Minimal continuum model of clogging in particle suspensions

Particle suspensions in confined geometries exhibit rich dynamics, including flowing, jamming, and clogging. It has been observed that jamming and clogging in particular are promoted by variations in channel geometry or fluid material properties -- such variations are often present in industrial systems (e.g. local confinements) and biological systems (e.g. stiffening of red blood cells in deoxygenated conditions in sickle cell disease). In this thesis we shed light on the macroscopic dynamics of particulate suspensions in these conditions. We first present a single-phase model of a particle suspension and analyze its behaviour when subjected to a spatially varying rheology and wall friction. We find that the suspension's viscous resistance and wall friction can act as two resistors in parallel: in a channel where both wall friction and yield stress increase along the flow direction, a low wall friction can lead to the formation of plug flow at the channel's exit. Next, we proceed to a more detailed two-phase continuum model of particle suspensions that accounts for spatio-temporally varying material properties. The model comprises a ``wet solid'' phase with material properties dependent on the particle volume fraction, and a seepage Darcy flow of fluid through the particles. We find that spatially varying geometry (or material properties) can induce emergent heterogeneity in the particle fraction and trigger the abrupt transition to a high-particle-fraction ``clogged'' state. We extend this model to incorporate wall-slip, a phenomenon commonly observed in blood flow through microchannels, and compare our results with experimental observations of sickle cell disease blood flow under deoxygenated conditions.