A fragmentation model for crystal attrition

In industrial crystallizers, attrition at the surface of parent crystals disperses fines into the vessel, thus influencing the crystal size distribution. Attrition occurs primarily due to collisions between particles or with the impeller or walls of the equipment. We model this phenomenon by extending our distribution kinetics model of crystal growth to include attrition and random fragmentation and investigate how the contributions of attrition, fragmentation, growth, and Ostwald ripening influence the evolution of the crystal size distribution. When the rates of both attrition and fragmentation are negligible, growth and Ostwald ripening dominate and the crystals grow continuously. When fragmentation dominates, a steady state in particle size is reached irrespective of the size of the attrition product particle. When the rates of fragmentation and attrition are comparable, evolution to steady state occurs if the attrition product crystal is larger than the critical nucleus size.