Transversely isotropic thin film flows

Abstract

Many industrial and biological fluids such as cervical mucus have an underlying fibrous microstructure; fibres embedded within a ground matrix give directionally dependent, or anisotropic, material properties. These properties in turn can be critical to ensure key biological functionality. For example, changes in the fibrous reinforcement of cervical mucus during the menstrual cycle regulates the passage of spermatozoa; these rheological properties are typically investigated by attempting to stretch a thread of mucus to determine the current level of fertility. This thesis aims to understand how the presence of fibres alters the mechanical behaviour of such materials by considering three canonical examples of thin film flows: the squeezing of a film, and the extensional flows of a sheet or a thread. The effect of fibres is incorporated via a transversely isotropic fluid stress tensor which models the suspension as a continuum with an evolving single preferred direction, alongside conservation of mass and momentum. Exploiting the small aspect ratio in each situation, we derive governing equations which we solve via analytical and numerical means. We find throughout that the behaviours of a transversely isotropic fluid are markedly different to that of a Newtonian fluid.