Asymmetric Three-Phase Surface Tension Forces in Agglomerating Particulate Systems

In accurate simulation of surface tension dominating systems, such as particulate systems in the nano- and mesoscale, the computation of interface curvature is essential. In a previous work a formulation using discrete differential geometry was demonstrated that could be used to find exact equilibrium solutions of surfaces. However, it was also shown that this formulation, as well all other tested formulations from those found in literature, fail to find accurate point-wise estimates for curvatures for particle-particle capillary liquid bridges. In this communication we elaborate on how total curvatures can be used for computing forces of parameterized models as well as in direct numerical simulations and demonstrate the infeasibility of using point-wise estimates on any asymmetric discretization. Near-exact numerical solutions are demonstrated for asymmetrically triangulated Catenoids and a minimal surface suitable for modeling liquid bridges between particles of different diameters.

Automated summary

Accurate computation of interface curvature is crucial in simulating surface tension-dominated systems. Prior research has shown that a formulation using discrete differential geometry can find exact equilibrium solutions of surfaces, but fails to provide accurate point-wise estimates for curvatures of particle-particle capillary liquid bridges. This communication elaborates on the use of total curvatures in computing forces of parameterized models and demonstrates the infeasibility of using point-wise estimates on any asymmetric discretization.