Sedimentation of particles and aggregates in colloids considering both streaming and seepage

Sedimentation of colloids is a common phenomenon in various industrial processes. Aggregation of nanoparticles is expected to occur during the processes. However, previous studies often ignore the important features of aggregates, e.g. porosity and possible seepage, leading to a mathematical description of the sedimentation processes of low reliability. In this study, we successfully elaborated the partial differential equation of the dynamic concentration distribution of regimented colloids based on the Stokes approximation and diffusion along the negative gradient of concentration. The permeability of aggregates was obtained by the finite volume method and the ratios of the velocities of flowing around (u _f) to seepage through (u _s) aggregates over various primary particle sizes and aggregation structures were obtained based on the Darcy equations. After validation of the model, the effects of size and density of the particles and aggregates on the concentration profiles were investigated. Our results indicate that both an increase in size and density of particles and aggregates can accelerate the sedimentation process, and lead to more 'thorough' sedimentation. We mathematically explain why suspensions with high particle concentration are more unstable. What is more, replacing gravity with other volume forces, e.g. centrifugal force and magnetic forces, our model is expected to be applicable to centrifugation or magnetic sedimentation processes.