Fragmentation as an aggregation process: the role of defects

Abstract

A cohesive object will eventually break into fragment when experiencing a strong deformation, during an impact for instance. Using necklaces of cohesive magnetized spheres suddenly expanded, we have shown that the fragmentation of this one-dimensional material results from an inverse aggregation cascade (Vledouts et al. 2015 Proc. R. Soc. A 471, 20150678. (doi:10.1098/rspa.2015). Here, we explore a variant of this process by changing the force law between the attracting spheres, using hydrogel beads linked by capillary bridges. We also investigate the role of (weak) defects in the cohesion strength and the consequences of a distribution of forces between the beads. It is found that fragment do form by a cascade of aggregations, which is interrupted earlier when the force disorder is stronger.

Fragmentation versus Cohesion

“…In order to see how cohesion and disgregation compete, it is instructive as a starting exercise to work out the caricatural problem of the sudden forced radial expansion of an assembly of attracting particles arranged in a circle: the shatter of necklace of magnets (Vledouts, Vandenberghe & Villermaux 2015, 2016b. A set of spherical magnets is assembled in a necklace positioned on a cone with an incline at 45 • .…”

“…An initial impulse in the radial direction is communicated to each sphere, and the necklace expands at R ¶ a oe FIGURE 3. Fragmentation of a necklace of spherical magnets (Vledouts et al 2015(Vledouts et al , 2016b. (i) A ring made of spherical magnets of diameter a = 5 mm, mass m = 0.5 g and mutual contact force φ(a) is placed on a cone, which is let fall on the ground.…”

“…Aggregation thus proceeds as long as u p,q < u c , or p,q > 1, and the necklace fragmentation is completed as soon as p,q < 1 for all neighbouring fragments of size p and q. The fragment trajectories described by (2.9), the cluster coalescence time scales, the mean fragment growth and the details of the aggregation cascade are discussed by Vledouts et al (2015); the role of pre-existing defects along the necklace is considered in Vledouts et al (2016b).…”

An existence‐uniqueness result for the pure binary collisional breakage equation

“…The formulation (7)(8) is based on the Leibnitz integration rule and the mass conservation property (4). It is pertinent to mention that literature reveals most theoretical research works have comprised only with linear breakage [25][26][27][28][29][30][31][32][33][34][35][36][37][38][39][40][41][42] and only few investigations have been presented to nonlinear breakage due to interactions between fragments, such as collision-induced fragmentation. 18,[20][21][22][23][24]36 These circumstances are motivated the present study.…”

“…It is pertinent to mention that literature reveals most theoretical research works have comprised only with linear breakage and only few investigations have been presented to nonlinear breakage due to interactions between fragments, such as collision‐induced fragmentation . These circumstances are motivated the present study.…”