The Natural Breakup Length of a Steady Capillary Jet: Application to Serial Femtosecond 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 XFE...
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doaj-6dbe1fd232dd4fdd960ec9bba34032352021-08-26T13:39:38ZengMDPI AGCrystals2073-43522021-08-011199099010.3390/cryst11080990The Natural Breakup Length of a Steady Capillary Jet: Application to Serial Femtosecond CrystallographyAlfonso M. Gañán-Calvo0Henry N. Chapman1Michael Heymann2Max O. Wiedorn3Juraj Knoska4Braulio Gañán-Riesco5José M. López-Herrera6Francisco Cruz-Mazo7Miguel A. Herrada8José M. Montanero9Saša Bajt10Departamento de Ingeniería Aeroespacial y Mecánica de Fluidos, Universidad de Sevilla, 41092 Sevilla, SpainCenter for Free-Electron Laser Science, Deutsches Elektronen-Synchrotron DESY, Notkestrasse 85, 22607 Hamburg, GermanyInstitute for Biomaterials and Bimolecular Systems, University of Stuttgart, Pfaffenwaldring 51, 70569 Stuttgart, GermanyCenter for Free-Electron Laser Science, Deutsches Elektronen-Synchrotron DESY, Notkestrasse 85, 22607 Hamburg, GermanyCenter for Free-Electron Laser Science, Deutsches Elektronen-Synchrotron DESY, Notkestrasse 85, 22607 Hamburg, GermanyIngeniatrics Tec. S.L., 41900 Camas, SpainDepartamento de Ingeniería Aeroespacial y Mecánica de Fluidos, Universidad de Sevilla, 41092 Sevilla, SpainDepartamento de Ingeniería Aeroespacial y Mecánica de Fluidos, Universidad de Sevilla, 41092 Sevilla, SpainDepartamento de Ingeniería Aeroespacial y Mecánica de Fluidos, Universidad de Sevilla, 41092 Sevilla, SpainDepartamento de Ingeniería Mecánica, Energética y de los Materiales and Instituto de Computación Científica Avanzada (ICCAEx), Universidad de Extremadura, 06006 Badajoz, SpainThe Hamburg Centre for Ultrafast Imaging, Universität Hamburg, Luruper Chaussee 149, 22761 Hamburg, GermanyOne 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.https://www.mdpi.com/2073-4352/11/8/990capillary jetsbreakup lengthflow focusingcapillary instability |
collection |
DOAJ |
language |
English |
format |
Article |
sources |
DOAJ |
author |
Alfonso M. Gañán-Calvo 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 Saša Bajt |
spellingShingle |
Alfonso M. Gañán-Calvo 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 Saša Bajt The Natural Breakup Length of a Steady Capillary Jet: Application to Serial Femtosecond Crystallography Crystals capillary jets breakup length flow focusing capillary instability |
author_facet |
Alfonso M. Gañán-Calvo 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 Saša Bajt |
author_sort |
Alfonso M. Gañán-Calvo |
title |
The Natural Breakup Length of a Steady Capillary Jet: Application to Serial Femtosecond Crystallography |
title_short |
The Natural Breakup Length of a Steady Capillary Jet: Application to Serial Femtosecond Crystallography |
title_full |
The Natural Breakup Length of a Steady Capillary Jet: Application to Serial Femtosecond Crystallography |
title_fullStr |
The Natural Breakup Length of a Steady Capillary Jet: Application to Serial Femtosecond Crystallography |
title_full_unstemmed |
The Natural Breakup Length of a Steady Capillary Jet: Application to Serial Femtosecond Crystallography |
title_sort |
natural breakup length of a steady capillary jet: application to serial femtosecond crystallography |
publisher |
MDPI AG |
series |
Crystals |
issn |
2073-4352 |
publishDate |
2021-08-01 |
description |
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. |
topic |
capillary jets breakup length flow focusing capillary instability |
url |
https://www.mdpi.com/2073-4352/11/8/990 |
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