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
