Effect of initial Rayleigh mode on drop deformation and breakup under impulsive acceleration

Abstract

One of the fundamental ways of representing a droplet shape is through its Rayleigh-mode decomposition, in which each mode corresponds to a distinct surface-energy content. The influence of these modes on free oscillation dynamics has been studied extensively; however, their role in droplet deformation, breakup, and fragmentation under impulsive acceleration remains largely unexplored. Here we systematically quantify how prescribed initial axisymmetric Rayleigh modes affect the deformation and breakup of an impulsively accelerated drop. Using experimentally validated, VOF-based multiphase direct numerical simulations, we isolate the coupled effects of finite-amplitude surface oscillation modes and the associated initial surface-energy state by initializing drops with well-defined $(n,0)$ modes (and phases) while conserving volume at finite amplitudes. We show that breakup is governed not simply by the initial drag of the imposed shape, but by the dynamic coupling between the free modal oscillations and the forced aerodynamic (or shear-driven) deformation: constructive superposition can strongly amplify deformation, whereas destructive superposition can stabilize the drop even under otherwise disruptive forcing. Across all systems studied, the outcome is controlled by how efficiently the external work is partitioned into recoverable oscillatory energy versus centre-of-mass translation and viscous dissipation, with viscosity and density ratio acting as key mediators that respectively damp modal interactions and restrict the time window for energy uptake.