Dynamics of drop impact on solid surfaces: Evolution of impact force and self-similar spreading

Leonardo Gordillo, Ting Pi Sun, Xiang Cheng

Research output: Contribution to journalArticlepeer-review

28 Scopus citations


We investigate the dynamics of drop impacts on dry solid surfaces. By synchronising high-speed photography with fast force sensing, we simultaneously measure the temporal evolution of the shape and impact force of impacting drops over a wide range of Reynolds numbers . At high , when inertia dominates the impact processes, we show that the early time evolution of impact force follows a square-root scaling, quantitatively agreeing with a recent self-similar theory. This observation provides direct experimental evidence on the existence of upward propagating self-similar pressure fields during the initial impact of liquid drops at high . When viscous forces gradually set in with decreasing , we analyse the early time scaling of the impact force of viscous drops using a perturbation method. The analysis quantitatively matches our experiments and successfully predicts the trends of the maximum impact force and the associated peak time with decreasing . Furthermore, we discuss the influence of viscoelasticity on the temporal signature of impact forces. Last but not least, we also investigate the spreading of liquid drops at high following the initial impact. Particularly, we find an exact parameter-free self-similar solution for the inertia-driven drop spreading, which quantitatively predicts the height of spreading drops at high . The limit of the self-similar approach for drop spreading is also discussed. As such, our study provides a quantitative understanding of the temporal evolution of impact forces across the inertial, viscous and viscoelastic regimes and sheds new light on the self-similar dynamics of drop-impact processes.

Original languageEnglish (US)
Pages (from-to)190-214
Number of pages25
JournalJournal of Fluid Mechanics
StatePublished - Apr 10 2018

Bibliographical note

Publisher Copyright:
© 2018 Cambridge University Press.


  • boundary layers
  • drops
  • interfacial flows (free surface)


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