Unveiling nanodroplet impact force on material interfaces

Abstract

Nanodroplet impact on nanoscale material interfaces is widely involved in nanoscience and nanotechnology, affecting the technical reliability through complicated liquid‒solid interaction force, that is, the droplet impact force. However, our understanding of the nanodroplet impact force is still blank. Herein, we reveal that the nanoscale size (∼10 nm) and high impact velocity (>100 m/s) of nanodroplets lead to unique characteristics of impact force, significantly differing from those of macrodroplets (∼1 mm). The nanodroplet impact force profile holds a single-peak feature, which is independent of droplet parameters and material wettability. The significant water-hammer pressure induces the abnormal rising of impact force, yielding unexpectedly high peak values governed by the Mach number (more than 10 orders of magnitude higher than droplet gravity). Our findings of droplet impact force at the nanoscale reveal the potential challenge of the damage of material surfaces by nanodroplet impact, highlighting one crucial factor for advancing nanolithography and nanoprinting.

References

[1] Zhu Y, Piehowski PD, Zhao R, et al. Nanodroplet processing platform for deep and quantitative proteome profiling of 10-100 mammalian cells. Nat Commun. 2018; 9: 882.

[2] Galliker P, Schneider J, Eghlidi H, Kress S, Sandoghdar V, Poulikakos D. Direct printing of nanostructures by electrostatic autofocussing of ink nanodroplets. Nat Commun. 2012; 3: 890.

[3] Dyett BP, Zhang X. Accelerated formation of H₂ nanobubbles from a surface nanodroplet reaction. ACS Nano. 2020; 14: 10944-10953.

[4] Ning Y, Gan Y, Dong C, Qi R. Numerical simulations and experimental verifications at micro-, meso-, and macroscales of droplet evaporation: a comprehensive review with special focus on saline droplets. Droplet. 2025; 4:e147.

[5] Ren L, Cheng N, Man X, et al. General programmable growth of hybrid core-shell nanostructures with liquid metal nanodroplets. Adv Mater. 2021; 33:2008024.

[6] Zhang K, Xu H, Fan J, Ouyang C, Wu H, Wang F. A strategy to drive nanoflow using Laplace pressure and the end effect. Droplet. 2024; 3:e136.

[7] Ossiander M, Meretska ML, Hampel HK, et al. Extreme ultraviolet metalens by vacuum guiding. Science. 2023; 380: 59-63.

[8] Tseng LT, Karadan P, Kazazis D, et al. Resistless EUV lithography: photon-induced oxide patterning on silicon. Sci Adv. 2023; 9:eadf5997.

[9] Hail CU, Höller C, Matsuzaki K, et al. Nanoprinting organic molecules at the quantum level. Nat Commun. 2019; 10: 1880.

[10] Deng W, Zhai T, Li Gao, Xu C, Zhao X, Liu Y. Recent progress of experimental fluid mechanics for EUV sources. Adv Mech. 2024; 54: 138-172.

[11] Vinokhodov AY, Krivokorytov MS, Sidelnikov YV, Krivtsun VM, Medvedev VV, Koshelev KN. Droplet-based, high-brightness extreme ultraviolet laser plasma source for metrology. J Appl Phys. 2016; 120:163304.

[12] Avila SRG, Ohl C. Fragmentation of acoustically levitating droplets by laser-induced cavitation bubbles. J Fluid Mech. 2016; 805: 551-576.

[13] Kelin AL, Kurilovich D, Lhuissier H, et al. Drop fragmentation by laser-pulse impact. J Fluid Mech. 2020; 893: A7.

[14] Jansson PAC, Hansson BAM, Hemberg O, et al. Liquid-tin-jet laser-plasma extreme ultraviolet generation. Appl Phys Lett. 2004; 84: 2256-2258.

[15] Cheng X, Sun T, Gordillo L. Drop impact dynamics: impact force and stress distributions. Annu Rev Fluid Mech. 2022; 54: 57-81.

[16] Mitchell BR, Klewicki JC, Korkolis YP, Kinsey BL. The transient force profile of low-speed droplet impact: measurements and model. J Fluid Mech. 2019; 867: 300-322.

[17] Gordillo L, Sun T, Chen X. Dynamics of drop impact on solid surfaces: evolution of impact force and self-similar spreading. J Fluid Mech. 2018; 840: 190-214.

[18] Zhang B, Sanjay V, Shi S, et al. Impact forces of water drops falling on superhydrophobic surfaces. Phys Rev Lett. 2022; 129:104501.

[19] Hu Z, Chu F, Wu X. Double-peak characteristic of droplet impact force on superhydrophobic surfaces. Extreme Mech Lett. 2022; 52:101665.

[20] Fernández-Toledano JC, Braeckeveldt B, Marengo M, De Coninck J. How wettability controls nanoprinting. Phys Rev Lett. 2020; 124:224503.

[21] Hu Z, Ran H, Shan H, Chu F, Wang Z, Wang R. Reconsideration on the maximum deformation of droplets impacting on solid surfaces. Droplet. 2025; 4:e163.

[22] Wang Y, Wang Y, He X, et al. Scaling laws of the maximum spreading factor for impact of nanodroplets on solid surfaces. J Fluid Mech. 2022; 937: A12.

[23] Li T. Molecular dynamics simulations of droplet coalescence and impact dynamics on the modified surfaces: a review. Comput Mater Sci. 2023; 230:112547.

[24] Hu Z, Chu F, Shan H, Wu X, Dong Z, Wang R. Understanding and utilizing droplet impact on superhydrophobic surfaces: phenomena, mechanisms, regulations, applications, and beyond. Adv Mater. 2024; 36:2310177.

[25] Ma Q, Wang Y, Wang Y, et al. Phase diagram for nanodroplet impact on solid surfaces. Phys Fluids. 2021; 33:102007.

[26] Li B, Li X, Chen M. Spreading and breakup of nanodroplet impinging on surface. Phys Fluids. 2017; 29:012003.

[27] Wang Y, Wang Y, Zhang L, et al. Impact dynamics of nanodroplets on pillared surfaces. Phys Rev Fluids. 2024; 9:073602.

[28] Kim H, Park U, Lee C, Kim H, Kim MH, Kim J. Drop splashing on a rough surface: how surface morphology affects splashing threshold. Appl Phys Lett. 2014; 104:161608.

[29] Visser CW, Frommhold PE, Wildeman S, Mettin R, Lohse D, Sun C. Dynamics of high-speed micro-drop impact: numerical simulations and experiments at frame-to-frame times below 100 ns. Soft Matter. 2015; 11: 1708-1722.

[30] Kobayashi K, Konno K, Yaguchi H, Fujii H, Sanada T, Watanabe M. Early stage of nanodroplet impact on solid wall. Phys Fluids. 2016; 28:032002.

[31] Perumanath S, Chubynsky MV, Pillai R, Borg MK, Sprittles JE. Rolling and sliding modes of nanodroplet spreading: molecular simulations and a continuum approach. Phys Rev Lett. 2023; 131:164001.

[32] Wang Y, Wang Y, Zhang L, et al. Impact dynamics of nanodroplets on pillared surfaces. Phys Rev Fluids. 2024; 9:073602.

[33] Molinero V, Moore EB. Water modeled as an intermediate element between carbon and silicon. J Phys Chem B. 2009; 113: 4008-4016.

[34] Li J, Oron A, Jiang Y. Droplet jump-off force on a superhydrophobic surface. Phys Rev Fluids. 2023; 8:113601.

[35] Shu Y, Chu F, Hu Z, et al. Superhydrophobic strategy for nature-inspired rotating microfliers: enhancing spreading, reducing contact time, and weakening impact force of raindrops. ACS Appl Mater Interfaces. 2022; 14:57340.

[36] Pasandideh-Fard M, Qiao YM, Chandra S, Mostaghimi J. Capillary effects during droplet impact on a solid surface. Phys Fluids. 1996; 8: 650-659.

[37] Thenarianto C, Koh XQ, Lin M, Jokinen V, Daniel D. Energy loss for droplets bouncing off superhydrophobic surfaces. Langmuir. 2023; 39: 3162-3167.

[38] Tatekura Y, Watanabe M, Kobayashi K, Sanada T. Pressure generated at the instant of impact between a liquid droplet and solid surface. R Soc Open Sci. 2018; 5:181101.

[39] Heymann FJ. High-speed impact between a liquid drop and a solid surface. J Appl Phys. 1969; 40: 5113-5122.

[40] Marzbali M, Dolatabadi A. High-speed droplet impingement on dry and wetted substrates. Phys Fluids. 2020; 32:112101.

[41] Haller KK, Poulikakos D, Ventikos Y, Monkewitz P. Shock wave formation in droplet impact on a rigid surface: lateral liquid motion and multiple wave structure in the contact line region. J Fluid Mech. 2003; 490: 1-14.

[42] Kwon HM, Paxson AT, Varanasi KK, Patankar NA. Rapid deceleration-driven wetting transition during pendant drop deposition on superhydrophobic surfaces. Phys Rev Lett. 2011; 106:036102.

[43] Deng T, Varanasi KK, Hsu M, et al. Nonwetting of impinging droplets on textured surfaces. Appl Phys Lett. 2009; 94:133109.

[44] Wang Y, Wang Y, Xie F, et al. Spreading and retraction kinetics for impact of nanodroplets on hydrophobic surfaces. Phys Fluids. 2020; 32:092005.

[45] Wu W, Liu Q, Wang B. Curved surface effect on high-speed droplet impingement. J Fluid Mech. 2021; 909: A7.

[46] Tretola G, Vogiatzaki K. Unveiling the dynamics of ultra high velocity droplet impact on solid surfaces. Sci Rep. 2022; 12: 7416.

[47] Wang Y, Wang Y, Gao S, Yang Y, Wang X, Chen M. Universal model for the maximum spreading factor of impacting nanodroplets: from hydrophilic to hydrophobic surfaces. Langmuir. 2020; 36: 9306-9316.

RIGHTS & PERMISSIONS

2026 The Author(s). Droplet published by Jilin University and John Wiley & Sons Australia, Ltd.