# CLASSICAL AND STATISTICAL THERMODYNAMICS OF CONTINUOUS MIXTURES

#### Abstract

In this work we propose theories and formalisms for dealing with mixtures containing an infinite number of components. In chapter 4 we develop several statistical concepts that must be taken into account in the modelling of a continuous mixture. In particular we discuss the type of distribution law which characterizes the composition of the mixture, the nature of the distributed variable and the necessary number of distributed variables. It is shown that, in general, distributed variable are partially correlated. It is thus possible to approximate a continuous mixture with a series of single-variable composition distributions, each of them corresponding to a specific family of compounds. Chapter 5 deals with the classical liquid-vapor equilibrium problem for petroleum fractions using a continuous version of Raoult's law. It is shown that several distribution laws are flexible enough to represent simultaneously the compositions of the liquid and vapor phases, with different sets of parameters. Chapter 6 considers the effect of polydispersivity upon the liquid-vapor equilibrium behavior of a mixture described by the Redlich-Kwong equation of state. It is found that the properties do not depend on the specific distribution law but only on its first two moments. In chapters 7 and 8, it is shown that a polydisperse fluid can be modelled as a pure substance, in a four-dimensional space, under the influence of an external field. The fourth dimension corresponds to the identity variable. The external field acts only along the direction of the composition coordinate. This idea allows us to derive all the statistical thermodynamic properties on the basis of those for a pure non-homogeneous fluid. The most convenient representation for dealing with a polydisperse fluid is the semigrand canonical ensemble. Within this ensemble, a perturbation theory for narrow distributions is developed through an asymptotic integration of the partition function. Two equivalent versions of such perturbation are generated. One of them is expressed in terms of a small parameter (nu) which measures the width of the chemical potential function, while the other expansion is expressed directly in terms of the variance of the distribution.

#### Subject Area

Chemical engineering

#### Recommended Citation

BRIANO, JULIO GUSTAVO, "CLASSICAL AND STATISTICAL THERMODYNAMICS OF CONTINUOUS MIXTURES" (1983). *Dissertations available from ProQuest*. AAI8315993.

https://repository.upenn.edu/dissertations/AAI8315993