Title:

Dynamics of athermal suspensions

Suspensions are systems composed of particles dispersed in a fluid. This is an industrially important set of materials, whose members are capable of exhibiting a diverse range of phenomena. The behaviour of dense suspensions, where the volume fraction of particles is close to the volume fraction of jamming at which the suspension is unable to flow in the limit of vanishing imposed stress, is particularly challenging to model and explain. In this thesis, we report theoretical research on three dense athermal suspensions, supported in each case by particle simulations. By studying systems in which particles do not undergo Brownian motion, we are able to identify behaviour generic to both thermal and athermal suspensions, and provide insight into the underlying cause. The particle simulations are found to be of great importance in challenging the assumptions of models, testing model predictions and providing direct microstructural insight into the mechanisms by which dense suspensions evolve. We first extend a model of discontinuous shear thickening in steadystate homogeneous dense suspensions under simple shear to a dynamical onedimensional model of the suspension, spatially resolved along the vorticity axis with periodic boundary conditions. This model encapsulates a theory of shear thickening in which a suspension of frictional particles transitions from frictionless to frictional rheology as repulsive interparticle forces that prevent contact between particles at low stress are overcome at high stress. We show that in our model, large homogeneous systems are linearly unstable to perturbations along this axis at high volume fractions within a range of imposed stresses. We characterise two longtime inhomogeneous states, both of which are unsteady but periodic. We then test our predictions with particle simulations of a suspension of frictional particles with shortranged repulsions, finding both states at least transiently, according to parameter regime. The second suspension we consider corresponds to the first in the limit of vanishing interparticle repulsion, after a reversal of the direction of shear from steady state. This system is strongly dimensionally and symmetrically constrained: shearrate provides the only timescale, while the system is invariant under inversion of the vorticity axis (or, equivalently, simultaneous inversion of the flow and flow gradient axes). We leverage these constraints to develop a systematic approach to modelling the evolution of the ``fabric tensor'', a traceless and symmetric rank2 tensor related to the secondorder spherical harmonic expansion of the distribution of (near)contact pairs of particles commonly used in the literature to encode the suspension microstructure, as a function of itself and the imposed velocity gradient tensor. By fitting the models to data from particle simulations of the appropriate system, we show that such models are unsuccessful at linear order in the fabric tensor components, and are unlikely to contain any physical insight at higher orders. We then test the suitability of the fabric tensor as a description of the microstructure directly using the particle simulations, and conclude that a secondorder spherical harmonic description captures the pair distribution poorly shortly after reversal. We find that a fourthorder description captures the pair distribution well. Finally, we study a suspension of soft elastic particles close to and above jamming using particle simulations with periodic boundary conditions. We prepare the suspension at a nonzero temperature and then allow it to relax athermally to the global system's local minimum. We observe nontrivial dynamics, such as slow powerlaw decay of the root mean squared velocity of particles, and coarsening with a powerlaw growth of velocity correlation lengths. This suggests that generic athermal physics may in fact underlie nontrivial dynamics commonly associated to thermal effects.
