The Maximum Number of Solid Phases in a Multiphase Reacting System

Abstract

shown for absorption conditions using an ethanol-water system that the surface tension will fall from 72 dyn/cm to approximately 49 dyn/cm, a change of approximately 33%.From the photographic study, the droplet falling back toward the interface either (a) was assimilated by the bulk fluid, (b) bounced back into the gas phase one or more times before coalescing, or (c) was assimilated but produced a secondary droplet which reentered the gaseous space. Data concerning this behavior are presented in Table I, and photographs illustrating (b) and (c) are shown in Figures 2, 3, and 4.It is suggested that this anomalous behavior is equivalent to the heat-transfer analog, the Leidenfrost effect. Thus the coalescence time is governed by the action of the vapor being expelled from between the two liquid interfaces. At the same time the droplet approaching the interface deforms the underlying liquid which on restoration imparts an added force causing the droplet to reenter the gas phase.

Some Remarks on the Calculation of Complex Chemical Equilibria by General Methods

“…In addition, any of the general-purpose algorithms can treat cases of restricted equilibria by a method of modifying the species formula vectors and atom-balance constraints, due to Schott (1964). The present discussion of these cases should serve to clear up some of the problems experienced by users of such algorithms, as expressed in recent articles in this journal (Samuels, 1971;Madeley and Toguri, 1937a;Bjornbom, 1975).…”

“…For solid-gas systems of the type discussed by Samuels (1971), which are important in metallurgical applications, the inclusion of too many condensed solids in the computation will Ind. Eng.…”

“…Recently, a number of articles have appeared in this journal suggesting that difficulties may be encountered for specific types of equilibrium problems when such methods are used (Samuels, 1971; Madeley and Toguri, 1973a;Bjornbom, 1975). Samuels (1971) and Balzhiser et al (1972) suggested that the RAND "free-energy minimization method" (White et al, 1958) fails when too many solids are included in the compu-tation. Madeley and Toguri (1973a) suggested use of an alternative algorithm to partially overcome this problem.…”

Computing Chemical Equilibrium Compositions in Multiphase Systems

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The first-order free energy minimization technique has been adapted for use in multiphase systems. It has been found that the number of phases that maybe included in a computation is independent of the phase rule.Recently, Samuels (1971) and Smith (1972) have discussed the maximum number of phases which may be included in immiscible solid-gas equilibrium computations using the

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“…Recently, Samuels (1971) and Smith (1972) have discussed the maximum number of phases which may be included in immiscible solid-gas equilibrium computations using the…”