Unifying Theory of Scaling in Drop Impact: Forces and Maximum Spreading Diameter

The dynamics of drop impact on a rigid surface strongly depends on the droplet's velocity, its size, and its material properties. The main characteristics are the droplet's force exerted on the surface and its maximal spreading radius. The crucial question is how do they depend on the (dimensionless) control parameters, which are the Weber number We (nondimensionalized kinetic energy) and the Ohnesorge number Oh (dimensionless viscosity). Here, we perform direct numerical simulations over the huge parameter range 1≤We≤10^{3} and 10^{-3}≤Oh≤10^{2} and in particular develop a unifying theoretical approach, which is inspired by the Grossmann-Lohse theory for wall-bounded turbulence [Grossmann and Lohse, J. Fluid Mech. 407, 27 (2000)JFLSA70022-112010.1017/S0022112099007545; Phys. Rev. Lett. 86, 3316 (2001)PRLTAO0031-900710.1103/PhysRevLett.86.3316]. The key idea is to split the energy dissipation rate into the different phases of the impact process, in which different physical mechanisms dominate. The theory can consistently and quantitatively account for the We and Oh dependences of the maximal impact force and the maximal spreading diameter over the huge parameter space. It also clarifies why viscous dissipation plays a significant role during impact, even for low-viscosity droplets (low Oh), in contrast to what had been assumed in some prior theories.