Viscous fingering of a thixotropic fluid in a porous medium or a narrow fracture

We consider the flow of a fluid with a modified Bautista–Manero rheology injected radially into a porous medium or unidirectionally into a widening fracture. Linear stability analysis of the flows demonstrates that viscous fingering instabilities are possible, supported essentially by the thixotropic nature of the fluid: the growth rate of unstable perturbations scales approximately with the relaxation rate of the fluid, while their spatial scale is set in the radial case by where is the areal injection rate, and in the fracture case by a ‘relaxation lengthscale’ which cannot be deduced by purely dimensional reasoning. It appears likely that the same instability mechanism can occur in other shear-thinning thixotropic fluids.