Universal breakup of colloidal clusters in simple shear flow

We have studied the long-term dynamics of shear-induced breakage of individual colloidal clusters, covering a wide range of fractal dimensions, using Stokesian dynamics. We found that the time evolution of the normalized average size of the fragments generated by the breakup process could be scaled using a unique dimensionless time defined by multiplying the real time with the cluster breakage rate constant (τ = t·kB). Clusters with different masses but the same fractal dimension exhibited almost identical breakage dynamics when exposed to equal overall hydrodynamic forces (ηγRg,0²). The steady-state values of the average size, mass, and standard deviation of fragment mass distribution showed a universal scaling depending only on the overall hydrodynamic force, irrespective of the initial cluster properties. We also identified two asymptotic regimes for the evolution of the fractal dimension, ⟨df⟩, of fragments: open clusters (d f ≤ 2.1) produced dense fragments with a limiting ⟨df⟩ ≈ 2.4 ± 0.1; conversely, dense clusters (df ≥ 2.5) produced fragments with ⟨df⟩ ≈ 2.5 ± 0.1