Abstract
dc:description.abstractThe production of long, thin polymeric fibers is a main objective of the textile industry. Melt-spinning is a particularly simple and effective technique. In this work, we shall discuss the equations of melt-spinning in viscous and viscoelastic flow. These quasilinear hyperbolic equations model the uniaxial extension of a fluid thread before its solidification. We will address the following topics: first we shall prove existence, uniqueness, and regularity of solutions. Our solution strategy will be developed in detail for the viscous case. For non-Newtonian and isothermal flows, we shall outline the general ideas. Our solution technique consists of energy estimates and fixed-point arguments in appropriate Banach spaces. The existence result for a simple transport equation is the key to understanding the quasilinear case. The second issue of this exposition will be the stability of the unforced frost line formation. We will give a rigorous justification that, in the viscous regime, the linearized equations obey the ``Principle of Linear Stability''. As a consequence, we are allowed to relate the stability of the associated strongly continuous semigroup to the numerical resolution of the spectrum of its generator. By using a spectral collocation method, we shall derive numerical results on the eigenvalue distribution, thereby confirming prior results on the stability of the steady-state solution.
Degree
thesis:*- Name thesis:degree_name
- Ph. D.
- Level thesis:degree_level
- doctoral
- Discipline thesis:degree_discipline
- Mathematics
- Department dc:contributor.department
- Mathematics
- Grantor dc:publisher
- Virginia Tech
- Year dc:date.issued
- 1998
Author and committee
dc:creator, dc:contributor.*- Author dc:creator
-
- Hagen, Thomas Ch.
- Chair dc:contributor.committeechair
-
- Renardy, Michael J.
- Committee members dc:contributor.committeemember
-
- Herdman, Terry L.
- Rogers, Robert C.
- Renardy, Yuriko Y.
- Baird, Donald G.
Subjects
dc:subject × 4Rights
dc:rights- Statement dc:rights
-
- In Copyright
- Licence dc:rights.uri
Identifiers
dc:identifier.*- Dc Identifier Other
- etd-110298-102457
- OAI identifier oai:identifier
- oai:vtechworks.lib.vt.edu:10919/29437