Multiphase Open Phase Processes Differential Equations

Abstract

The thermodynamic approach for the description of multiphase open phase processes is developed based on van der Waals equation in the metrics of Gibbs and incomplete Gibbs potentials. Examples of thermodynamic modeling of the multiphase and multicomponent A3B5 systems (In-Ga-As-Sb and In-P-As-Sb) and Na+, K+, Mg2+, Ca2+//Cl−, SO42−-H2O water–salt system are presented. Topological isomorphism of different type phase diagrams is demonstrated.

Solubility of Rare Earth Chlorides in Ternary Water-Salt Systems in the Presence of a Fullerenol—C60(OH)24 Nanoclusters at 25 °C. Models of Nonelectrolyte Solubility in Electrolyte Solutions

“…Naturally, such a conclusion will be based on a semi-empirical model, in our case, the Pitzer model of strong electrolytes [17,18], and it is naturally impossible to call it strictly thermodynamic. The same conclusion is easily obtained using other semi-empirical models, such as the Bromley model [12] or the regular solutions model [14]. So, consider the branch of crystallization of unsolvated nonelectrolyte (NE) in a solution containing a polar solvent and a strong electrolyte (E = M νc X νa ), ν c and ν a -number of cations and anions in molecule E: lnSP(NE) = ln(m NE )+ ln(γ NE ) = ln(m 0 NE )+ ln(γ 0 NE ) = const (6) where: m NE , γ NE -molality and activity coefficient of NE in a ternary solution of NE-E-H 2 O, m 0 NE , γ 0 NE -also in a binary system of NE-H 2 O, SP(NE)-thermodynamic solubility product of NE.…”

“…Solubility diagrams in four ternary systems are simple eutonic, both consist of two branches, corresponding to the crystallization of fullerenol crystal-hydrate and rare-earth chloride crystal-hydrates, and contain one eutonic nonvariant point corresponding to saturation with both solid phases [12][13][14]. On the long branches of C 60 (OH) 24 *18H2O crystallization, a pronounced salting-out effect is observed-the solubility of C 60 (OH) 24 *18H2O decreases by almost 2 orders of magnitude compared to the solubility of fullerenol in pure water.…”

EXTREME STATE PARAMETERS IN THE CONDITIONS OF TWO-PHASE AND MULTI-PHASE EQUILIBRIUM (Review)

“…To verify phase equilibrium experimental data in the conditions nearby extrema characteristics of state parameters (for example, azeotropes, Hetero-azeotropes, Van Rijn points, extrema of liquidus temperature of solid solutions, etc); 2. To determine concentration regions of phases compositions, which may be produced in the conditions of "closed phase processes" [1] (when finite masses of all phases are in equilibrium with each other, and no phases are removing from heterogeneous system) at constant parameters of state. The examples of such processes are, for example: single-time distillation of vapor from the solution at fixed T and P; single-time solid solution crystallization from the melts at fixed T, single-time solid solution crystallization from the solutions at fixed T, P and chemical potential of the solvent (w) -μ w , etc (see, for example [2][3][4][5][6];…”

“…3. To determine concentration regions of phases compositions, which may be produced in the conditions of "opened phase processes" [1] (when one or several equilibrium phases masses are infinitely small, and one or several phases are constantly removing from heterogeneous system) at constant change of some parameters of state. The examples of such processes are, for example: multistage distillation of vapor from the solution in distillation columns in the conditions of change T P or P T ; multistage solid solution crystallization from the melts in the conditions of change T P (implemented, for example, in processes of materials purification by "zone melting" or in "recrystallization columns"), multistage solid solution crystallization from the solutions in the conditions of solvent evapo-…”

“…Both equations(1) and(2), written in the variables of phases () and (), are equivalent. The last equation (3) is so named additional condition of phase equilibrium shift.…”