Thesis

Reduced-order modelling of thin-film flow over a spinning disk

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Awarding institution
  • University of Strathclyde
Date of award
  • 2026
Thesis identifier
  • T18191
Person Identifier (Local)
  • 202180174
Qualification Level
Qualification Name
Department, School or Faculty
Abstract
  • This thesis examines the mathematical modelling and analysis of a thin-film flow of Newtonian liquid over a topographically-patterned disk rotating with constant angular velocity. A novel reduced-order model is derived using the weighted residual integral boundary-layer method, which includes the effects of inertia, viscosity, centrifugation, Coriolis force and capillarity. The predictions of this model are tested extensively against direct numerical simulations, with excellent agreement being found throughout. For the case of a planar disk, the fully-developed state exhibits four characteristic spatial regions: the spin-up, inner, middle and outer regions. A small random noisy forcing at the inlet is found to have a strong effect on the dynamics of the system. Analytical insight is obtained into the behaviour of the system in the far field. A linear stability analysis is performed in the inner, middle and outer regions, which are found to be neutrally stable, convectively unstable and stable, respectively. For the case of a topographically-patterned disk, a family of topographies is introduced with parameters controlling the asymmetry, smoothness, amplitude and spatial frequency of the topography. The amplitude of the topography has a significant effect on the flow, even for small amplitudes, while the other three parameters have only a minor effect. Finally, control of the free surface towards a prescribed target free-surface profile in the outer region using the topography of the disk as the control mechanism is studied. At leading order, an exact solution for the topography is obtained and recovers the target free-surface profile exactly when substituted into the transient problem. At first order, a perturbation solution is obtained for the topography. Hence, this solution produces small errors in the free surface computed from the transient problem compared to the target free-surface profile.
Advisor / supervisor
  • Wray, Alexander W.
  • Wilson, Stephen K.
Resource Type
DOI

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