Internal stresses in low-Reynolds-number fractal aggregates*

We present a numerical model of the stresses around and within fractal-structured aggregates in low-Reynolds-number flows. Assuming that aggregates are made of cubic particles, we first use a boundary integral method to compute the stresses acting on the boundary of the aggregates. From these external stresses, we compute the internal stresses to gain insight on their breakup, or disaggregation. We focus on systems in which aggregates are either settling under gravity or subjected to a background shear flow and study two types of aggregates with fractal dimension slightly less or slightly more than two. We partition the aggregates into multiple shells based on the distance between the individual cubes in the aggregates and their center of mass and observe the distribution of internal stresses in each shell. Our findings indicate that the magnitude of large internal stresses is distributed in a manner consistent with a power-law and that large stresses are least likely to occur near the far edges of the aggregates. In addition, after breaking aggregates at the face with the maximum internal stress, we compute the mass distribution of sub-aggregates and observe significant differences between the settling and shear setups for the two types of aggregates, with the low-fractal-dimension aggregates being more likely to split approximately evenly.

Information obtained by our numerical model can be of interest to experimentalists studying the rupture of aggregates and provide insights to develop more refined dynamical models that incorporate disaggregation.