Insights into phthalocyanine blue pigment dispersion: Modeling particle size distribution and grinding rate constants

The study presents an advanced mathematical model aimed at enhancing the understanding of pigment dispersion processes, with a particular focus on analyzing the dynamics of particle size distribution and determining grinding rate constants. Pigmented dispersions are crucial in various industries, including paints, coatings, and inks, where achieving optimal particle size distribution is vital for product quality. This investigates the relationship between grinding duration and pigment dispersion, aiming to establish empirical equations for the grinding rate constant as a function of particle size distribution and feed rate. Through experimental validation, the developed kinetic model provides insights into the dynamics of pigment dispersion and offers predictive capabilities for optimizing dispersion processes. Understanding the underlying mechanisms of pigment dispersion through mathematical modeling contributes to enhancing the performance and quality of final products in diverse industrial applications. The development of a new kinetic model, effective mathematical model is proposed to accurately simulate the evolution was applicable for the particle size from 32.67 to 122.4 nm distribution of pigment during comminution processes. In addition, it was observed that the kinetic model was not applicable for the particle size from 166.2 to 190.1 nm and also confirmed that the grinding was completed within 40 min, which was possible for uniform particle size distribution.