Hostname: page-component-76c49bb84f-lxspr Total loading time: 0 Render date: 2025-07-06T18:21:05.627Z Has data issue: false hasContentIssue false
  • English
  • Français

Thickness model for viscous impinging liquid sheets

Published online by Cambridge University Press:  30 June 2025

Ziyang Peng Open the ORCID record for Ziyang Peng [Opens in a new window] ,
Xuan Liu ,
Zhuo-Yang Song Open the ORCID record for Zhuo-Yang Song [Opens in a new window] ,
Bo Wang ,
Zhengxuan Cao ,
Erjun Wu ,
Jiarui Zhao ,
Ying Gao ,
Xiaodong Chen Open the ORCID record for Xiaodong Chen [Opens in a new window]  and
Wenjun Ma Open the ORCID record for Wenjun Ma [Opens in a new window]
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
Get access Rights & Permissions [Opens in a new window]

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

Information

Type
JFM Rapids
Information
Journal of Fluid Mechanics , Volume 1014 , 10 July 2025 , R3
Check for updates
Copyright
© The Author(s), 2025. Published by Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Article purchase

Temporarily unavailable

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), 268–278.10.1556/1846.2016.00015CrossRefGoogle Scholar
Bremond, N. & Villermaux, E. 2006 Atomization by jet impact. J. Fluid Mech. 549 (-1), 273–306.10.1017/S0022112005007962CrossRefGoogle 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/S002211200400967XCrossRefGoogle 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 ScholarPubMed
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.103.024801CrossRefGoogle ScholarPubMed
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/s003480000258CrossRefGoogle 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).10.1063/1.2795780CrossRefGoogle 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), 622–627.10.1063/1.1429250CrossRefGoogle Scholar
Crissman, C.J., 2022 Sub-micron thick liquid sheets produced by isotropically etched glass nozzles. Lab Chip 22 (7), 1365–1373.10.1039/D1LC00757BCrossRefGoogle ScholarPubMed
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.202311254CrossRefGoogle 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 ScholarPubMed
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.2024.19CrossRefGoogle 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.690100533CrossRefGoogle Scholar
Ibrahim, E.A. & Przekwas, A.J. 1991 Impinging jets atomization. Phys. Fluids A: Fluid Dyn. 3 (12), 2981–2987.10.1063/1.857840CrossRefGoogle Scholar
Kim, Y.H. 2023 High-harmonic generation from a flat liquid-sheet plasma mirror. Nat. Commun. 14 (1), 2328.10.1038/s41467-023-38087-3CrossRefGoogle ScholarPubMed
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.2023.84CrossRefGoogle Scholar
Li, R. & Ashgriz, N. 2006 Characteristics of liquid sheets formed by two impinging jets. Phys. Fluids 18 (8).10.1063/1.2338064CrossRefGoogle Scholar
Loh, Z.-H. 2020 Observation of the fastest chemical processes in the radiolysis of water. Science 367 (6474), 179–182.10.1126/science.aaz4740CrossRefGoogle ScholarPubMed
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.2014.08.024CrossRefGoogle 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.85.751CrossRefGoogle Scholar
Majumdar, N. & Tirumkudulu, M.S. 2018 Dynamics of radially expanding liquid sheets. Phys. Rev. Lett. 120 (16), 164501.10.1103/PhysRevLett.120.164501CrossRefGoogle ScholarPubMed
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/aaa8d1CrossRefGoogle Scholar
Oefelein, J.C. & Yang, V. 1993 Comprehensive review of liquid-propellant combustion instabilities in F-1 engines. J. Propul. Power 9 (5), 657–677.10.2514/3.23674CrossRefGoogle 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).10.1063/1.4774347CrossRefGoogle 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.2023.101CrossRefGoogle Scholar
Sanjay, V. & Das, A.K. 2017 Formation of liquid chain by collision of two laminar jets. Phys. Fluids 29 (11).10.1063/1.4998288CrossRefGoogle 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).10.1063/5.0155182CrossRefGoogle ScholarPubMed
Streeter, M.J.V. 2025 Stable laser-acceleration of high-flux proton beams with plasma collimation. Nat. Commun. 16 (1), 1004.10.1038/s41467-025-56248-4CrossRefGoogle ScholarPubMed
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.27.015485CrossRefGoogle ScholarPubMed
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).10.1063/5.0098973CrossRefGoogle 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.aao1175CrossRefGoogle ScholarPubMed
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/s41467-018-03378-7CrossRefGoogle ScholarPubMed
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/s41586-021-03793-9CrossRefGoogle ScholarPubMed
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.B35105CrossRefGoogle 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/s41567-024-02505-0CrossRefGoogle Scholar
Supplementary material: File

Peng et al. supplementary material

Peng et al. supplementary material
Download Peng et al. supplementary material(File)
File 923.4 KB