Mechanism of flow-induced biomolecular and colloidal aggregate breakup

Abstract

The drift-diffusion equation is first solved analytically for the dissociation rate and lifetime of a biomolecular or colloidal dimer bonded by realistic intermolecular potentials, under shear flow. Then we show using rigidity percolation concepts that the lifetime of a generic cluster formed under shear is controlled by the typical lifetime of a single bond in its interior. The latter, however, is also affected by collective stress transmission from other bonds in the aggregate, which we account for by introducing a semiempirical, analytical stress transmission efficiency $0\ensuremath{\leqslant}\ensuremath{\Gamma}\ensuremath{\leqslant}1$ calibrated on several simulation data sets. We show that aggregate breakup is a thermally activated process in which the activation energy is controlled by the interplay between intermolecular forces and the shear drift. The collective contribution to the overall shear drift term is dominant for large enough fractal aggregates, while surface erosion prevails for small and compact aggregates. The crossover between the two regimes occurs when $\ensuremath{\Gamma}N\ensuremath{\simeq}2$, where both the number of particles in the cluster $N$ and the stress transmission efficiency $\ensuremath{\Gamma}$ depend on the aggregate structure through the fractal dimension ${d}_{f}$. The analytical framework for the aggregate breakup rate is in quantitative agreement with experiments and can be used in future studies in the population balance modeling of colloidal and protein aggregation.