Fractal viscous fingering in clay slurries

Abstract

The fractal growth of viscous fingers on injection of a low-viscosity fluid into a high-viscosity fluid represents a type of hydrodynamic instability which was first demonstrated by Nittman et al.^1,2, by pushing water through an aqueous polymer solution. The conditions for the occurrence of the fractal morphology (in place of classical smooth fingering of the Saffman–Taylor³ type) are a combination of high viscosity contrast and low interfacial tension, which leads to a high capillary number and, most probably, non-newtonian rheological properties^2,4. In fact, these are conditions which are easily fulfilled on injecting a solvent into a concentrated suspension of colloidal particles in the same solvent. In particular, we show here that fractal viscous fingering generally occurs when water flows through clay slurries in a radial Hele–Shaw cell, but the fractal dimension of the pattern is strongly dependent on the concentration of the clay slurry. Given the importance of clay/water systems in nature, this result has far-reaching consequences, which we discuss.