Oscillation Modes of Droplets on Vibrating Substrates: A Many-Body DPD Study

We study droplet oscillations on vibrating solid substrates at the macroscopic scale using Many-body Dissipative Particle Dynamics (MDPD). Focusing on harmonic oscillations induced by one-dimensional horizontal sinusoidal substrate vibrations, our results reveal three distinct oscillation modes: a stable oscillation mode (Mode I), a rotational mode (Mode II), and a shear-dominated breakup mode (Mode III). We systematically investigate these oscillation modes across a range of liquid properties and substrate wettabilities to explore the mechanisms governing mode transitions. Additionally, we examine the Helmholtz free energy of oscillating droplets in each mode by determining the number of contact surfaces within the droplet directly from simulations. The role of rotational dynamics in Mode II is also analyzed. This work contributes to the understanding and optimization of systems involving droplet transport on vibrating substrates.