Evaluation of the local kinetics of a colloidal system through diffusion–sedimentation phenomena: A numerical approach

This work presents a numerical solution to determine the concentration profiles of a colloidal system formed by titanium dioxide (TiO 2 ) particles in water as a function of the time and the spatial coordinate through a classic mathematical model. The model describes the local kinetics given by the diffusion and sedimentation phenomena in the system. Using Python programming, local kinetics is solved numerically from partial differential equations (PDEs) using the finite difference method (FDM). For particle diameter > 200 nm, there are no significant changes in the concentration profiles, indicating then that the particle size does not directly influence the behavior of the system and thus maintains the law of mass conservation. The sedimentation time decreases, but the sedimentation time for particle diameter > 200 nm is practically the same (τ = 1.75). The numerical solution of the mathematical model has applications in production processes with industrial interest, particularly in the design and production of paints and coatings with long storage times.