Fragmentation and Aggregation of Solids

Powders dispersed in liquids consist of agglomerates—a collection of aggregates—which in turn are composed of primary particles. Agglomerates 

The current level of understanding of how aggregates form and break is not up to par with droplet breakup and coalescence. The reasons for this discrepancy are many Aggregates involve multibody interactions shapes may be irregular, potential forces that are imperfectly understood and quite susceptible to contamination effects. 

analyses of how aggregates break have resorted to idealizations inspired by traditional fluid mechanical analysis, two limit cases being per- 

The physicochemical forces between colloidal particles are described by the DLVO theory (DLVO refers to Deijaguin and Landau, and Verwey and Overbeek). This theory predicts the potential between spherical particles due to attractive London forces and repulsive forces due to electrical double layers. This potential can be attractive, or both repulsive and attractive. Two minima may be observed The primary minimum characterizes particles that are in close contact and are difficult to disperse, whereas the secondary minimum relates to looser dispersible particles. For more details, see Schowalter (1984). Undoubtedly, real cases may be far more complex Many particles may be present, particles are not always the same size, and particles are rarely spherical. However, the fundamental physics of the problem is similar. The incorporation of all these aspects into a simulation involving tens of thousands of aggregates is daunting and models have resorted to idealized descriptions. 

The spherical fragments, initially in close contact, move relative to each other according to Eq. (B.l). The underlying physics is revealed more clearly by recasting equation (B.l) in the following dimensionless form  

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