Slip Flow Analysis in an Experimental Chamber Simulating Differential Pumping in an Environmental Scanning Electron Microscope

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This paper presents mathematical-physics analyses in the field of the influence of inserted sensors on the supersonic flow behind the nozzle. It evaluates differences in the flow in the area of atmospheric pressure and low pressure on the boundary of continuum mechanics. To analyze the formation of detached and conical shock waves and their distinct characteristics in atmospheric pressure and low pressure on the boundary of continuum mechanics, we conduct comparative analyses using two types of inserted sensors: flat end and tip. These analyses were performed in two variants, considering pressure ratios of 10:1 both in front of and behind the nozzle. The first variant involved using atmospheric pressure in the chamber in front of the nozzle. The second type of analysis was conducted with a pressure of 10,000 Pa in front of the nozzle. While this represents a low pressure at the boundary of continuum mechanics, it remains above the critical limit of 113 Pa. This deliberate choice was made as it falls within the team’s research focus on low-pressure regions. Although it is situated at the boundary of continuum mechanics, it is intentionally within a pressure range where the viscosity values are not yet dependent on pressure. In these variants, the nature of the flow was investigated concerning the ratio of inertial and viscous flow forces under atmospheric pressure conditions, and it was compared with flow conditions at low pressure. In the low-pressure scenario, the ratio of inertial and viscous flow forces led to a significant reduction in the value of inertial forces. The results showed an altered flow character, characterized by a reduced tendency for the formation of cross-oblique shockwaves within the nozzle itself and the emergence of shockwaves with increased thickness. This increased thickness is attributed to viscous forces inhibiting the thickening of the shockwave itself. This altered flow character may have implications, such as influencing temperature sensing with a tipped sensor. The shockwave area may form in a very confined space in front of the tip, potentially impacting the results. Additionally, due to reduced inertial forces, the cone shock wave’s angle is a few degrees larger than theoretical predictions, and there is no tilting due to lower inertial forces. These analyses serve as the basis for upcoming experiments in the experimental chamber designed specifically for investigations in the given region of low pressures at the boundary of continuum mechanics. The objective, in combination with mathematical-physics analyses, is to determine changes within this region of the continuum mechanics boundary where inertial forces are markedly lower than in the atmosphere but remain under the influence of unreduced viscosity.

Section: Methodsmentioning

confidence: 99%

Section: Experimental Chambermentioning

confidence: 99%

Comparative Analysis of Supersonic Flow in Atmospheric and Low Pressure in the Region of Shock Waves Creation for Electron Microscopy

Šabacká,

Maxa,

Bayer

et al. 2023

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“…A characteristic sign of the ESEM chambers is chambers separated by small apertures with great pressure gradients. A flow in such apertures separating chambers with significant pressure differences has peculiar physics properties and goes by the term of critical flow [ 22 , 23 , 24 ]. When the pressure gradients on both sides of an aperture differ, a flow going from the place with the higher pressure to the one with the lower pressure occurs.…”

Section: Theory Of Critical Flowmentioning

confidence: 99%

“…The form of the resulting mesh is in Figure 19. Due to the very low Reynolds numbers due to low pressure, the laminar flow was set with the low-pressure boundary slip option, tested experimentally also in [23].…”

Section: Variant 900 Pa In the Specimen Chambermentioning

confidence: 99%

“…It is a series of follow-up experiments and mathematical physics analyses gradually investigating conditions at the boundary of continuum mechanics for use in ESEM. Due to the very low Reynolds numbers due to low pressure, the laminar flow was set with the low-pressure boundary slip option, tested experimentally also in [23].…”

Section: Variant 900 Pa In the Specimen Chambermentioning

confidence: 99%

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Impact of Supersonic Flow in Scintillator Detector Apertures on the Resulting Pumping Effect of the Vacuum Chambers

Maxa

Neděla

Šabacká

et al. 2023

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The article describes the combination of experimental measurements with mathematical–physics analyses in flow investigation in the chambers of the scintillator detector, which is a part of the environmental scanning electron microscope. The chambers are divided with apertures by small openings that keep the desirable pressure differences between three chambers: The specimen chamber, the differentially pumped intermediate chamber, and the scintillator chamber. There are conflicting demands on these apertures. On the one hand, the diameter of the apertures must be as big as possible so that they incur minimal losses of the passing secondary electrons. On the other hand, it is possible to magnify the apertures only to a certain extent so the rotary and turbomolecular vacuum pump can maintain the required operating pressures in separate chambers. The article describes the combination of experimental measurement using an absolute pressure sensor and mathematical physics analysis to map all the specifics of the emerging critical supersonic flow in apertures between the chambers. Based on the experiments and their tuned analyses, the most effective variant of combining the sizes of each aperture concerning different operating pressures in the detector is determined. The situation is made more difficult by the described fact that each aperture separates a different pressure gradient, so the gas flow through each aperture has its own characteristics with a different type of critical flow, and they influence each other, thereby influencing the final passage of secondary electrons detected by the scintillator and thus affecting the resulting displayed image.

The Impact of Nozzle Opening Thickness on Flow Characteristics and Primary Electron Beam Scattering in an Environmental Scanning Electron Microscope

Maxa,

Šabacká,

Mazal

et al. 2024

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This paper describes the methodology of combining experimental measurements with mathematical–physics 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’s 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–physical analysis in the Ansys Fluent system is described.