# Comparative study of drainage in soils and foams, early-time and late-time solutions

• Yaw Akyampon Boakye-Ansah

Student thesis: Doctoral Thesis

### Abstract

Richards equation has been known and used to describe unsaturated flow of liquids in porous media since it was proposed by Richards in 1931. This is a highly nonlinear equation with no exact solution in general. There has however been significant research in developing specific solutions of this equation using various analytical and/or numerical approaches. In comparison, the foam drainage equation has been derived to describe flow of water through a complex network of foam channels (Plateau borders). It is a nonlinear equation, again with no solution in general, although a number of analytical solutions are known. Research in the physics and mathematics of foams have produced considerable knowledge that have helped advance the theory of drainage and propagation of liquid through foams. Not much has been done to compare and contrast these equations (Richards equation and the foam drainage equation) although they obey the same governing fundamental laws. Flow situations involving these two governing equations can be designated as either early-time nonlinear diffusion or late-time travelling wave propagation problems.;Various complex analytical (and also numerical) mathematical techniques are required to solve such problems. Material properties such as capillary suction head, hydraulic conductivity and capillary diffusivity are also required before these problems can be studied. In order to find material properties for Richards equation, soil material property functions derived by van Genuchten and Brooks & Corey are employed in this thesis. The foam drainage equation (of which various forms exist) has the analogous material properties embedded in its formulation. This research has obtained solutions for Richards equation and for foam drainage comparing them both for early-time diffusion and for late-time travelling wave solutions. The obtained solutions can be used to predict such physical behaviours as the amount of fluid needed to be injected to flood an oil reservoir or alternatively to irrigate a piece of land without flooding it. Knowledge from these solutions will be of immense benefit to many practical situations similar to those mentioned above.
Date of Award 30 Mar 2021 English University Of Strathclyde University of Strathclyde Paul Grassia (Supervisor) & Demosthenes Kivotides (Supervisor)

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