Some problems in thin-film flow

Student thesis: Doctoral Thesis

Abstract

Thin-film flows are ubiquitous in nature and industry, and this thesis considersthree different thin-film flow problems that are inspired by and relevant to a number of real-world situations. Firstly, we consider the steady and unsteady coating flow of a thin film of viscous fluid on the outside of a uniformly rotating horizontal circular cylinder in the presence of an irrotational airflow with circulation. In particular, it is shown that steady full-film solutions corresponding to a thin film of fluid that covers the entire cylinder are possible only when the flux and mass of the fluid do not exceed critical values, which are determined in terms of the speed of the far-field airflow and the circulation of the airflow. Furthermore, a long-time analysis shows that unsteady full-film solutions are unconditionally stable. Secondly, we consider the squeeze-film flow of a thin film of fluid in the gap between an impermeable disk and an open-base porous bed, subject to a constant load. In particular, we determine the finite time required for the impermeable disk and the porous bed to contact, and the behaviour of the particle paths and penetration depths of the fluid within the porous bed. These are described in terms of the permeability and porosity of the porous bed and the slip length at the interface between the fluid and porous bed. In particular, in the asymptotic limits of small and large permeability, the contact time, particle paths, and penetration depths exhibit qualitatively different behaviour. Finally, we consider the steady flow of a thin rivulet of evaporating fluid down an inclined substrate. In particular, for three different models of evaporation, we analyse the variation of the length, width and contact angle of the rivulet as theparameters appearing in the problem vary, such as the input flux of the rivulet, the angle of inclination of the substrate, and the parameters of the relevant model of evaporation. In particular, it is shown that, rather surprisingly, the length of the rivulet only depends weakly on the mode of evaporation.
Date of Award11 Mar 2024
Original languageEnglish
Awarding Institution
  • University Of Strathclyde
SponsorsEPSRC (Engineering and Physical Sciences Research Council) & University of Strathclyde
SupervisorStephen Wilson (Supervisor) & Brian Duffy (Supervisor)

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