Criteria for equilibrium separation in a closed separator

If two or more immiscible phases are kept in a closed container for a sufficient length of time, isolated from their surroundings, the phases come to equilibrium with one another. The amount of separation achieved at equilibrium is of considerable interest. We need to know the thermodynamic criteria for equilibrium to determine this separation. In this section, such criteria are specified for a variety of equilibrium conditions encountered in separation processes, including those where a single phase is exposed to an external force field in a closed vessel. Chapter 4 covers the extent of separation achieved under equilibrium conditions in a closed container. 

Thermodynamic equilibrium between two or more phases or two or more regions requires the existence of thermal, mechanical and idiemliral equilibrium. The 

We are more interested in chemical equilibrium, achieved after transfer of species between two or more phases or regions. The criteria for equilibrium here will directly allow the calculation of different concentrations of a given species in different phases. This calculation presumes the existence of thermal and mechanical equilibrium. If the region is subjected to an external force field, the criterion for equilibrium separation is affected by the external potential field. This and other related criteria will be indicated in Section 3.3.1 without extensive and formal derivations (for which the reader should refer to different thermodynamics texts and references). The development of such criteria will be preceded by a brief illustration of the variety of two-phase systems encountered in separation processes. Our emphasis will be on two immiscible phase systems. 

Of the 13 two-phase combinations identified, two combinations, gas-ion exchanger and supercritical fluid-ion 

Echoes of this may have mistakenly led to the formulation Corpora non agunt nisi fluida sive soluta - substances do not react unless in a liquid or a dissolved state (Helfferich, 1995). 

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In Section 3.1, we distinguish between hulk and relative displacements and describe the external and internal forces that cause separation-inducing displacements. This section then identifies species migration velocities and the resulting fluxes as a function of various potential gradients. Section 3.2 is devoted to a quantitative analysis of separation phenomena and multicomponent separation ability in a closed vessel as influenced by two basic types of forces. The criteria for equilibrium separation in a closed separator vessel and individual species equilibrium between immiscible phases are covered in Section 3.3. Section 3.4 treats flux expressions containing mass-transfer coefficients in multiphase systems. Flux expressions for transport through membranes are also introduced here. 

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