In this thesis we use a combination of analytical and numerical methods to analyse two aspects of the steady flow of rivulets of fluid, namely the effects of nonNewtonian rheology, and the transport of a passive solute in a rivulet of Newtonian fluid. In Chapters 2â€“4 we consider rivulet flow of nonNewtonian fluids. Firstly, we obtain the solution for unidirectional gravitydriven flow of a uniform thin rivulet of a powerlaw fluid down a planar substrate, and then we use this solution to describe the flow of a rivulet with prescribed constant contact angle but slowly varying semiwidth down a slowly varying substrate, specifically the flow in the azimuthal direction around the outside of a large horizontal circular cylinder. Secondly, we use the solution for unidirectional flow to describe the flow of arivulet with prescribed constant semiwidth but slowly varying contact angledown a slowly varying substrate. Thirdly, we consider rivulet flow of generalised Newtonian fluids down a vertical planar substrate. In particular, we obtain the solutions for rivulet flow of a Carreau fluid and of an Ellis fluid, highlighting their similarities and differences. In Chapters 5 and 6 we investigate both the shorttime advection and the longtime Taylorâ€“Aris dispersion of a passive solute in uniform nonthin and thin rivulets, respectively, of a Newtonian fluid undergoing steady unidirectional flow driven by gravity and/or a prescribed uniform surface shear stress on a verticalplanar substrate. In particular, we obtain an explicit expression for the effective diffusivity of the solute in a thin rivulet as a function of the surface shear stress, the volume flux along the rivulet, and either the semiwidth or the contact angle of the rivulet.
Date of Award  5 Oct 2017 

Original language  English 

Awarding Institution   University Of Strathclyde


Supervisor  Stephen Wilson (Supervisor) & Brian Duffy (Supervisor) 
