二维颗粒反应的分数维模型

Fractal Reaction Model for Irregular Particles in Two Dimensions

本文将分数维理论引入颗粒与流体的非均相反应系统,提出不规则颗粒二维反应的分数维模型.在假稳态条件下,对不规则颗粒的核收缩反应方程求得解析解.结果表明,当反应受膜扩散控制、灰层扩散控制和化学反应控制时,颗粒的分数维越高,反应总速率越快;而在膜扩散控制阶段,分数维对相对反应时间没有影响.

Fractal theory has been introduced into heterogeneous reaction systems to describe the reaction of solid particles with fluid, and a fractal reaction model in two dimensions is proposed for irregular particles. Based on the characterization of irregular particle shape, the reaction time which are determined and controlled by fluid film diffusion, ash diffusion and chemical reaction are theoretically analyzed. A pseudosteady-state equation of material balance and its solution as the concentration profile of reacting fluid are given for the shrinking-core model for irregular particles with constant radii. Meanwhile, some parameters related to reaction time complete reaction time, relative reaction time and the amount of reacting fluid per unit time, are also expressed with fractal dimension and shape coefficient. The results indicate that the higher the fractal dimension, the higher the total reaction rate, and the shape coefficient also influences the reaction time.