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Title: Dynamics of flexible fibres in a flowing suspension
Author: Salinas Franco, A.
Awarding Body: University College of Swansea
Current Institution: Swansea University
Date of Award: 1982
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A three dimensional mathematical model of a flexible fibre in a sheared suspension is proposed. The model, which includes fibre stiffness and distributed couples, was made up of differential force and moment balances from standard theory on three-dimensional bending curves. The viscous forces are calculated from the first term of the slender body theory. An inextensibility constraint is included to ensure the preservation of the arc length in time (19). The system is assumed to be quasi-static (inertialess) which makes it possible to separate the problem into a spatial boundary value at a time initial value problem. In the differential equations describing the fibre at each time, the derivatives are replaced by their equivalent finite difference approximations, giving a set of simultaneous algebraic equations which is solved by an LU decomposition band solver scheme. The solution of the boundary value problem yields the slip velocity at each node on the fibre, from which a new fibre position can be found by the time integration. The time integration is carried out using the modified Euler predictor-corrector method including a second order predictor formula. Automatic time-step size control is applied. This scheme was compared with Gear's method. The performance of the modified Euler method proved to be superior in this problem. The reliability of the model in physical terms was determined by comparing simulated fibre rotations in Couette flow with the equivalent real fibre rotations recorded in the laboratory. For the two fibre aspect ratios studied, the agreement was very good. In general when an experimental fibre configuration is not available, uncertainty exists about the initial condition to be used: In Couette flow, the obvious one of a straight fibre on the streamlines cannot be used; although the motion is there very slow, a small time-step is apparently still necessary to maintain stability. This makes it impractical to simulate fibre motion very close to the streamlines. The linear theory proposed by Hinch (19) for deformation decay rates of perfectly flexible, nearly straight fibres was reconfirmed, for Couette flow. The range of validity of that theory as a function of fibre stiffness was investigated. Results are presented on radial migration of a fibre suspended in Poiseuille flow. A qualitative description of the phenomenon and approximate quantitative results are obtained, and compared with experimental observations in the literature.
Supervisor: Not available Sponsor: Not available
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral
EThOS ID:  DOI: Not available