Modeling slender viscoelastic jets and fibers with torsion
All thin-filament models to date are torsionless and consider only leading-order approximations in a slender asymptotic sense. This dissertation first presents a higher-order perturbation theory for slender viscoelastic jets and fibers, which allows full consideration of axisymmetric torsion. It then illustrates the practical applications of this higher-order perturbation theory through four practical examples. The steady equations through three orders for all four examples are solved to illustrate several points: (1) it is necessary to go to the higher-order corrections in order to check the leading-order approximation or to consider the torsional coupling; (2) many leading-order steady solutions are asymptotically valid and robust to neglected higher-order physical effects (the higher-order corrections are computed and found being small); (3) other leading-order solutions are invalid in the presence of higher-order effects; specifically, it is shown that corrections due to weak elastic relaxation can be as large as the Newtonian leading-order approximation; (4) it is straightforward using this higher-order perturbation theory to determine if a particular leading-order solution is a valid approximation of physical behavior; (5) torsion can have effect on both the mathematical structure of the model and higher-order corrections of the leading-order approximations.
- Research Organization:
- Oxford Univ. (United Kingdom)
- OSTI ID:
- 7114631
- Resource Relation:
- Other Information: Thesis (Ph.D.)
- Country of Publication:
- United States
- Language:
- English
Similar Records
Area-preserving dynamics of a long slender finger by curvature: A test case for globally conserved phase ordering
Asymptotic solution of the diffusion equation in slender impermeable tubes of revolution. I. The leading-term approximation