5.12 ... 

Binary system. The binary system composed of two processes is the most basic system and it is quite frequently applied. Generally one of the binary processes is the target and the other donates exergy to it or accepts exergy from it. Hence the latter process may be called a coupled process or simply coupler. 

When one of the binary processes is energy-accepting (i.e., AH >0), the other is always energy-donating (i.e.,AH < 0). By denoting the direction factors of both processes by Dha and Dhd, respectively, the above equation reduces to... 

The process system which contains several couplers for a single target may be converted to a binary process system by assembling all coupled processes into one coupler as schematically shown in Fig. 21. 

In the simple binary process considered above, the 2500 ft3 reactor with a 17-tray stripper gives the process with the smallest total annual cost 936,000/yr versus 1,550,000,Nr for the best of the CSTR-in-series flowsheets. Thus this process with recycle is more economical, from the viewpoint of steady state, than the alternative process consisting of reactors in series. This is the point we made in Sec. 2.2 about the economic advantage for recycle. 

This attempted correlation fails (for example, 1/Ti plotted versus D does not pass through the origin) precisely because and D are many-body variables, whereas, as shown previously, vibrational energy relaxation in this case is a binary process. 

Simplex Combination Binary Process Simplex Combination Ternary Process... 

Reactive distillation occurs in multiphase fluid systems, with an important role of the interfacial transport phenomena. It is an inherently multicomponent process with much more complexity than similar binary processes. Multi-component thermodynamic and diffusional coupling in the phases and at the interface is accompanied by complex hydrodynamics and chemical reactions [4, 42, 43]. As a consequence, an adequate process description has to be based on specially developed mathematical models. However, sophisticated RD models are hardly applicable for plant design, model-based control and online process optimization. For such cases, a reasonable model reduction should be applied [44],... 

Individual coalescence and breakup events are essentially impossible to observe in a bubble swarm. They must be inferred indirectly from the bubble size distribution. Instrumentation has not yet been able to resolve the details of the coalescence process itself [13-15]. Because of this, models of bubble swarms often use simple exponential coalescence rates assuming a random binary process [16,17]. 

Prince and Blanch s [19] bubble size distribution is the only one that appears to match the exponential model in Figure 10. They designed an experiment to achieve an equilibrium with equal breakup and coalescence rates. If coalescence is cluster-wise and breakup is binary, it would take many binary breakup events to balance one coalescence of a large cluster, and the binary process, which is characterized by an exponential distribution would dominate. 

The Pareto distribution fits this relation just as it did the cluster coalescence model. Recall that the tail of the Pareto distribution is so fat in the latter case that the mean is not even defined. The situation is not quite so severe with the 3/2 exponent—the mean is defined, but the variance is not. We conclude that the Pareto distribution need not require that all coalescences occur simultaneously in clusters, but can also apply to a binary process. 

First of all, let us recall the consequences of T-reversal invariance. Let us consider the following binary process a -f A- b -f B and also the reverse process. Through the 7-invariance condition, these two different processes with reversed momenta and spins k/j- -kf, s- -s) are related by... 

Structurally, air Pb regulation in the European Union is a binary process. The scientific and health risk rationales for controls on lead in various environmental media are first articulated by multistate bodies like the WHO, the UNEP, and the ILO. Subsequently, ministerial actions either collectively by EU Directives via the European Commission or through national ministries give consideration to and may often adopt WHO guidelines as regulations. 

The elementary interaction that occurs between an incident particle and a lattice atom is a collision. This binary process occurs in a time of < 10 s, and the surrounding lattice can be considered to be at rest during this time period (the frequency of the thermal oscillations of the atoms is 10 s" ). The collisions with the lattice... 

Let us call these outcomes D (for default), having a probability q, and S (for survival) having probability of —q). We can represent this as a binary process, shown as FIGURE 10.15. 

Over multiple periods, this binary process can be illustrated as shown in FIGURE 10.16. 

Experimental values of ternary diffusion coefficients characteristic of liquids are shown in Table 7.4-2. In cases like KCl NaCl water, KCl sucrose-water, and tolu-ene-chlorobenzene-bromobenzene, the cross-term diffusion coefficients are small, less than ten percent of the main diffusion coefficients. In these cases, we can safely treat the diffusion as a binary process. 

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