Numerical simulations of simultaneous pair-drop impacts and their energetics

We present three-dimensional direct numerical simulations of the simultaneous impact of two identical drops on an hydrophobic substrate, varying the relative strength of capillary and viscous effects respectively through Weber and Reynolds numbers of impact. The interaction between the two drops is characterized by the appearance of a lamella arising from the collision of the two droplets’ spreading rims. We examine the width, the height, and the general morphological evolution of the central sheet; the numerical data is validated against prior experiments and used to guide the development of an energetic model for the maximum elevation of the central sheet. In particular, the rise of the central sheet resembles the spreading behaviour single-drop impacts, especially at high Weber and Reynolds numbers. This fact can be used to estimate scalings in the capillary- and viscous-dominated regimes, which can be used to collapse the trajectories. These insights provide a route for a more complete understanding of the dynamics for the central rising sheet, and anticipate the detailed study of its fragmentation characteristics

💡 Research Summary

This paper presents high‑resolution three‑dimensional direct numerical simulations (DNS) of two identical droplets impacting simultaneously on a hydrophobic substrate. By varying the Weber (We) and Reynolds (Re) numbers, the authors explore the relative importance of inertia, surface tension, and viscosity in the formation and evolution of the central rising sheet that emerges when the spreading rims of the two droplets collide. The computational framework uses the open‑source Basilisk code with adaptive mesh refinement (AMR) and a volume‑of‑fluid (VOF) interface‑capturing method. The governing Navier‑Stokes equations are solved with a continuum surface force model for surface tension, and the simulations are performed for pure water and a 40 % glycerol‑water mixture (density and viscosity ratios appropriate for these liquids in air).

The numerical setup places the droplets at a fixed lateral spacing Δx = 1.8 D₀, with a static contact angle of 90° on the substrate. Gravity is included but found to be negligible for the parameter range considered (We ∈