Effects of liquid viscosity and air injection rate on air invasion in a highly compacted granular material

Abstract

Using laboratory experiments on a network scale together with numerical simulations on a granular scale, we investigate the displacement process as air invades a highly compacted granular material. Experiments in a vertically placed Hell-Shaw cell reveal a non-monotonic behavior of branching formation as air injection rate Q increases from 0.1 to 50 ml min–1 when the liquid viscosity is less than 22.5 mPa s. In the low-injection-rate region where Q < 1 ml min–1, fractures grow in random directions, and the number of branches increases as the air injection rate decreases. However, after the transition to the high-injection-rate region where Q≥ 1 ml min–1, the number of branches increases with increasing air injection rate. At a given air injection rate, increasing the liquid viscosity from 1.01 to 219 mPa s leads to an increasingly concentrated air flow. The numerical simulations exhibit good agreement with the experimental results. More importantly, they shed light on the physics underlying the growth of the fractures by capturing the distribution of the magnitude of velocity, as well as computing the inter-grain force chains in the granular material. The simulations suggest that a high liquid viscosity concentrates the velocity field and force chains and reduces the speeds and inter-grain forces of the grains adjacent to fractures, while a higher air injection rate increases the grain speeds and inter-grain forces. In addition, the distribution of the forces chains behaviors non-monotonically as the air injection rate decreases, which explains the non-monotonic behavior of branching formation observed in the experiments.