Doctor of Philosophy / Department of Mechanical and Nuclear Engineering / Mingchang (James) Chen / To describe the behavior of a gas composed of spherical particles that rotate, the kinetic theory approach is presented. First-order approximations to the Boltzmann-Curtiss transport equation yield conservation equations that govern the translational velocity and rotation of the particles. The resulting equations match the form of the equations of morphing continuum theory (MCT), a theory derived from the principles of rational continuum thermomechanics. A direct comparison of corresponding terms provides expressions related to the new coefficients within MCT, showing a clear departure from classical expressions derived from a kinetic treatment of classical fluids. The identical expressions for the coefficients in the Cauchy stress and viscous diffusion terms in the kinetic linear momentum equation suggests that the coupling coefficient introduced by MCT outweighs the contribution of the classical kinematic viscosity. The kinetic theory equations reduce to the form of the Navier-Stokes equations when the local rotation is equated to the angular velocity, but the predominance of the coupling coefficient results in a viscous term that differs slightly from the classical expression derived using the Boltzmann distribution function. For simple cases of irrotational and incompressible flows, the kinetic equations mimic the form of the classical momentum equations derived from classical kinetic theory. This result is consistent with the fact that the difference between the two kinetic approaches is the local rotation of spherical particles. Preliminary numerical simulations of the MCT governing equations are discussed, with an emphasis on the importance of the new coupling coefficient. Turbulent incompressible profiles are achieved by setting dimensionless parameters to particular values. The key parameter involves the ratio of the coupling coefficient to the kinematic viscosity. The relationship between the coupling coefficient and kinematic viscosity is shown to be the driving force for the development of transitional and turbulent boundary layer profiles. Compressible turbulence results are generated using the same dimensionless parameter values that generated turbulence in the incompressible case. For supersonic flow over a cylinder, MCT displays an inverse energy cascade from small to large scales. In addition to visualizing turbulent processes, the results from MCT display the importance of coupling the linear and angular momenta equations, which is strengthened when the coupling coefficient increases. The expressions from kinetic theory coupled with the numerical results in MCT indicate that the physical phenomena driving a fluid composed of spherical particles depends heavily on the physical properties of the coupling coefficient.

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ix, 109 leaves : ill., tables ; 30cm. / Title page, contents and abstract only. The complete thesis in print form is available from the University Library. / Thesis (Ph.D.1976) from the Dept. of Physical and Inorganic Chemistry, University of Adelaide

Thesis (Ph. D.)--University of Wisconsin--Madison, 1961. / Typescript. Vita. eContent provider-neutral record in process. Description based on print version record. Includes bibliographical references.

Thesis--University of Wisconsin--Madison. / Typescript. Vita. eContent provider-neutral record in process. Description based on print version record. Includes bibliographical references (leaf 139).

Thesis (Ph. D.)--University of Wisconsin--Madison, 1955. / Typescript. Vita. eContent provider-neutral record in process. Description based on print version record. Includes bibliographical references (leaves 129-131).

[No abstract available] / Science, Faculty of / Chemistry, Department of / Graduate

Equations of change for the various hydrodynamic densities are derived for a dilute gas with degenerate internal states. To obtain a consistent set of hydrodynamic equations it is necessary to expand the collision term of the usual Waldmann-Snider Boltzmann equation (W-S equation) in position gradients of the distribution function [formula omitted]. In particular, the extension of the W-S equation to terms "linear" in the position gradients of [formula omitted] yields the correct form for the equation of change for the internal angular momentum density. Specifically, the production term in this equation of change is t he antisymmetric part of the pressure tensor, which is in accord with a hydrodynamic derivation. In addition, equations of change for the mass density, linear momentum density, and total energy density are also obtained. These results are shown to be similar to equations of change derived via a density-operator technique. Unfortunately, this " linear" extension of the W-S equation does not give a closed set of equations of change. However, a consistent set of equations is obtained if a restriction is placed on the form of the extended W-S equation. / Science, Faculty of / Chemistry, Department of / Graduate

A classical gas whose particles interact through a weak long range attraction and a strong short range repulsion is studied. The Liouville equation is solved as an infinite order perturbation expansion. The terms in this series are classified by Prigogine type diagrams according to their order in the ratio of the range of the interaction to the average interparticle distance. It is shown that., provided the range of the short range force is much less than the average interparticle distance which in turn is much less than the range of the long range forces the terms can be grouped into two classes. The one class, represented by chain diagrams, constitutes the significant contributions of the short range interaction; the other, represented by ring diagrams, makes up, apart from a self-consistent field term, the significant contributions from, the long range force. These contributions are summed to yield a kinetic equation. The orders of magnitude of the terms in this equation are compared for various ranges of the parameters of the system. Retaining only the dominant terms then produces a set of eight kinetic equations each of which is valid for a definite range of the parameters of the system. The short-time stability of the system is examined and a criterion for stability obtained. The equilibrium two-particle correlation function and an equation of state are determined, the latter being compared to the Van de Waals equation of state. / Science, Faculty of / Physics and Astronomy, Department of / Graduate