Equilibrium in External Fields

External fields are applied widely in separation systems. The most common fields used are based on electrical and sedimentation (both centrifugal and gravitational) forces. Gradients in solvent composition and temperature maintained by actions external to the system may also be considered as external fields defined in their broadest context (see Chapter 8). All of these fields are capable of changing the equilibrium distribution of chemical components. Furthermore, they may be selective, affecting one component differently from another, a basic requirement for separation. 

As before, we transfer dnt moles of component i from region a to region j3 at equilibrium. We have 

Equation 2.27 is general for dilute solutes it accounts for the inter-molecular forces of phase transfer in the term and the potential energy of external fields in /a-xi. The two enter equally in a mathematical sense. Either may be zero, the former in one-phase systems and the latter in field-free systems. However, in a physical sense, Aand A/i xl are dissimilar in that 

A/x changes abruptly at phase boundaries and A/x 1 changes continuously in space. This difference is crucial to the type of separations achieved in multiphase systems versus external field systems, as we shall see later. 

A more complete discussion of thermodynamic equilibrium in an external field can be found in the book by Guggenheim [9] or treatments by other authors[10,11]. 

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