{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T05:51:06Z","timestamp":1760248266672,"version":"build-2065373602"},"reference-count":53,"publisher":"MDPI AG","issue":"7","license":[{"start":{"date-parts":[[2024,3,28]],"date-time":"2024-03-28T00:00:00Z","timestamp":1711584000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Czech Science Foundation","award":["GA 22-25799S"],"award-info":[{"award-number":["GA 22-25799S"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>This paper describes the methodology of combining experimental measurements with mathematical\u2013physics analyses in the investigation of flow in the aperture and nozzle. The aperture and nozzle separate the differentially pumped chamber from the specimen chamber in an environmental scanning electron microscope (ESEM). Experimental measurements are provided by temperature and pressure sensors that meet the demanding conditions of cryogenic temperature zones and low pressures. This aperture maintains the required pressure difference between the chambers. Since it separates the large pressure gradient, critical flow occurs on it and supersonic gas flow with the characteristic properties of critical flow in the state variables occurs behind it. As a primary electron beam passes through the differential pumped chamber and the given aperture, the aperture is equipped with a nozzle. The shape of the nozzle strongly influences the character of the supersonic flow. The course of state variables is also strongly influenced by this shape; thus, it affects the number of collisions the primary beam\u2019s electrons have with gas molecules, and so the resulting image. This paper describes experimental measurements made using sensors under laboratory conditions in a specially created experimental chamber. Then, validation using mathematical\u2013physical analysis in the Ansys Fluent system is described.<\/jats:p>","DOI":"10.3390\/s24072166","type":"journal-article","created":{"date-parts":[[2024,3,28]],"date-time":"2024-03-28T12:22:46Z","timestamp":1711628566000},"page":"2166","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":6,"title":["The Impact of Nozzle Opening Thickness on Flow Characteristics and Primary Electron Beam Scattering in an Environmental Scanning Electron Microscope"],"prefix":"10.3390","volume":"24","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-0640-0406","authenticated-orcid":false,"given":"Ji\u0159\u00ed","family":"Maxa","sequence":"first","affiliation":[{"name":"Institute of Scientific Instruments of the CAS, Kr\u00e1lovopolsk\u00e1 147, 612 64 Brno, Czech Republic"},{"name":"Faculty of Electrical Engineering and Communication, Brno University of Technology, Technick\u00e1 10, 616 00 Brno, Czech Republic"}]},{"given":"Pavla","family":"\u0160aback\u00e1","sequence":"additional","affiliation":[{"name":"Faculty of Electrical Engineering and Communication, Brno University of Technology, Technick\u00e1 10, 616 00 Brno, Czech Republic"}]},{"given":"Jan","family":"Mazal","sequence":"additional","affiliation":[{"name":"Faculty of Military Robotics, University of Defence, 662 10 Brno, Czech Republic"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-6029-5435","authenticated-orcid":false,"given":"Vil\u00e9m","family":"Ned\u011bla","sequence":"additional","affiliation":[{"name":"Institute of Scientific Instruments of the CAS, Kr\u00e1lovopolsk\u00e1 147, 612 64 Brno, Czech Republic"}]},{"given":"Tom\u00e1\u0161","family":"Binar","sequence":"additional","affiliation":[{"name":"Faculty of Military Leadership, University of Defence, 662 10 Brno, Czech Republic"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-9793-9767","authenticated-orcid":false,"given":"Petr","family":"Ba\u010da","sequence":"additional","affiliation":[{"name":"Faculty of Electrical Engineering and Communication, Brno University of Technology, Technick\u00e1 10, 616 00 Brno, Czech Republic"}]},{"given":"Jaroslav","family":"Tal\u00e1r","sequence":"additional","affiliation":[{"name":"Faculty of Military Leadership, University of Defence, 662 10 Brno, Czech Republic"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-8528-4430","authenticated-orcid":false,"given":"Robert","family":"Bayer","sequence":"additional","affiliation":[{"name":"Faculty of Electrical Engineering and Communication, Brno University of Technology, Technick\u00e1 10, 616 00 Brno, Czech Republic"}]},{"given":"Pavel","family":"\u010cudek","sequence":"additional","affiliation":[{"name":"Faculty of Electrical Engineering and Communication, Brno University of Technology, Technick\u00e1 10, 616 00 Brno, Czech Republic"}]}],"member":"1968","published-online":{"date-parts":[[2024,3,28]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Drexler, P., \u010c\u00e1p, M., Fiala, P., Steinbauer, M., Kadlec, R., Ka\u0161ka, M., and Ko\u010di\u0161, L. (2019). A Sensor System for Detecting and Localizing Partial Discharges in Power Transformers with Improved Immunity to Interferences. Sensors, 19.","DOI":"10.3390\/s19040923"},{"key":"ref_2","unstructured":"Fiala, P., Sadek, V., Dohnal, P., and Bachorec, T. (2008, January 2\u20136). Basic experiments with model of inductive flowmeter. Proceedings of the Electromagnetics Research Symposium: PIERS 2008, Cambridge, MA, USA."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"1871","DOI":"10.1007\/s00706-005-0386-8","article-title":"SHS of NbSi2: A Comparison Between Experiments and Simulations","volume":"136","author":"Gennari","year":"2005","journal-title":"Monatshefte F\u00fcr Chem. Chem. Mon."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"600","DOI":"10.1016\/j.micron.2011.10.023","article-title":"Velocity and ejector-jet assisted differential pumping: Novel design stages for environmental SEM","volume":"43","author":"Danilatos","year":"2012","journal-title":"Micron"},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"166","DOI":"10.1111\/j.1365-2818.2010.03455.x","article-title":"Beam transfer characteristics of a commercial environmental SEM and a low vacuum SEM","volume":"242","author":"Danilatos","year":"2011","journal-title":"J. Microsc."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"159","DOI":"10.1111\/j.1365-2818.2011.03521.x","article-title":"Figure of merit for environmental SEM and its implications","volume":"244","author":"Danilatos","year":"2011","journal-title":"J. Microsc."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"26","DOI":"10.1111\/j.1365-2818.2009.03148.x","article-title":"Optimum beam transfer in the environmental scanning electron microscope","volume":"234","author":"Danilatos","year":"2009","journal-title":"J. Microsc."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"63307","DOI":"10.1063\/1.3086622","article-title":"Modeling and experiments on differential pumping in linear plasma generators operating at high gas flows","volume":"105","author":"Koppers","year":"2009","journal-title":"J. Appl. Phys."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"4870","DOI":"10.1063\/1.1559936","article-title":"Modeling gas flow through microchannels and nanopores","volume":"93","author":"Roy","year":"2003","journal-title":"J. Appl. Phys."},{"key":"ref_10","unstructured":"Dan\u011bk, M. (1990). Aerodynamika a Mechanika Letu, VVL\u0160 SNP."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"112954","DOI":"10.1016\/j.ultramic.2020.112954","article-title":"Simulation-based optimisation of thermodynamic conditions in the ESEM for dynamical in-situ study of spherical polyelectrolyte complex particles in their native state","volume":"211","author":"Maxa","year":"2020","journal-title":"Ultramicroscopy"},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"35","DOI":"10.1016\/j.nbt.2018.05.005","article-title":"Effects of copper and arsenic stress on the development of Norway spruce somatic embryos and their visualization with the environmental scanning electron microscope","volume":"48","author":"Trojan","year":"2019","journal-title":"New Biotechnol."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"014503","DOI":"10.1063\/1.5100852","article-title":"Vitrification and increase of basicity in between ice Ih crystals in rapidly frozen dilute NaCl aqueous solutions","volume":"151","author":"Gasser","year":"2019","journal-title":"J. Chem. Phys."},{"key":"ref_14","first-page":"39","article-title":"The impact of critical flow on the primary electron beam passage through differentially pumped chamber","volume":"6","author":"Maxa","year":"2011","journal-title":"Adv. Mil. Technol."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"1593","DOI":"10.1007\/s00706-012-0861-y","article-title":"Pressure dependence of the tin\u2013phosphorus phase diagram","volume":"143","author":"Ritscher","year":"2012","journal-title":"Monatshefte F\u00fcr Chem. Chem. Mon."},{"key":"ref_16","doi-asserted-by":"crossref","unstructured":"Stelate, A., Tihla\u0159\u00edkov\u00e1, E., Schwarzerov\u00e1, K., Ned\u011bla, V., and Petr\u00e1\u0161ek, J. (2021). Correlative Light-Environmental Scanning Electron Microscopy of Plasma Membrane Efflux Carriers of Plant Hormone Auxin. Biomolecules, 11.","DOI":"10.3390\/biom11101407"},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"2468","DOI":"10.3390\/s23052468","article-title":"A Method for Detecting the Vacuum Degree of Vacuum Glass Based on Digital Holography","volume":"23","author":"Li","year":"2023","journal-title":"Sensors"},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"1834","DOI":"10.1007\/s12010-014-1174-x","article-title":"Physical and Bioengineering Properties of Polyvinyl Alcohol Lens-Shaped Particles Versus Spherical Polyelectrolyte Complex Microcapsules as Immobilisation Matrices for a Whole-Cell Baeyer\u2013Villiger Monooxygenase","volume":"174","author":"Gemeiner","year":"2014","journal-title":"Appl. Biochem. Biotechnol."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"150295","DOI":"10.1063\/5.0150295","article-title":"Performance of double expansion ramp nozzle","volume":"35","author":"Rathakrishnan","year":"2023","journal-title":"Phys. Fluids"},{"key":"ref_20","doi-asserted-by":"crossref","unstructured":"Dutta, P.P., Benken, A.C., Li, T., Ordonez-Varela, J.R., and Gianchandani, Y.B. (2023). Passive Wireless Pressure Gradient Measurement System for Fluid Flow Analysis. Sensors, 23.","DOI":"10.3390\/s23052525"},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"151","DOI":"10.3849\/aimt.01268","article-title":"Analysis of impact of conic aperture in differentially pumped chamber","volume":"14","author":"Maxa","year":"2019","journal-title":"Adv. Millitary Technol."},{"key":"ref_22","doi-asserted-by":"crossref","unstructured":"Maxa, J., Ned\u011bla, V., \u0160aback\u00e1, P., and Binar, T. (2023). Impact of Supersonic Flow in Scintillator Detector Apertures on the Resulting Pumping Effect of the Vacuum Chambers. Sensors, 23.","DOI":"10.3390\/s23104861"},{"key":"ref_23","doi-asserted-by":"crossref","unstructured":"Xue, Z., Zhou, L., and Liu, D. (2023). Accurate Numerical Modeling for 1D Open-Channel Flow with Varying Topography. Water, 15.","DOI":"10.3390\/w15162893"},{"key":"ref_24","doi-asserted-by":"crossref","unstructured":"Liu, Q., and Feng, X.-B. (2020). Numerical Modelling of Microchannel Gas Flows in the Transition Flow Regime Using the Cascaded Lattice Boltzmann Method. Entropy, 22.","DOI":"10.3390\/e22010041"},{"key":"ref_25","unstructured":"Salga, J., and Ho\u0159en\u00ed, B. (1997). Tabulky Proud\u011bn\u00ed Plynu, UNOB."},{"key":"ref_26","doi-asserted-by":"crossref","unstructured":"Th\u00e9venin, D., and Janiga, G. (2008). Optimization and Computational Fluid Dynamics, Springer. [1st ed.].","DOI":"10.1007\/978-3-540-72153-6"},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"84110","DOI":"10.1063\/5.0157903","article-title":"Lattice Boltzmann simulations of flow inside a converging and diverging nozzle with the insertion of single and multiple circular cylinders","volume":"35","author":"Yadav","year":"2023","journal-title":"Phys. Fluids"},{"key":"ref_28","first-page":"562","article-title":"Numerical Study of The Effect of Wall Injection on The Cavitation Phenomenon In Diesel Injector","volume":"8","author":"Hassanzadeh","year":"2014","journal-title":"Eng. Appl. Comput. Fluid Mech."},{"key":"ref_29","first-page":"952","article-title":"Efficacy of applying discontinuous boundary condition on the heat transfer and entropy generation through a slip microchannel equipped with nanofluid","volume":"16","author":"Liu","year":"2022","journal-title":"Eng. Appl. Comput. Fluid Mech."},{"key":"ref_30","unstructured":"Moran, M.J., and Shapiro, H.N. (1998). Fundamentals of Engineering Thermodynamics, Wiley. [3rd ed.]."},{"key":"ref_31","unstructured":"\u0160korp\u00edk, J. (2023). Transforma\u010dn\u00ed Technologie: Proud\u011bn\u00ed Plyn\u016f a Par Tryskami, [2nd ed.]."},{"key":"ref_32","unstructured":"Uruba, V. (2014). Trbulence, \u010cVUT v Praze, Fakulta strojn\u00ed. [2nd ed.]."},{"key":"ref_33","doi-asserted-by":"crossref","unstructured":"Baehr, H.D., and Kabelac, S. (2009). Thermodynamik, Springer. [14th ed.].","DOI":"10.1007\/978-3-642-00556-5"},{"key":"ref_34","unstructured":"(2022, October 21). Ansys Fluent Theory Guide. Available online: www.ansys.com."},{"key":"ref_35","doi-asserted-by":"crossref","unstructured":"Barth, T., and Jespersen, D. (1989, January 9\u201312). The design and application of upwind schemes on unstructured meshes. Proceedings of the 27th Aerospace Sciences Meeting, Reno, NV, USA.","DOI":"10.2514\/6.1989-366"},{"key":"ref_36","doi-asserted-by":"crossref","unstructured":"Li, X., Wu, Y., Shan, X., Zhang, H., and Chen, Y. (2023). Estimation of Airflow Parameters for Tail-Sitter UAV through a 5-Hole Probe Based on an ANN. Sensors, 23.","DOI":"10.3390\/s23010417"},{"key":"ref_37","doi-asserted-by":"crossref","unstructured":"Bayer, R., Maxa, J., and \u0160aback\u00e1, P. (2021). Energy Harvesting Using Thermocouple and Compressed Air. Sensors, 21.","DOI":"10.3390\/s21186031"},{"key":"ref_38","first-page":"151556","article-title":"Flow structure and parameter evaluation of conical convergent\u2013divergent nozzle supersonic jet flows","volume":"35","author":"Xiao","year":"2023","journal-title":"Phys. Fluids"},{"key":"ref_39","doi-asserted-by":"crossref","unstructured":"\u0160aback\u00e1, P., Maxa, J., Bayer, R., Vyroubal, P., and Binar, T. (2022). Slip Flow Analysis in an Experimental Chamber Simulating Differential Pumping in an Environmental Scanning Electron Microscope. Sensors, 22.","DOI":"10.3390\/s22239033"},{"key":"ref_40","unstructured":"Dej\u010d, M.J. (1967). Technick\u00e1 Dynamika Plyn\u016f, SNTL."},{"key":"ref_41","unstructured":"Uruba, V. (2006). Metody Anal\u00fdzy Sign\u00e1l\u016f P\u0159i Studio Nestacion\u00e1rn\u00edch Jev\u016f v Proud\u00edc\u00edch Tekutin\u00e1ch, Habilita\u010dn\u00ed Pr\u00e1ce."},{"key":"ref_42","doi-asserted-by":"crossref","first-page":"369","DOI":"10.1149\/08701.0369ecst","article-title":"Analysis of Pitot Tube Static Probe Angle in the Experimental Chamber Conditions","volume":"87","author":"Maxa","year":"2018","journal-title":"ECS Trans."},{"key":"ref_43","unstructured":"Bryer, D.W., and Pankhurst, R.C. (1971). Pressure-Probe Methods for Determining Wind Speed and Flow Direction, Her Majesty\u2019s Stationery Office. [1st ed.]."},{"key":"ref_44","doi-asserted-by":"crossref","first-page":"147","DOI":"10.1016\/0376-0421(75)90014-7","article-title":"Pressure probes for fluid measurement","volume":"16","author":"Chue","year":"1975","journal-title":"Prog. Aerosp. Sci."},{"key":"ref_45","doi-asserted-by":"crossref","unstructured":"Pieni\u0105\u017cek, J., Cieci\u0144ski, P., Ficek, D., and Szumski, M. (2023). Dynamic Response of the Pitot Tube with Pressure Sensor. Sensors, 23.","DOI":"10.3390\/s23052843"},{"key":"ref_46","first-page":"274","article-title":"Principal Parameters in Flow Separation Patterns of Over-Expanded Single Expansion RAMP Nozzle","volume":"8","author":"Yu","year":"2014","journal-title":"Eng. Appl. Comput. Fluid Mech."},{"key":"ref_47","first-page":"1902","article-title":"A prediction model of wall shear stress for ultra-high-pressure water-jet nozzle based on hybrid BP neural network","volume":"16","author":"Chen","year":"2022","journal-title":"Eng. Appl. Comput. Fluid Mech."},{"key":"ref_48","doi-asserted-by":"crossref","unstructured":"Reimer, L. (1985). Scanning Elektron Microscopy: Physics of Image Formation and Microanalysis, Springer.","DOI":"10.1007\/978-3-662-13562-4"},{"key":"ref_49","unstructured":"Frank, L., and Kr\u00e1l, J. (2002). Metody Anal\u00fdzy Povrch\u016f: Iontov\u00e9, Sondov\u00e9 a Speci\u00e1ln\u00ed Metody, Academia."},{"key":"ref_50","doi-asserted-by":"crossref","unstructured":"Mart\u00ednez-Gonz\u00e1lez, A., Moreno-Hern\u00e1ndez, D., Guerrero-Viramontes, J.A., Le\u00f3n-Rodr\u00edguez, M., Zamarripa-Ram\u00edrez, J.C.I., and Carrillo-Delgado, C. (2019). Temperature Measurement of Fluid Flows by Using a Focusing Schlieren Method. Sensors, 19.","DOI":"10.20944\/preprints201811.0455.v1"},{"key":"ref_51","first-page":"29","article-title":"Weak Versus Strong No-Slip Boundary Conditions for the Navier-Stokes Equations","volume":"4","author":"Abbas","year":"2010","journal-title":"Eng. Appl. Comput. Fluid Mech."},{"key":"ref_52","first-page":"70","article-title":"Cavitation in Injector Nozzle Holes\u2014A Parametric Study","volume":"8","author":"Mohan","year":"2014","journal-title":"Eng. Appl. Comput. Fluid Mech."},{"key":"ref_53","first-page":"412","article-title":"CFD Study of Effects of Geometry Variations on Flow in a Nozzle","volume":"6","author":"Yu","year":"2012","journal-title":"Eng. Appl. Comput. Fluid Mech."}],"container-title":["Sensors"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1424-8220\/24\/7\/2166\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T14:20:05Z","timestamp":1760106005000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1424-8220\/24\/7\/2166"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024,3,28]]},"references-count":53,"journal-issue":{"issue":"7","published-online":{"date-parts":[[2024,4]]}},"alternative-id":["s24072166"],"URL":"https:\/\/doi.org\/10.3390\/s24072166","relation":{},"ISSN":["1424-8220"],"issn-type":[{"type":"electronic","value":"1424-8220"}],"subject":[],"published":{"date-parts":[[2024,3,28]]}}}