DLA simulation with sticking probability for viscous fingering

The morphological evolution of viscous fingering, which occurred in two-dimensional Hele-Shaw cells with various displaced fluids, were simulated using a modified diffusion-limited aggregation (DLA) model on off-lattices. Different from other DLA models, the present model introduced three adjusted parameters. They control the morphological evolution of DLA clusters from a skeletal pattern to a fleshy pattern, so that experimental viscous fingering occurred in a Hele-Shaw cell can be simulated with various shapes. The fractal dimension of fractal clusters can be calculated simultaneously. The present algorithm was used to simulate the experiments of glue and glycerol displaced by water respectively in a Hele-Shaw cell. The present simulation and experiment are in good agreement. In addition, the calculation results of fractal dimensions for viscous fingering indicated that the great viscosity of displaced fluid responds to high fractal dimension for same driving fluid. The present computer model can simulate different viscous fingerings for various experimental conditions and provides a new investigation site for fluid dynamic behaviors of viscous fingering.