Elongational Flows in Polymer Processing
| dc.contributor.author | Hagen, Thomas Ch. | en |
| dc.contributor.committeechair | Renardy, Michael J. | en |
| dc.contributor.committeemember | Herdman, Terry L. | en |
| dc.contributor.committeemember | Rogers, Robert C. | en |
| dc.contributor.committeemember | Renardy, Yuriko Y. | en |
| dc.contributor.committeemember | Baird, Donald G. | en |
| dc.contributor.department | Mathematics | en |
| dc.date.accessioned | 2014-03-14T20:17:53Z | en |
| dc.date.adate | 1998-05-11 | en |
| dc.date.available | 2014-03-14T20:17:53Z | en |
| dc.date.issued | 1998-12-01 | en |
| dc.date.rdate | 1998-05-11 | en |
| dc.date.sdate | 1998-11-03 | en |
| dc.description.abstract | The 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. | en |
| dc.description.degree | Ph. D. | en |
| dc.identifier.other | etd-110298-102457 | en |
| dc.identifier.sourceurl | http://scholar.lib.vt.edu/theses/available/etd-110298-102457/ | en |
| dc.identifier.uri | http://hdl.handle.net/10919/29437 | en |
| dc.publisher | Virginia Tech | en |
| dc.relation.haspart | hagenetd.pdf | en |
| dc.rights | In Copyright | en |
| dc.rights.uri | http://rightsstatements.org/vocab/InC/1.0/ | en |
| dc.subject | Fiber Spinning | en |
| dc.subject | Linear Stability | en |
| dc.subject | Quasilinear Hyperbolic Equations | en |
| dc.subject | Spectral Determinacy | en |
| dc.title | Elongational Flows in Polymer Processing | en |
| dc.type | Dissertation | en |
| thesis.degree.discipline | Mathematics | en |
| thesis.degree.grantor | Virginia Polytechnic Institute and State University | en |
| thesis.degree.level | doctoral | en |
| thesis.degree.name | Ph. D. | en |
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