Shape deformation, disintegration, and coalescence of suspension drops: Efficient simulation enabled by graph neural networks

Abstract

Understanding the behaviors of suspension drops (particle swarms) as they settle in a viscous fluid holds significant importance across various applications. Due to hydrodynamic interactions (HIs), suspension drops would undergo a series of intricate behaviors, including shape deformation, disintegration, and coalescence. This work presents the hydrodynamic interaction graph neural network (HIGNN), developed in our prior work (Ma et al., 2022), as an efficient and accurate modeling framework for simulating the dynamics of suspension drops and investigating the various behaviors they exhibit. The HIGNN effectively incorporates the many-body nature of HIs, a feature lacking in most previous simulations that employ the Stokeslet assumption. In the meanwhile, the HIGNN achieves superior computational efficiency compared to traditional, high-fidelity numerical tools such as Stokesian dynamics and PDE solvers. Moreover, the HIGNN, once trained, is applicable to predicting suspension drops across a range of particle concentrations and under diverse forces (such as gravity and Coulombic interactions). Training the HIGNN only requires the data containing a small number of particles, leading to low training cost. Our results demonstrate that the HIGNN can effectively reproduce the various behaviors of suspension drops that were previously reported in literature. More specifically, a single, initially spherical drop slowly evolves into a torus-shaped drop, as particles escape from its rear and form a tail along the sedimenting direction. Subsequently, the torus breaks into secondary droplets, each undergoing a similar transition (deformation into a torus followed by disintegration), thereby leading to a repeating cascade. Further, we quantitatively analyze the correlation between the drop’s sedimentation velocity and volume fraction. We also propose new scaling laws for evaluating both the leakage rate of particles and the expansion rate of the horizontal radius of a suspension drop. For single suspension drops, we also systematically investigate how their dynamics is affected by their initial shapes and the formed tori’s aspect ratios, as well as with or without Coulombic interactions between particles. For a pair of suspension drops, we study the process of coalescence of two vertically aligned particles and examine the effect of introducing a horizontal offset on the subsequent breakup of the coalesced drop. All simulations were executed on a single GPU, with the computation of velocities for several thousand particles requiring less than five seconds per time step. This computational efficiency enables fast and resource-saving simulations of large suspension drops over extended time scales.