The preceding chapters introduced first the notion of separation and then a variety of indices to describe separation. These indices were used to characterize quantitatively the amount of separation achieved in a closed or an open separation vessel. The quantitative description included systems at steady or unsteady state involving chemical or particulate systems. Systems studied were either binary or multicomponent or a continuous mixture. Not considered in these two chapters was the fundamental physicochemical basis for these separations; appropriately, this is the focus of our attention in this chapter.

In Section 3.1, we distinguish between bulk 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.