Effects of Friction and Viscous Forces on Fluid Invasion

Multiphase flow involving fluids and particles is inherently complex due to the coupled effects of viscosity, capillary forces, and particle-scale friction. The fluids exhibit viscous behavior, which manifests as instabilities at the interface; changes in fluid viscosity also significantly affect the interface. In this study, we injected aqueous solutions of varying viscosities into a layer of dry, hydrophobic particles. As the viscous and frictional forces changed, we observed alterations in the number and width of the finger-like invasion patterns. When the pressure gradient exceeds a critical threshold, the finger-like structures expand radially outward. The fractal dimension of the invasion patterns was calculated using the standard box-counting method applied to binarized invasion masks, allowing the space-filling degree and morphological transition of the patterns to be quantified under different particle layer filling ratios, injection rates, particle sizes, and liquid viscosities.