Some theoretical aspects of fibre suspension flows

This thesis is concerned with properties of equations governing fibre suspensions. Of particular interest is the extent to which solutions, and their properties, depend on the type of closure used. For this purpose two closure rules are investigated: the linear and the quadratic closures. We show that the equations are consistent with the second law of thermodynamics, or dissipation inequality, when the quadratic closure is used. When the linear closure is used, a sufficient condition for consistency is that the particle number Np satisfies Np ≤ 35/2. Likewise, flows are found to be monotonically stable for the quadratic closure, and for the linear closure with Np ≤ 35/2. The second part of the thesis is concerned with one-dimensional problems, and their solution by finite element. The hyperbolic nature of the evolution equation for the orientation tensor necessitates a modification of the standard Galerkin-based approach. We investigate the conditions under which convergence is obtained, for unidirectional flows, with the use of the Streamline Upwind (SU) method, and the Streamline upwind Petrov/Galerkin (SUPG) method.

Grantor dc:publisher.institution

Department of Mathematics and Applied Mathematics

Year dc:date.issued

1999

Author dc:creator

• Diatezua, Jacquie Kiangebeni

Advisor dc:contributor.advisor

• Reddy, Daya

Language dc:language.iso

eng

Handle dc:identifier.uri

http://hdl.handle.net/11427/9707

OAI identifier oai:identifier

oai:open.uct.ac.za:11427/9707