ABSTRACT
This chapter reviews theories based on integral equations. The most logical terminology would be to reserve the terms liquid and vapor for the two coexisting phases and call all other states fluid. A more common terminology is to call the fluid a liquid if its density exceeds the critical density and a gas if its density is lower. Alternative integral equations for the cavity functions of hard spheres can be derived using geometrical and physical arguments. Theories and results for hard sphere systems based on geometric approaches include the scaled particle theory, and related theories, and approaches based on zero-separation theorems. Several colloidal systems that are of practical importance contain spherically symmetric particles the size of which changes continuously. Polydisperse fluid mixtures can be described by a continuous probability density of one or more particle attributes, such as particle size.
