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Article

The Natural Breakup Length of a Steady Capillary Jet: Application to Serial Femtosecond Crystallography

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Departamento de Ingeniería Aeroespacial y Mecánica de Fluidos, Universidad de Sevilla, 41092 Sevilla, Spain
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Laboratory of Engineering for Energy and Environmental Sustainability, Universidad de Sevilla, 41092 Sevilla, Spain
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Center for Free-Electron Laser Science, Deutsches Elektronen-Synchrotron DESY, Notkestrasse 85, 22607 Hamburg, Germany
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The Hamburg Centre for Ultrafast Imaging, Universität Hamburg, Luruper Chaussee 149, 22761 Hamburg, Germany
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Department of Physics, Universität Hamburg, Luruper Chaussee 149, 22761 Hamburg, Germany
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Institute for Biomaterials and Bimolecular Systems, University of Stuttgart, Pfaffenwaldring 51, 70569 Stuttgart, Germany
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Ingeniatrics Tec. S.L., 41900 Camas, Spain
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Department of Mechanical and Aerospace Engineering, Princeton University, Princeton, NJ 08544, USA
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Departamento de Ingeniería Mecánica, Energética y de los Materiales and Instituto de Computación Científica Avanzada (ICCAEx), Universidad de Extremadura, 06006 Badajoz, Spain
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Deutsches Elektronen-Synchrotron DESY, Notkestrasse 85, 22607 Hamburg, Germany
*
Author to whom correspondence should be addressed.
Academic Editor: Borislav Angelov
Crystals 2021, 11(8), 990; https://doi.org/10.3390/cryst11080990
Received: 14 July 2021 / Revised: 11 August 2021 / Accepted: 12 August 2021 / Published: 20 August 2021
(This article belongs to the Special Issue Time Resolved Crystallography)
One of the most successful ways to introduce samples in Serial Femtosecond Crystallography has been the use of microscopic capillary liquid jets produced by gas flow focusing, whose length-to-diameter ratio and velocity are essential to fulfill the requirements of the high pulse rates of current XFELs. In this work, we demonstrate the validity of a classical scaling law with two universal constants to calculate that length as a function of the liquid properties and operating conditions. These constants are determined by fitting the scaling law to a large set of experimental and numerical measurements, including previously published data. Both the experimental and numerical jet lengths conform remarkably well to the proposed scaling law. We show that, while a capillary jet is a globally unstable system to linear perturbations above a critical length, its actual and shorter long-term average intact length is determined by the nonlinear perturbations coming from the jet breakup itself. Therefore, this length is determined solely by the properties of the liquid, the average velocity of the liquid and the flow rate expelled. This confirms the very early observations from Smith and Moss 1917, Proc R Soc Lond A Math Phys Eng, 93, 373, to McCarthy and Molloy 1974, Chem Eng J, 7, 1, among others, while it contrasts with the classical conception of temporal stability that attributes the natural breakup length to the jet birth conditions in the ejector or small interactions with the environment. View Full-Text
Keywords: capillary jets; breakup length; flow focusing; capillary instability capillary jets; breakup length; flow focusing; capillary instability
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MDPI and ACS Style

Gañán-Calvo, A.M.; Chapman, H.N.; Heymann, M.; Wiedorn, M.O.; Knoska, J.; Gañán-Riesco, B.; López-Herrera, J.M.; Cruz-Mazo, F.; Herrada, M.A.; Montanero, J.M.; Bajt, S. The Natural Breakup Length of a Steady Capillary Jet: Application to Serial Femtosecond Crystallography. Crystals 2021, 11, 990. https://doi.org/10.3390/cryst11080990

AMA Style

Gañán-Calvo AM, Chapman HN, Heymann M, Wiedorn MO, Knoska J, Gañán-Riesco B, López-Herrera JM, Cruz-Mazo F, Herrada MA, Montanero JM, Bajt S. The Natural Breakup Length of a Steady Capillary Jet: Application to Serial Femtosecond Crystallography. Crystals. 2021; 11(8):990. https://doi.org/10.3390/cryst11080990

Chicago/Turabian Style

Gañán-Calvo, Alfonso M., Henry N. Chapman, Michael Heymann, Max O. Wiedorn, Juraj Knoska, Braulio Gañán-Riesco, José M. López-Herrera, Francisco Cruz-Mazo, Miguel A. Herrada, José M. Montanero, and Saša Bajt. 2021. "The Natural Breakup Length of a Steady Capillary Jet: Application to Serial Femtosecond Crystallography" Crystals 11, no. 8: 990. https://doi.org/10.3390/cryst11080990

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