Transport-Limited Aggregation and Dense Granular Flow

In this thesis, transport of interacting particles is studied in two different physical systems. In the first part, a model for interfacial growth driven by general transport processes is proposed to generalize Laplacian growth such as diffusion-limited aggregation (DLA) and viscous fingering. The fractal properties, crossover in morphology, and relation between continuous and stochastic growth are studied in the context of a representative case, advection-diffusion-limited aggregation (ADLA). The model is extended on curved surfaces and the effect of curvature is also discussed. In the second part, dense granular flow inside silos and hoppers is investigated using high-speed imaging and the results are compared to existing theories. While mean velocity fields are in qualitative agreement, the diffusion and mixing of particles are contradictory to the microscopic assumptions. A new model for dense granular flow is suggested to resolve the inconsistency. Thesis Supervisor: Martin Z. Bazant Title: Associate Professor of Applied Mathematics