Origin and value of a limit size during shear aggregation revisited

International audienceduring the aggregation of fine particles in a shear flow a limite size value a(L) for aggregates is reached. Most researchers have related a(L) to the shear rate ý by means of a powder law. We examine in this paper the different ways in order to model the phenomena leading to a limit size. The main results in the field of drop-drop and bubble-particle systems are briefly reviewed to help us to propose a coherent description of phenomena occurring in particle-particle systems. Kernels for coalescence, aggregation, breakage and erosion are recalled. An improvement of the aggregation kernel in the case of the collision between aggregates is proposed. We show that an analysis of the whole process in term of aggregation-fragmentation competition will be preferred to a collision which would be less efficient between large aggregates. In this framework we present a modelling relating aggregation kernel and fragmentation kernel to a limit size value. As a consequence, the main result is the exponent value a(L) -ý power law