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 λ ˆ − 1 of the fluid, while their spatial scale is set in the radial case by ( Q ˆ λ ˆ ) 1 / 2 where Q ˆ 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.