Mesoscopic model for the surface fractal dimension estimation of solid-solid and gas-solid dispersed systems

Abstract

The surface of dispersed systems in which the dispersion medium is solid presents a complex morphology that depends on the processes associated with the formation of the solid phase and the dispersion grade of the dispersed phase. Considering that this morphology is a manifestation of the stochastic processes in the disperse phase, a stochastic formalism was applied based on the master equation to obtain a model that predicts the fractal dimension behavior regarding the superficial area of the dispersed phase. The model involves a parameter that related the velocity constants associated with the dynamic processes. The predicted theoretical results were compared with the experimental results in two different dispersed systems: a dispersed phase constituted by solid particles and a dispersed phase constituted by gas, achieving an adequate correspondence between the theoretical and experimental results.