Analysis of Agglomerate Rupture in Linear Flow Fields

Abstract A dispersive mixing model focusing on the rupture of agglomerates as the step that primarily determines the dynamics of the mixing process was developed and analyzed. Rupture is predicted to occur when hydrodynamic forces exerted on the outer surface of the agglomerate exceed cohesive forces binding the agglomerate together. Agglomerates are modeled as clusters of aggregates bound by van der Waals forces. The magnitude and orientation of the rupturing hydrondynamic force depend on the local stress field in the fluid. Cleavage of the agglomerate is predicted to occur at the mid-plane of the agglomerate where the effects of hydrodynamic tension is the largest. Under the assumption that parent agglomerates and their fragments have the same shape, the kinetics of the rupture process is found to be independent of the absolute size of the agglomerate. Following from this is the result that the dispersion process is governed by flow dynamics, i.e., a minimum value of flow strength, which depends on the geometry of the bulk flow field, is required for rupture of the agglomerate. Agglomerate rupture was investigated in four flow geometries: simple shear; pure elongation; uniaxial extension, and biaxial extension. The efficiency of each flow geometry is compared on the basis of power and time requirements to achieve a given degree of dispersion.