This work presents a numerical solution to determine the concentration profiles of a colloidal system formed by titanium dioxide (TiO₂) 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.

这项工作提出了一个数值解决方案，用于确定由二氧化钛 (TiO ₂）通过经典数学模型将水中的颗粒作为时间和空间坐标的函数。该模型描述了系统中扩散和沉降现象给出的局部动力学。使用 Python 编程，使用有限差分法 (FDM) 从偏微分方程 (PDE) 中对局部动力学进行数值求解。对于颗粒直径 > 200 nm，浓度分布没有显着变化，表明颗粒尺寸不会直接影响系统的行为，从而保持质量守恒定律。沉降时间缩短，但粒径 > 200 nm 的沉降时间几乎相同 (τ = 1.75)。数学模型的数值解在具有工业意义的生产过程中具有应用，