TY - JOUR
T1 - Unifying Theory of Scaling in Drop Impact
T2 - Forces and Maximum Spreading Diameter
AU - Sanjay, Vatsal
AU - Lohse, Detlef
N1 - Publisher Copyright:
© 2025 authors. Published by the American Physical Society. Published by the American Physical Society under the terms of the "https://creativecommons.org/licenses/by/4.0/"Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI. Open access publication funded by the Max Planck Society.
PY - 2025/3/11
Y1 - 2025/3/11
N2 - 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≤103 and 10-3≤Oh≤102 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.
AB - 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≤103 and 10-3≤Oh≤102 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.
KW - UT-Hybrid-D
UR - http://www.scopus.com/inward/record.url?scp=86000667368&partnerID=8YFLogxK
U2 - 10.1103/PhysRevLett.134.104003
DO - 10.1103/PhysRevLett.134.104003
M3 - Article
AN - SCOPUS:86000667368
SN - 0031-9007
VL - 134
JO - Physical review letters
JF - Physical review letters
IS - 10
M1 - 104003
ER -