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Active matter is comprised of active particles whose underlying property is their ability to exert mechanical stresses on their environment by the conversion of stored or ambient free-energy. At sufficient particle number density, orientational order emerges due to steric, mechanical or behavioural mechanisms, generating collective motion in motile suspensions. On micrometre length scales, active particles such as bacteria can be categorised by their swimming type: `extensile' swimmers push themselves through their medium using flagellum, whereas `contractile' swimmers pull themselves. Activity drives an instability in ordered extensile (contractile) suspensions due to bend (splay) deformations in the suspension orientation (director) which generate active flow and enhance the director perturbation by shear-induced torque. This work comprises a two-part comprehensive extension to this fundamental instability in both 2D and 3D, and both unbounded and confined regimes. Active flow propagates in the same plane as the deformation that caused it, and in part one of this work, we show this causes a de-coupling of the governing equations in the unbounded 3D regime, resulting in the dominance of bend modes for extensile suspensions. Our main result concerns a new chirality term in the Jeffrey orbit equations which re-couples the governing equations by rotating the director out-of-plane from activity induced shear, and in an imposed-shear regime, enhances the instability growth rate by up to 10% versus the unbounded regime when alignment-to-shear and chiral-rotation effects are both present. In part two, we connect bulk growth rates to regimes of weak and strong confinement and show the critical confinement length h^c to suppress growth in 2D regime is related to the wavelength of maximum growth in the unbounded regime, and show further that alternative boundary conditions can reduce this critical value by an order of magnitude. The culmination of this work is the exploration of alternative steady states and boundary conditions for the suspension orientation: the effects of rotating the suspension relative to the boundaries, investigating torque-free boundary conditions, imposing a `swimmer slip' condition on the substrate, and the effects of inclination. We find regimes for which alignment-to-shear is stabilising, regimes where alignment-to-shear is de-stabilising, and predict new steady states using a steady torque-balanced equation for the director. This work invites discussion on appropriate boundary conditions for active matter by providing insight into the dynamics of 3D regimes of confinement, with experimentally realisable predictions for low Reynolds number suspensions. As part of an ongoing research narrative, this work utilises a robust codebase, broadly extendable to new regimes of interest, and will be published at a later date.

Bacteria are often found in surface associated structures called biofilms, composed of individual bacterial cells along with various extra-cellular components. They are a leading cause of antibiotic resistant infections and are a global issue. In this thesis, the focus is on the very early stages of biofilm formation and, in particular, the effect of bacterial motility on biofilm formation is investigated. Various microscopy techniques are used to determine that surface attached bacteria maintain moving flagella, which induce a flow around the bacteria. The flow due to such surface-attached bacteria has not previously been reported. In this thesis, holographic microscopy is used to determine the shape of the flow. The flow is found to be different when cells are exposed to a lactam analogue (which is thought to disrupt biofilm formation by interfering with cell-cell communication). In this thesis, a suggested explanation for this change in flow is an increase in flagellar reversal rate when the cells are exposed to the lactam analogue compared to a control set is presented. A simple model of the surface-attached cell with a motile flagellum is developed to capture the key elements of the flow. This simple model relies on singularity solutions to the Stokes equations and has low computational expenditure. This ease of computation allows the simulation of multiple cells so that the effect of the cells' induced flow on cell-cell communication can be investigated. Particle dispersion is found to be enhanced in the presence of simulated cells with the control reversal rate in comparison to those with the lactam reversal rate. This suggests that one effect of the lactam analogue is to lessen the transport of cell-cell communication molecules.

The quorum sensing (QS) signalling system allows colonies of bacteria to coordinate gene expression to optimise behaviour at low and high cell densities, giving rise to individual and group responses, respectively. The main aim of this thesis is to understand better the important roles of QS in bacterial colony dynamics. Thus a mathematical description was developed to thoroughly explore key mechanisms and parameter sensitivity. The nature of the QS system depends very much on the species. Pseudomonas aeruginosa was chosen as a model species for this study. P. aeruginosa is a Gram-negative bacterium that is responsible for a wide range of chronic infections in humans. Its QS signalling system is known to involve the las, rhl and pqs systems; this thesis focuses on the first two. The las system includes the LasR regulator and LasI synthase, which direct the synthesis of autoinducer 3O-C12-HSL. Similarly, the rhl system consists of the RhlR regulator and RhlI synthase, directing the synthesis of autoinducer C4-HSL. The mathematical model of the las system displays hysteresis phenomena and excitable dynamics. In essence, the system can have two stable steady states reflecting low and high signal molecule production, separated by one unstable steady state. This feature of the las system can give rise to excitable pulse generation with important downstream impact on the rhl system. The las system is coupled to the rhl system in two ways. First, LasR and 3O-C12-HSL activate the expression of their counterpart in the rhl system. Second, 3O-C12-HSL blocks activation of RhlR by C4-HSL. Furthermore, the las-rhl interaction provides a `quorum memory' that allows cells to trigger rhamnolipid production when they are at the edge of colony. It was demonstrated how the dynamical QS system in individual cells and with coupling between cells can affect the dynamics of the bacterial colony.

Cutaneous wound repair occurs as a continuous process in both space and time; however, studies of healing mechanisms and outcomes frequently generate spatially and temporally sparse datasets. We propose a range of techniques that allow the size, cellular processes and scar tissue properties of wounds to be measured and predicted at high spatial and temporal resolution. A non-invasive wound imaging system is shown to provide reliable measurements of wound diameter, perimeter and surface area, but is less reliable in producing 3D metrics such as volume and depth. Wound size and time post healing have a combined effect on reliability, with more reliable measurements obtained at earlier timepoints. A semi-automated pipeline is found to be appropriate for determining the cellular composition of the wound space, but cannot be applied to areas of healthy epidermis due to the close packing of keratinocytes. A range of mathematical models are employed to predict cell numbers within the wound space. An extended domain, partial differential equation model with spatial control of cell proliferation and migration is found to best recapitulate the cellular dynamics observed in vivo. However, if epidermal stratification is to be incorporated, an agent-based description may be preferable. Finally, we formulate a model system that can predict the alignment of collagen fibres and fibroblasts over continuous orientation space. Parameter sets that include large shear forces (which may result from elongated wound geometries or interventions such as suturing) can produce skewed distributions of orientation that cannot be established using discontinuous approaches. Together, this suite of computational approaches provides a powerful set of tools with which the mechanisms of cutaneous wound healing can be investigated, quantified and elucidated.