A Polygon-Based Deformable Particle Model for Droplet Coalescence Dynamics

We present a polygon-based deformable particle model (DPM) to investigate the coalescence dynamics of droplets. Droplets are represented as closed polygons with massive vertices whose behavior evolves according to a Verlet integration scheme under the influence of surface tension, area conservation, and perimeter constraints. Interfacial mechanics are captured through custom vertex-based force formulations with hashing and neighbor search optimizations to ensure efficiency in computation. During coalescence, surface tension drives minimization of interfacial length, while area and perimeter penalties preserve droplet integrity, enabiling realistic merging behavior. The model successfully reproduces key qualitative features of coalescence, including neck formation, shape relaxation, and eventual equilibration into a single droplet. This work highlights the potential of vertex-based DPMs as a key framework for studying multiphase interactions in soft matter and biological systems.