Studies in thin film flows

Rights statement
Awarding institution
  • University of Strathclyde
Date of award
  • 1999
Thesis identifier
  • T9869
Qualification Level
Qualification Name
Department, School or Faculty
  • Using the lubrication approximation to the Navier-Stokes equations we investigate the evolution and stability of a thin film of incompressible Newtonian fluid on a planar substrate subjected to a jet of air blowing normally to the substrate. For the simple model of the air jet we adopt, the initially axisymmetric problems we study are identical to those of a drop spreading on a turntable rotating at constant angular velocity (the simplest model for spin coating). We consider both drops without a dry patch (referred to as "non-annular") and drops with a dry patch at their centre (referred to as "annular"). First, both symmetric two-dimensional and axisymmetric three-dimensional drops are considered in the quasi-static limit of small capillary number. The evolution of both non-annular and annular drops and the stability of equilibrium solutions to small perturbations with zero wavenumber are determined. Using a specially developed finite-difference code we then investigate the linear stability of both an initially two-dimensional thin ridge of fluid and an initially axisymmetric thin drop of fluid to perturbations with non-zero wavenumber for the general case of non-Quasi-static motion (non-zero capillary number). For the ridge we examine the cases when the jet acts at the centre of the ridge and when the jet acts off-centre. For the drop we examine both non-annular and annular drops. For each problem we examine both the special case of quasi-static motion analytically and the general case of non-zero capillary number numerically.
Advisor / supervisor
  • Wilson, Steve (Stephen K.), 1954-
  • Sloan, David
Resource Type