Effect of initial Rayleigh mode on drop deformation under impulsive acceleration

Abstract

One of the fundamental ways of representing a droplet shape is through its Rayleigh-modes, where each mode corresponds to distinct surface-energy. Previous studies have focused on the effect of these modes on free oscillations of drops. In this paper, we systematically quantify how the different prescribed initial axisymmetric Rayleigh modes modulate aerodynamic energy uptake and the resulting deformation of an impulsively accelerated drop. Using experimentally validated VOF-based multiphase numerical simulations, we isolate the coupled effects of finite-amplitude surface oscillation modes and the associated initial surface-energy state by initializing the drops with well-defined $(n,0)$ modes and phases $\{0,\ddot{I}€\}$, while conserving the equivalent drop volume. We find that the deformation outcome is governed by the drag due to the drop's initial geometry, and the dynamic coupling between the free modal oscillations and the forced aerodynamic deformation. We find that constructive superposition amplify deformation, whereas destructive superposition can stabilize the drop even when the aerodynamic forcing is sufficient to deform an analogous spherical drop to breakup. Initial modes and phases that channel a larger fraction of the input power into deformation, in the form of oscillatory kinetic energy and additional surface energy, attain larger deformations and are closer to the fragmentation threshold. These coupling effects are especially pronounced in high-viscosity systems, where viscous dissipation is large and facilitates the transfer of a larger fraction of the total energy to translational kinetic energy instead of oscillatory kinetic energy. For low density-ratio systems, early-time coupling and energy transfer is the dominant mechanism that governs drop deformation.

49 pages, 27 figures