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Transport properties of the rough hard sphere fluid Kravchenko, Olga

Abstract

This thesis examines the dynamics and physical properties of the rough hard sphere fluid (RHSF). The RHSF model consists of spherical particles with well-defined radii that exchange linear and angular momenta upon collision. The simplicity of this model allows for a precise theoretical description that provides a basis for studying fluid properties on the most fundamental level. Extensive molecular dynamics calculations were made of transport properties as functions of density, tracer particle size, and degree of rotational-translational coupling. Results were compared with the smooth hard sphere case and it was found that transport coefficients change significantly due to rotational-translational coupling, becoming stronger with an increase in coupling. Tracer diffusion coefficients were examined for a range of tracer sizes and at various densities. As tracer particles become larger, their diffusion coefficient moves from an Enskog (molecular) to a Stokes-Einstein (hydrodynamic) functional form; the latter depends upon the boundary condition at the surface of the tracer. These boundary conditions for the RHSF are directly proportional to the degree of rotational-translational energy exchange, and can be tuned from "slip" to "stick" values. The validity of several kinetic theory equations have been examined as functions of density and translational-rotational coupling. At very low densities, Boltzmann theory was accurate even at low order except for describing the dependence upon rotational-translational coupling, where low order expansions are less accurate. Enskog theory performed well at low and moderate densities but deviated at larger densities, as expected. For thermal conductivity as a function of translational-rotational coupling even the qualitative behavior was incorrect. The Enskog predictions for diffusion were also found to be quite poor at low order. Finally, motivated by the results of the thesis, experimental diffusion coefficient data were analyzed, especially for nanoparticles. It was shown that defining the correct radius is crucial for describing such systems. In addition, a new formula for predicting tracer diffusion was tested.

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