Thickness model for viscous impinging liquid sheets

Ziyang Peng; Xuan Liu; Zhuo-Yang Song; Bo Wang; Zhengxuan Cao; Erjun Wu; Jiarui Zhao; Ying Gao; Xiaodong Chen; Wenjun Ma

doi:10.1017/jfm.2025.10219

Thickness model for viscous impinging liquid sheets

Published online by Cambridge University Press: 30 June 2025

Xuan Liu ,

Bo Wang ,

Erjun Wu ,

Ying Gao ,

and

Ziyang Peng*: Affiliation:
State Key Laboratory of Nuclear Physics and Technology, School of Physics, Peking University, Beijing 100871, PR China
Xuan Liu: Affiliation:
State Key Laboratory of Nuclear Physics and Technology, School of Physics, Peking University, Beijing 100871, PR China
Zhuo-Yang Song: Affiliation:
State Key Laboratory of Nuclear Physics and Technology, School of Physics, Peking University, Beijing 100871, PR China
Bo Wang: Affiliation:
School of Aerospace Engineering, Beijing Institute of Technology, Beijing 100081, PR China
Zhengxuan Cao: Affiliation:
National Key Laboratory of Shock Wave and Detonation Physics, Institute of Fluid Physics China, Academy of Engineering Physics, Mianyang, PR China
Erjun Wu: Affiliation:
School of Aerospace Engineering, Beijing Institute of Technology, Beijing 100081, PR China
Jiarui Zhao: Affiliation:
State Key Laboratory of Nuclear Physics and Technology, School of Physics, Peking University, Beijing 100871, PR China
Ying Gao: Affiliation:
State Key Laboratory of Nuclear Physics and Technology, School of Physics, Peking University, Beijing 100871, PR China
Xiaodong Chen*: Affiliation:
State Key Laboratory of Nuclear Physics and Technology, School of Physics, Peking University, Beijing 100871, PR China
Wenjun Ma*: Affiliation:
State Key Laboratory of Nuclear Physics and Technology, School of Physics, Peking University, Beijing 100871, PR China Beijing Laser Acceleration Innovation Center, Huairou, Beijing 101400, PR China Guangdong Institute of Laser Plasma Accelerator Technology, Guangzhou 510080, PR China
*: Corresponding authors: Wenjun Ma, wenjun.ma@pku.edu.cn; Ziyang Peng, pengjiang_123@stu.pku.edu.cn; Xiaodong Chen, xiaodong.chen@bit.edu.cn
Corresponding authors: Wenjun Ma, wenjun.ma@pku.edu.cn; Ziyang Peng, pengjiang_123@stu.pku.edu.cn; Xiaodong Chen, xiaodong.chen@bit.edu.cn
Corresponding authors: Wenjun Ma, wenjun.ma@pku.edu.cn; Ziyang Peng, pengjiang_123@stu.pku.edu.cn; Xiaodong Chen, xiaodong.chen@bit.edu.cn

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Abstract

Ultra-thin liquid sheets generated by impinging two liquid jets are crucial high-repetition-rate targets for laser ion acceleration and ultra-fast physics, and serve widely as barrier-free samples for structural biochemistry. The impact of liquid viscosity on sheet thickness should be comprehended fully to exploit its potential. Here, we demonstrate experimentally that viscosity significantly influences thickness distribution, while surface tension primarily governs shape. We propose a thickness model based on momentum exchange and mass transport within the radial flow, which agrees well with the experiments. These results provide deeper insights into the behaviour of liquid sheets and enable accurate thickness control for various applications, including atomization nozzles and laser-driven particle sources.

JFM classification

Interfacial Flows (free surface): Thin films Wakes/Jets: Jets Nonlinear Dynamical Systems: Low-dimensional models

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Type: JFM Rapids
Information: Journal of Fluid Mechanics , Volume 1014 , 10 July 2025 , R3

DOI: https://doi.org/10.1017/jfm.2025.10219 [Opens in a new window]
Copyright: © The Author(s), 2025. Published by Cambridge University Press

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References

Baber, R., Mazzei, L., Thanh, N.T.K. & Gavriilidis, A. 2016 Synthesis of silver nanoparticles using a microfluidic impinging jet reactor. J. Flow Chem. 6 (3), 268–278.10.1556/1846.2016.00015CrossRef Google Scholar

Bremond, N. & Villermaux, E. 2006 Atomization by jet impact. J. Fluid Mech. 549 (-1), 273–306.10.1017/S0022112005007962CrossRef Google Scholar

Bush, J.W.M. & Hasha, A.E. 2004 On the collision of laminar jets: fluid chains and fishbones. J. Fluid Mech. 511, 285–310.10.1017/S002211200400967XCrossRef Google Scholar

Buttersack, T., Haak, H., Bluhm, H., Hergenhahn, U., Meijer, G. & Winter, B. 2023 Imaging temperature and thickness of thin planar liquid water jets in vacuum. Struct. Dyn.-US 10 (3).Google Scholar PubMed

Chen, M., Pukhov, A., Yu, T.P. & Sheng, Z.M. 2009 Enhanced collimated gev monoenergetic ion acceleration from a shaped foil target irradiated by a circularly polarized laser pulse. Phys. Rev. Lett. 103 (2), 024801.10.1103/PhysRevLett.103.024801CrossRef Google Scholar PubMed

Choo, Y.J. & Kang, B.S. 2001 Parametric study on impinging-jet liquid sheet thickness distribution using an interferometric method. Exp. Fluids 31 (1), 56–62.10.1007/s003480000258CrossRef Google Scholar

Choo, Y.J. & Kang, B.S. 2007 The effect of jet velocity profile on the characteristics of thickness and velocity of the liquid sheet formed by two impinging jets. Phys. Fluids 19 (11).10.1063/1.2795780CrossRef Google Scholar

Choo, Y.-J. & Kang, B.-S. 2002 The velocity distribution of the liquid sheet formed by two low-speed impinging jets. Phys. Fluids 14 (2), 622–627.10.1063/1.1429250CrossRef Google Scholar

Crissman, C.J., 2022 Sub-micron thick liquid sheets produced by isotropically etched glass nozzles. Lab Chip 22 (7), 1365–1373.10.1039/D1LC00757BCrossRef Google Scholar PubMed

Du, T., Zhao, P., Liu, Y., Ma, N., Dong, X. & Huang, H. 2024 Balanced devil triangle: a satisfactory comprehensive performance magnetorheological fluids with cross-scale particles. Adv. Funct. Mater. 34 (4), 2311254.10.1002/adfm.202311254CrossRef Google Scholar

Ekimova, M., Quevedo, W., Faubel, M., Wernet, P. & Nibbering, E.T.J. 2015 A liquid flatjet system for solution phase soft-x-ray spectroscopy. Struct. Dyn.-US 2 (5).Google Scholar PubMed

Füle, M., Kovács, A.P., Gilinger, T., Karnok, M., Gaál, P., Figul, S., Marowsky, G. & Osvay, K. 2024 Development of an ultrathin liquid sheet target for laser ion acceleration at high repetition rates in the kilohertz range. High Power Laser Sci. Engng 12, e37.10.1017/hpl.2024.19CrossRef Google Scholar

Hasson, D. & Peck, R.E. 1964 Thickness distribution in a sheet formed by impinging jets. AIChE J. 10 (5), 752–754.10.1002/aic.690100533CrossRef Google Scholar

Ibrahim, E.A. & Przekwas, A.J. 1991 Impinging jets atomization. Phys. Fluids A: Fluid Dyn. 3 (12), 2981–2987.10.1063/1.857840CrossRef Google Scholar

Kim, Y.H. 2023 High-harmonic generation from a flat liquid-sheet plasma mirror. Nat. Commun. 14 (1), 2328.10.1038/s41467-023-38087-3CrossRef Google Scholar PubMed

Knight, B.M. 2024 Detailed characterization of kHz-rate laser-driven fusion at a thin liquid sheet with a neutron detection suite. High Power Laser Sci. Engng 12, e2.10.1017/hpl.2023.84CrossRef Google Scholar

Li, R. & Ashgriz, N. 2006 Characteristics of liquid sheets formed by two impinging jets. Phys. Fluids 18 (8).10.1063/1.2338064CrossRef Google Scholar

Loh, Z.-H. 2020 Observation of the fastest chemical processes in the radiolysis of water. Science 367 (6474), 179–182.10.1126/science.aaz4740CrossRef Google Scholar PubMed

Lu, J. & Corvalan, C.M. 2014 Influence of viscosity on the impingement of laminar liquid jets. Chem. Engng Sci. 119, 182–186.10.1016/j.ces.2014.08.024CrossRef Google Scholar

Macchi, A., Borghesi, M. & Passoni, M. 2013 Ion acceleration by superintense laser-plasma interaction. Rev. Mod. Phys. 85 (2), 751–793.10.1103/RevModPhys.85.751CrossRef Google Scholar

Majumdar, N. & Tirumkudulu, M.S. 2018 Dynamics of radially expanding liquid sheets. Phys. Rev. Lett. 120 (16), 164501.10.1103/PhysRevLett.120.164501CrossRef Google Scholar PubMed

Morrison, J.T., Feister, S., Frische, K.D., Austin, D.R., Ngirmang, G.K., Murphy, N.R., Orban, C., Chowdhury, E.A. & Roquemore, W.M. 2018 MeV proton acceleration at kHz repetition rate from ultra-intense laser liquid interaction. New J. Phys. 20 (2), 022001.10.1088/1367-2630/aaa8d1CrossRef Google Scholar

Oefelein, J.C. & Yang, V. 1993 Comprehensive review of liquid-propellant combustion instabilities in F-1 engines. J. Propul. Power 9 (5), 657–677.10.2514/3.23674CrossRef Google Scholar

Panao, M.R.O. & Delgado, J.M.D. 2013 Effect of pre-impingement length and misalignment in the hydrodynamics of multijet impingement atomization. Phys. Fluids 25 (1).10.1063/1.4774347CrossRef Google Scholar

Peng, Z. et al. 2024 A comprehensive diagnostic system of ultra-thin liquid sheet targets. High Power Laser Sci.Engng 12, e26.10.1017/hpl.2023.101CrossRef Google Scholar

Sanjay, V. & Das, A.K. 2017 Formation of liquid chain by collision of two laminar jets. Phys. Fluids 29 (11).10.1063/1.4998288CrossRef Google Scholar

Savart, F. 1833 Mémoire sur le choc de deux veines liquides animées de mouvements directement opposés. Ann. Chim. Phys. 54, 257–310.Google Scholar

Stemer, D. et al. 2023 Photoelectron spectroscopy from a liquid flatjet. J. Chem. Phys. 158 (23).10.1063/5.0155182CrossRef Google Scholar PubMed

Streeter, M.J.V. 2025 Stable laser-acceleration of high-flux proton beams with plasma collimation. Nat. Commun. 16 (1), 1004.10.1038/s41467-025-56248-4CrossRef Google Scholar PubMed

Taylor, G. 1961 Formation of thin flat sheets of water. Proc. R. Soci. Lond. Series A. Math. Phys. Sci. 259 (1296), 1–17.Google Scholar

Tcypkin, A.N., Ponomareva, E.A., Putilin, S.E., Smirnov, S.V., Shtumpf, S.A., Melnik, M.V., E, Y., Kozlov, S.A. & Zhang, X.-C. 2019 Flat liquid jet as a highly efficient source of terahertz radiation. Opt. Express 27 (11), 15485–15494.10.1364/OE.27.015485CrossRef Google Scholar PubMed

Treffert, F. et al. 2022 High-repetition-rate, multi-MeV deuteron acceleration from converging heavy water microjets at laser intensities of 1021 W/cm2. Appl. Phys. Lett. 121 (7).10.1063/5.0098973CrossRef Google Scholar

Visser, C.W., Kamperman, T., Karbaat, L.P., Lohse, D. & Karperien, M. 2018 In-air microfluidics enables rapid fabrication of emulsions, suspensions, and 3D modular (bio)materials. Sci. Adv. 4 (1), eaao1175.10.1126/sciadv.aao1175CrossRef Google Scholar PubMed

Woo, S. et al. 2018 Current-driven dynamics and inhibition of the skyrmion Hall effect of ferrimagnetic skyrmions in GdFeCo films. Nat. Commun. 9 (1), 959.10.1038/s41467-018-03378-7CrossRef Google Scholar PubMed

Xiaodong, C. & Vigor, Y. 2019 Recent advances in physical understanding and quantitative prediction of impinging-jet dynamics and atomization. Chinese J. Aeronaut. 32 (1), 45–57.Google Scholar

Yang, J. et al. 2021 Direct observation of ultrafast hydrogen bond strengthening in liquid water. Nature 596 (7873), 531–535.10.1038/s41586-021-03793-9CrossRef Google Scholar PubMed

Yang, L.-J., Zhao, F., Fu, Q.-F. & Cui, K.-D. 2014 Liquid sheet formed by impingement of two viscous jets. J. Propul. Power 30 (4), 1016–1026.10.2514/1.B35105CrossRef Google Scholar

Zhang, C., Zhang, Z., Wu, K., Xia, X. & Fan, X. 2021 Atomization of misaligned impinging liquid jets. Phys. Fluids 33 (9).Google Scholar

Ziegler, T. et al. 2024 Laser-driven high-energy proton beams from cascaded acceleration regimes. Nat. Phys. 20 (7), 1211–1216.10.1038/s41567-024-02505-0CrossRef Google Scholar