The motion of three-dimensional fractal aggregates in homogeneous shear flow

Abstract

A model for the motion of aggregates in low Reynolds number flow has been established by utilizing the Stokesian dynamics and applying the quaternion as global attitude parameter. The model has been validated by the theorical solution of sphere doublet in shear flow, the simple helical aggregates, and the experiment on the settling of some specific objects in still water. The motion of fractal aggregates has been further studied, aiming to get better understanding of the dynamic behavior of fine-grained sediment flocs in shear flow. The fractal aggregates have been generated using the diffusion-limited aggregation model, which has similar fractal dimension as natural flocs. The results illustrate that fractal aggregates undergo a complex rotation in shear flow, which exhibit a bi-periodic characteristic. The motion of a particle within the fractal aggregate shows three-dimensional trajectory in a simple shear flow, affected by its initial orientation. The major rotation period is approximately 4π/γ̇, which corresponds to the rotation period of a sphere with shear strength γ̇. The deviation decreases with the increase in the size of the fractal aggregate.