Continuum Modelling of Particulate Suspensions

Wet granular and particulate suspensions can exhibit rich behaviour: in some limits they can flow like a Newtonian fluid; in others they can behave like a rigid porous solid, through which the host fluid can move. More generally, their rheological behaviour is complex and difficult to fully capture in a continuum description. Here we explore simplified continuum models of suspensions that capture their ability to jam-up like a viscoplastic material when the applied stress is too small. In particular, suspensions can clog and jam up in confined geometries: it is widely observed in industrial processing that geometric constrictions result in clogging, for example, while clogging caused by stiffening of deoxygenated red blood cells is a key signature of sickle cell disease. We consider a two-phase continuum model of the particulate suspension to capture the key rheological behaviour of the suspension (based on ideas from granular friction and the so-called mu(J) model) and the differential seepage of fluid through the particulate phase (based on Darcy’s law). The crucial role of the latter in modulating particle flux can lead to dramatic emergent clogging in a channel: this phenomenon and related flow behaviour will be explored and discussed.