Drop Impact

"The highest excellence is like that of water."

    -- Lao Tzu, Tao Te Ching (~ 450 B.C.)

Fluid mechanics is one of the oldest branches of physics, the study of which can be traced back to the dawn of science in ancient Greece. Yet, the dynamics of fluid still elude a complete theoretical understanding with many important unsolved problems. For example, turbulence is generally regarded as one of the most difficult unsolved problems. A famous apocryphal story goes that Heisenberg was once asked what he would ask God, given the opportunity. His reply was: "When I meet God, I am going to ask him two questions: Why relativity? And why turbulence? I really believe he will have an answer for the first." As the most abundant material on Earth, fluid is tightly related to almost every aspect of natural and industrial processes. Hence, understanding the dynamics of fluid flows in different circumstances is of great importance and the study of fluid mechanics is one of the most active research areas in physics, chemical engineering and materials science. 

Our research focuses on experimental study of fluid flows in coating and transportation processes with a special emphasis on the instability and singularity developed in fast fluid flows. Specifically, we are interested in the singular dynamics of liquid drop during impact.  We have developed various state-of-the-art experimental techniques including high-speed photography, holographic imaging and confocal imaging to visualize fast three-dimensional fluid flows ranging from centimeter scales down to micron/nanometer scales.  

(1) Liquid drop impacts on solid and granular surfaces
(2) Impact forces and stresses
(3) Impact of non-Newtonian drops

When a granular material is impacted by a sphere, its surface deforms like a liquid yet it preserves a circular crater like a solid. Although the mechanism of granular impact cratering by solid spheres is well explored, our knowledge on granular impact cratering by liquid drops is still very limited. Here, by combining high-speed photography with high-precision laser profilometry, we investigate liquid-drop impact dynamics on granular surface and monitor the morphology of resulting impact craters. Surprisingly, we find that despite the enormous energy and length difference, granular impact cratering by liquid drops follows the same energy scaling and reproduces the same crater morphology as that of asteroid impact craters. Inspired by this similarity, we integrate the physical insight from planetary sciences, the liquidmarblemodel from fluid mechanics, and the concept of jamming transition from granular physics into a simple theoretical framework that quantitatively describes all of the main features of liquid-drop imprints in granular media. Our study sheds light on the mechanisms governing raindrop impacts on granular surfaces and reveals a remarkable analogy between familiar phenomena of raining and catastrophic asteroid strikes.

The video shown above from our research has won 2014 APS Division of Fluid Dynamics "The Gallery of Fluid Motion" Award. The image taken from our high-speed video shown below has been selected as back scatter by Physics Today and as PNAS featured image. Our research has been reported by Discover Channel, Popular Science, CBC news (Canada), SPIEGEL magazine (Germany), De Kennis van Nu (The Netherlands).

• Granular impact cratering by liquid drops: Understanding raindrop imprints through an analogy to asteroid strikes, R. Zhao, Q. Zhang, H. Tjugito, X. Cheng, Proc. Natl. Acad. Sci. USA 112, 342 (2015).
• Q. Zhang, M. Gao, R. Zhao, and X. Cheng, “Scaling of liquid-drop impact craters in wet granular media”, Phys. Rev. E 92, 042205 (2015). (Selected as “Editors’ Suggestion”)
• R. Zhao, Q. Zhang, and X. Cheng, “Raindrop imprints and asteroid strikes”, Phys. Today 68(3), 72 (2015).
• R. Zhao, Q. Zhang, H. Tjugito, and X. Cheng, “Raindrop impact on a sandy surface”, Phys. Fluids 27, 091111 (2015).

How much force can a raindrop exert upon impact? What are the pressure and shear stress distributions beneath a rapidly spreading drop during impact? These questions extend beyond mere curiosity: repeated droplet impacts can lead to severe surface erosion in both natural and engineered environments, necessitating effective prevention and mitigation strategies.

In our lab, we have developed a suite of experimental techniques that enable high-resolution measurements of the transient impact force, as well as detailed mapping of the pressure and shear stress fields exerted by droplets on substrates with varying stiffness. Our results reveal that an impacting drop releases its kinetic energy in an explosive, shock-like process, producing a rapidly propagating pressure peak at early times. In this sense, even an ordinary raindrop behaves like a microscopic “bomb” at the onset of impact, generating erosion effects that can exceed those caused by solid particle impacts.

For further details, please refer to our review paper and related publications on this topic:

• X. Cheng, T.-P. Sun, and L. Gordillo, “Drop Impact Dynamics: Impact Force and Stress Distributions”, Annu. Rev. Fluid Mech. 54, 57-81 (2022).

• L. Gordillo, T.-P. Sun, and X. Cheng, “Dynamics of drop impact on solid surfaces: evolution of impact force and self-similar spreading”, J. Fluid Mech. 840, 190-214 (2018).

• T.-P. Sun, F. Alvarez-Novoa, K. Andrade, P. Gutierrez, L. Gordillo, and X. Cheng, “Stress distribution and surface shock wave of drop impact”, Nat. Commun. 13, 1703 (2022). 

Many liquids encountered in industrial and biological contexts are non-Newtonian, exhibiting complex, rate-dependent viscosities. However, the influence of such rheological behavior on droplet impact dynamics remains far from fully understood. By combining simulations, experiments, and scaling analysis, we establish a general framework for predicting the maximum spreading of droplets composed of generalized Newtonian fluids, encompassing both shear-thinning and shear-thickening behaviors. Through an analysis of the energy budget at maximum spreading, we identify a characteristic shear rate that governs viscous dissipation during impact. This insight enables us to map the spreading behavior of non-Newtonian droplets onto an equivalent Newtonian framework, revealing the quantitative dependence of the maximum spreading diameter on impact conditions and fluid rheology. Furthermore, we examine the impact dynamics of strongly shear-thickening fluids, demonstrating how the interplay between inertia and dilatancy controls the rapid impact dynamics.

Overall, our study addresses a long-standing challenge in understanding non-Newtonian droplet impact and provides practical guidance for designing fluids with tailored impact responses.

• A. Mobaseri, S. Kumar, and X. Cheng, “Maximum spreading of impacting shear-thinning and shear-thickening drops”, Proc. Natl. Acad. Sci. USA 122, e2500163122 (2025). 

• A. Mobaseri, L. Gordillo, C. Burton, S. Yoon, D. Lee, S. Kumar, M. M. Driscoll, and X. Cheng, “Inertia-Dilatancy Interplay Governs Shear-Thickening Drop Impact”, Phys. Rev. Lett. 136, 148201 (2026). (Featured in Physics; Highlighted as “Editors’ Suggestion”)