Numerical simulations of simultaneous pair-drop impacts and their energetics

Single drop impacts have been extensively studied, but frequently in practice, adjacent droplets may impact in close proximity and thereby interact with one another. This interaction is characterised by the appearance of a lamella arising from the collision of the two droplets' spreading rims. We consider the energetics of this lamella, solely in terms of the parameters of the impacting drops. We conduct three-dimensional (3-D) direct numerical simulations of pair-drop impact to investigate the width, the height, and the general morphology evolution of the central sheet, which align well with previously published experiments, and we proceed to study the energetics of the process. We find that the kinetic energy and surface tension energy dominate the evolution of the central sheet, with viscous dissipation playing a secondary role. This can be quantified through a novel energetic model that accurately predicts the maximum height of the central sheet, validated against the experimental and numerical data. Additionally, in the asymptotic regimes at high We and Re, the spreading behaviour of central sheets resemble the spreading behaviors of the familiar single-drop problem. This enables a scaling law for the maximum central sheet height to be proposed, with the support of numerical data. These insights promise a more complete understanding of the dynamics for the central rising sheet and lay the groundwork for further exploration of its fragmentation.