Order and hydrodynamic fluctuations in active suspensions

In this Thesis we study theoretically some aspects of the dynamics of soft active suspensions. Following a bottom-up approach, we derive the continuum equations for a suspension starting from underlying models for the microscopic dynamics, where the microscopic objects are constructed out of spheres subjected to forces at low Reynolds number. Examples of systems examined here are collections of rotating objects in two dimensions, swimmers and a chain of oscillators. Their macroscopic properties are described by means of scalar and pseudo-scalar or vector and tensor or complex-valued quantities. In our work we explicitly address the fast, periodic nature of the microscopic dynamics and devise a general framework, that is based on a procedure of averaging, to incorporate these dynamical features and study their effects on the long-wavelength, low-frequency description of the system. There, all the resulting parameters are determined by time-averages of the microscopic properties. By exploiting a superposition of rotations we introduce a novel, minimal model swimmer at low Reynolds number that can both translate and rotate in a plane. We examine its dynamics by extending the analysis of the internal motions to the regime of strong deformation and compare to the well-known three-bead swimmer under the same conditions. For swimmers suspensions we consider a model where it is possible to generate spatially homogeneous symmetry breaking and examine its stability to small fluctuations. We find that the hydrodynamic interactions are enough to promote order; this, however, is unstable to small perturbations that exceed a critical angle from the ordering direction. Finally we introduce a new generic model of self-sustained oscillator to study hydrodynamic synchronisation. Here we find an interplay between hydrodynamic interactions and the oscillators features that make them good synchronisers. We then investigate the long-wavelengths dynamics of an array.EThOS - Electronic Theses Online ServiceGBUnited Kingdo