  We study the dynamics of proppants carried by fluid driven into an evolving
penny-shaped fracture. The behaviour of the slurry flow is investigated in two
phases: pressurised injection and elastic closure. During injection the slurry
is modelled using a frictional rheology that takes into account the
shear-induced migration and jamming of the proppants. Making pragmatic
assumptions of negligible toughness and cross-fracture fluid slip, we find
self-similar solutions supporting a range of proppant concentration profiles.
In particular, we define an effective viscosity, which equates the fracture
evolution of a slurry flow with a given proppant volume fraction, to a
Newtonian flow with a particular viscosity. Using this framework, we are able
to make predictions about the geometry of the growing fracture and the
significance of tip screen-out. In the closure phase, proppants are modelled as
incompressible and radially immobile within the narrowing fracture. The effects
of proppant concentration on the geometry of the residual propped fracture are
explored in full. The results have important applications to industrial
fracking and geological dike formation by hot, intruding magma.
