Flow Path Research Articles

Estimation of Effective Fracture Aperture in Glacial Tills by Analysis of Dye Tracer Penetration.

This study advances a methodology to estimate effective apertures of fractures in glacial tills based on dye tracer infiltration tests and numerical simulations. The approach uses the visible penetration depth of the dye tracer along fracture flow paths as primary information to calculate effective fracture apertures. Further data used in the calculation are the dye tracer input concentration and retardation, the duration of the tracer injection, and the hydraulic gradient applied to control the infiltrating water fluxes. The method does not require measurement of hydraulic conductivity for the fractured till and enables direct observation of flow and transport patterns within the fractures (e.g., uniform flow and dye tracer distribution, channeling due to aperture variability, and presence of biogenic macropores in fractures). The approach was successfully verified by using the estimated effective fracture aperture values in Large Undisturbed Columns (LUCs) to consistently simulate both the observed LUC effluent breakthrough of a conservative bromide tracer and the water fluxes with the hydraulic gradient applied in the experiments. Sensitivity analyses revealed that estimation of small effective fracture apertures (<10 μm) required accurate determination of the dye tracer retardation factor. By contrast, in the case of larger effective apertures (>20 μm), the sensitivity of the estimated effective fracture aperture to variations in the porous material and solute transport parameters was low compared to the dominant sensitivity to the water flow through the fractures (cubic relation between flow and aperture). The proposed approach may be extended beyond laboratory applications and assist in characterizing field-scale fracture networks.

A five field formulation for flow simulations in porous media with fractures and barriers via an optimization based domain decomposition method

The present work deals with the numerical resolution of coupled 3D–2D problems arising from the simulation of fluid flow in fractured porous media modeled via the Discrete Fracture and Matrix (DFM) model. According to the DFM model, fractures are represented as planar interfaces immersed in a 3D porous matrix and can behave as preferential flow paths, in the case of conductive fractures, or can actually be a barrier for the flow, when, instead, the permeability in the normal-to-fracture direction is small compared to the permeability of the matrix. Consequently, the pressure solution in a DFM can be discontinuous across a barrier, as a result of the geometrical dimensional reduction operated on the fracture. The present work is aimed at developing a numerical scheme suitable for the simulation of the flow in a DFM with fractures and barriers, using a mesh for the 3D matrix non conforming to the fractures and that is ready for domain decomposition. This is achieved starting from a PDE-constrained optimization method, currently available in literature only for conductive fractures in a DFM. First, a novel formulation of the optimization problem is defined to account for non permeable fractures. These are described by a filtration-like coupling at the interface with the surrounding porous matrix. Also the extended finite element method with discontinuous enrichment functions is used to reproduce the pressure solution in the matrix around a barrier. The method is presented here in its simplest form, for clarity of exposition, i.e. considering the case of a single fracture in a 3D domain, also providing a proof of the well posedness of the resulting discrete problem. Four validation examples are proposed to show the viability and the effectiveness of the method.

A novel compact supercritical CO2 solar receiver based on impinging jet: Heat transfer performance and thermal stress analysis

The compact solar receiver can withstand high temperature and high pressure, which provides promising solutions for direct supercritical CO2 (S-CO2) solar receiver applications. However, it still suffers from local high temperature and large thermal stress due to the non-uniform heating boundary condition. The impinging jet method can significantly enhance the local heat transfer coefficient, holding significant potential in reducing the local high temperature of the compact S-CO2 receiver. Inspired by this, a novel design for a compact S-CO2 receiver using the impinging jet was proposed in this work. The heat transfer performance and stress behavior of the jet channel within the receiver were numerically investigated. The results showed that the jet channel has a significantly higher heat transfer performance than the rectangular channel, and the shorter flow path of the jet channel also effectively reduces the pressure loss. Meanwhile, the jet pattern significantly enhances the temperature uniformity, thereby reducing the thermal stress. In addition, increasing the channel aspect ratio improves the thermo-hydraulic performance, but increase the stress at the same time. The increase in the number of jet holes and the jet hole diameters not only enhance the thermo-hydraulic performance, but also reduce the stress of the jet channel.

Analysis and Optimization of the Flow Path within the Protonic Ceramic Fuel Cell Stack

With the development of human society, the demand for energy is increasing, and energy, an essential global necessity, is decreasing significantly and is in danger of being depleted. Fuel cell is the fourth power generation facility after hydroelectric, thermal and nuclear power. Fuel cell flow channel is an important part of fuel cell, which has the functions of transferring reaction gas, discharging products and excess unreacted gas, and balancing fuel cell temperature. This thesis focuses on the model design and optimization of a 10-layer flat-plate proton ceramic fuel cell (PCFC) reactor. First, we design a 10-layer flat-plate PCFC reactor model structure, then we simulate the reactor using Fluent, analyze the multi-field coupling operating characteristics inside the target reactor, optimize the reactor based on the results, and finally, we analyze and discuss the optimization results.

Impact of Solder Voids on IGBT Thermal Behavior: A Multi-Methodological Approach

This study investigates the thermal behavior of Insulated Gate Bipolar Transistors (IGBTs) with a focus on the influence of solder voids within the device. Utilizing a combination of Finite Element Method (FEM) simulations, X-ray imaging, and SEM-EDX analysis, we accurately modeled the internal structure of IGBTs to assess the impact of void characteristics on thermal resistance. The findings reveal that the presence and characteristics of solder voids—particularly their size, number, and distribution—significantly affect the thermal resistance of IGBT devices. Experimental measurements validate the FEM model’s accuracy, confirming that voids disrupt the heat flow path, which can lead to increased thermal resistance and potential device failure. Five regression models, including Gaussian process regression (GPR) and neural networks, were employed to predict the thermal resistance based on void characteristics, with the GPR models demonstrating superior performance. The optimal GPR RQ model consistently provided accurate predictions with an RMSE of 0.0050 and R2 of 0.9728. Using the void percentage as the only input parameter for the regression models significantly impacted the prediction accuracy, showing the importance of the void extraction method. This study shows the necessity of minimizing solder voids and offers a robust methodological framework for a better prediction of the reliability of IGBTs.

Complex hydrology and variability of nitrogen sources in a karst watershed.

Streams draining karst areas with rapid groundwater transit times may respond relatively quickly to nitrogen reduction strategies, but the complex hydrologic network of interconnected sinkholes and springs is challenging for determining the placement and effectiveness of management practices. This study aims to inform nitrogen reduction strategies in a representative agricultural karst setting of the Chesapeake Bay watershed (Fishing Creek watershed, Pennsylvania) with known elevated nitrate contamination and a previous documented groundwater residence time of less than a decade. During baseflow conditions, streamflow did not increase with drainage area. Headwaters and the main stem lost substantial flow to sinkholes until eventually discharging along large springs downstream. Seasonal hydrologic conditions shift the flow and nitrogen load spatially among losing and gaining stream sections. A compilation of nitrogen source inputs with the geochemistry and the pattern of enrichment of δ15N and δ18O suggest that the nitrogen in streams and springs during baseflow represents a mixture of manure, fertilizer, and wastewater sources with low potential for denitrification. The pH and calcite saturation index increased along generalized flow paths from headwaters to springs and indicate shorter groundwater residence times in baseflow during the spring versus summer. Given the substantial investment in management practices, fixed monitoring sites could incorporate synoptic water sampling to properly monitor long-term progress and help inform management actions in karst watersheds. Although karst watersheds have the potential to respond to nitrogen reduction strategies due to shorter groundwater residence times, high nitrogen inputs, effectiveness of conservation practices, and release of legacy nutrients within the karst cavities could confound progress of water quality goals.

Optimization of Cavitation Performance of High-Speed Centrifugal Pump Based on the Meta-Model of optimal Prognosis

Abstract Using a specific type of high-speed centrifugal pump as an example, this study conducted a parameterized optimization design on geometric parameters of the impeller’s flow path. A response sample space was generated with the flow path geometric parameters as input and pressure increment and cavitation volume as output. Based on the Meta-Model of optimal Prognosis, the optimal surrogate model was fitted, and a global sensitivity analysis was conducted. The results indicated that the impeller’s inlet edge parameter and mid-curve parameter had a significant impact on the pressure increment and cavitation volume of the pump. Using a genetic algorithm, the optimal flow path geometric parameters were obtained, and numerical simulation methods were applied to verify the obtained parameters. The results showed that after optimization, the pressure coefficient of the centrifugal pump increased by 0.035, and the cavitation performance improved by 22.28%. The impeller cavitation area and void volume were significantly reduced, and the flow path pressure distribution and flow state were improved.

Seasonal and spatial variations of water recharging in the Yangtze River using hydrogen and oxygen stable isotopes

Water and material cycles in rivers are controlled by diverse sources of recharge and flow paths, which exhibit spatial and temporal variations in the contributions of water sources and hydrologic processes. To assess the variation of water recharging, the stable isotope abundances of hydrogen and oxygen (δ2H and δ18O) of 152 water samples collected from the Yangtze River mainstream during May (the flat season) and September (the wet season) in 2021 were analyzed. Bayesian modelling was used to calculate the contribution rates of precipitation, glacier snow meltwater, and groundwater. The isotopic compositions of precipitation and the river exhibited comparable seasonal and spatial characteristics. The Bayesian model results showed that the mainstream was governed by precipitation, with a greater contribution of precipitation in the lower reaches during the wet season. Lakes had a larger contribution during the flat season, as evidenced by the greater increase in the magnitude of δ18O values in the mid-lower reaches during this period. The mid-lower reaches of the river had a decreased river evaporation line (REL) slope, which could be owe to lake replenishment. In addition to intensifying the seasonal variations in the contribution ratios of the lakes, the emplacement of the Three Gorges Dam (TGD) reduced the groundwater contribution of the reservoir. This study enhances our understanding of the hydrological and material cycles in the Yangtze River Basin and provides vital baseline knowledge on the contribution of different recharge sources in the mainstream.

Impact of Pressure-Dependent Interfacial Tension and Contact Angle on Capillary Heterogeneity Trapping of CO2 in Storage Aquifers

Summary Carbon dioxide (CO2) capillary trapping increases the total amount of CO2 that can be effectively immobilized in storage aquifers. This trapping, manifesting itself as accumulated CO2 columns at a continuum scale, is because of capillary threshold effects that occur below low-permeability barriers. Considering that capillary pressure is dictated by heterogeneous pore throat size, the trapped CO2 column height and associated CO2 saturation will vary spatially within a storage aquifer. This variation will be influenced by two pressure-dependent interfacial parameters—CO2/brine interfacial tension (IFT) and CO2/brine/rock contact angle. Our objective is to understand how the pressure dependence of these two parameters affects the heterogeneity of capillary trapped CO2 at a continuum scale. Our conceptual model is a 1D two-zone system with the upper zone being a flow barrier (low permeability) and the lower zone being a flow path (high permeability). The inputs to this model include microfacies-dependent capillary pressure vs. saturation curves and permeability values. The input capillary pressure curves were collected in the literature that represents carbonate microfacies (e.g., dolograinstone) in a prevalent formation in the Permian Basin. We then used the Leverett j-function to scale the capillary pressure curve for the two zones that are assigned with the same or different microfacies. During scaling, we considered the influence of pressure on both the IFT and contact angle of CO2/brine/dolomite systems. We varied the zone permeability contrast ratio from 2 to 50. We then assumed capillary gravity equilibriums and calculated the CO2 saturation buildup corresponding to various trapped CO2 column heights. The CO2 saturation buildup is defined as the CO2 saturation in the lower layer minus that in the upper one. We found that the saturation buildup can be doubled when varying pressure in a storage aquifer, after considering pressure-dependent IFT and contact angles. Thus, assuming these two parameters to be constant across such aquifers would cause large errors in the quantification of capillary trapping of CO2. The whole study demonstrates the importance of considering pressure-dependent interfacial properties in predicting the vertical distribution of capillary trapped CO2. It has important implications in developing a better understanding of leakage risks and consequent storage safety.

Transient temperature measurement of silicon carbide Schottky barrier diode based on thermal reflection.

In this article, we present a transient temperature detection device for silicon carbide (SiC) Schottky barrier diodes (SBDs) based on thermal reflection theory. We constructed a thermal reflection temperature measurement device based on a 530-nm green laser. This device is more suitable for transient temperature measurement of SiC SBDs than previous thermal reflection equipment. The accuracy of temperature measurement by our device was confirmed by comparison with the results of infrared thermal imaging. The high temporal resolution characteristics of the thermal reflection technology allowed the detection of millisecond-level transient temperature changes in SiC SBDs. In addition, we investigated the complementarity of transient temperature change curves during heating and cooling processes, as well as the reasons for the differences between these curves. Finally, we used the structural function method combined with the Bayesian deconvolution algorithm to obtain the thermal resistance along the heat flow path of the device and validated the results using an established thermal resistance testing method.

Design and thermal-hydraulic analysis of multi-target system with 100 MeV proton linear accelerator for the production of 67Cu and 68Ge radioisotopes

Radioisotopes are widely used in the fields of medicine, science, and industry. The growing demand for medical radioisotopes has driven research on alternative production methods. In particular, both isotopes of 67Cu and 68Ge play vital roles in the medical environment in many countries to be used in the radio-immunotherapy and the positron emission tomography imaging, respectively. This study designed a multi-target system consisting of two Zn and one Ga2O3 plates to enable simultaneous production of the medical radioisotopes 67Cu and 68Ge using 100 MeV proton beams. To understand the thermal effect on the multi-targets, we examined the distribution of energy absorbed in each solid plate target when exposed to an accelerated proton beam through the thermal-fluid analysis based on ANSYS simulation. For confirming thermal stability for two Zn targets and one Ga2O3 target, the modified water flow path inside the multi-target system was designed effectively with the controlled distribution of multiple sub-holes between main inlet and the following four channels. It was confirmed that the newly designed multi-target system of Zn and Ga2O3 solid plates shows higher thermal stability than the case of uniform distribution of water inlet, which means it could be exposed to a higher current beam of 7.57% to decrease the processing time.

Leakage flow mixing in shrouded axial turbines and its control strategies using casing optimization

The geometry of the shroud cavity, which accommodates the rotor shroud leakage flow, is very important due to its impact on the leakage flow path as well as the interaction between the leakage flow and mainstream. The research in this paper numerically investigates the potential for reducing the leakage loss by optimization to the casing. The spatial loss audit and the loss breakdown based on loss mechanisms undertaken in the first part of this study are the foundation to develop promising strategies for minimizing the leakage loss. The profiled casing in the exit cavity effectively deflects the leakage jet into the axial direction when it re-enters the mainstream. The mixing loss is significantly reduced due to the notable decrease in axial velocity disparity of the two streams. On this basis, the exit and inlet cavity are further shaped to both form a step. Reductions in the shroud leakage loss are achieved by alleviating the flow nonuniformity in the exit cavity and reducing the leakage flow rate, respectively. The work in this study contributes to the refinement of control methods for the shroud leakage loss.

Computational analysis of nasal airflow and its alteration by a nasal dilator

Nasal airflow obstruction correlates with several ailments, such as higher patency, increased friction at the mucosal wall or the so-called Little's area, improper air conditioning, and snoring. Nasal dilators are frequently employed, mainly due to their ease of access and use, combined with their non-permanent and non-surgical nature. Their overall efficacy, however, has not been clearly demonstrated so far, with some studies reporting conflicting outcomes, mainly because being based on subjective evaluations. This study employs Computational Fluid Dynamics simulations to analyze the flow inside a real nose, performs an objective assessment of a nasal dilator's effect in terms of airflow and air conditioning, reporting flow paths, friction levels, heat and water fluxes and detailed temperature and humidity distributions. Coincidentally, the studied nose presents a septal deviation, with one nostril being wider than the other. The tubes of the dilator used in both nostrils are identical, as with any standard commercial dilator. Consequently, the dilator widens one nostril, as intended, but results in an obstruction in the other. This allows simultaneously addressing two situations, the nominal function of the dilator, as well as an off-design case. Results indicate a 24 % increase in nasal patency in the design situation. The effect, however, is limited, as quantified by appropriate measures, such as the flow-generated friction at the nose surfaces and the temperature fluxes. Hence, the effect of such a dilator in nominal conditions is perhaps not as large as might be hoped. In the off-design situation, nasal resistance increases by 62 %, an undesirable effect, illustrating the consequences of using an inappropriate dilator.

Visualization Experimental Study on In-Situ Triggered Displacement Mechanism by Microencapsulated Polymer in Porous Media

Summary Polymer flooding in deep reservoir profile control presents challenges in balancing injectivity and effective mobility control. To address this, we propose a solution by utilizing a microencapsulated polymer that can be easily injected and thickens over time. However, limited research has been conducted on the flow characteristics and the impact on oil mobilization by such profile control agents. In this study, we approximately simulated the time-varying flow process of microencapsulated polymer through in-situ triggered experiments at high temperature and pressure. The flow characteristics and oil displacement mechanism of the microencapsulated polymer under different trigger times were analyzed, and the displacement efficiency during the triggered viscosity enhancement process in porous media was quantitatively evaluated. The experimental results reveal that microencapsulated polymer exhibits a dual mechanism of near-wellbore reservoir particle temporary plugging and deep formation consistency control mechanisms. The transient aggregation of capsule particles alters the flow path, intensifying after expansion. The interaction between the microcapsule particles and the partially released polymer further enhances the resistance-enhancing property of the solution. The viscosity-enhanced microencapsulated polymer fluid improves the displacement efficiency. Microscopic oil displacement and coreflooding experiments resulted in a decrease in oil saturation of 39.5 and 18.33%, respectively. This study provides valuable microscopic insights into the flow behavior and oil displacement performance of microencapsulated polymer, offering essential guidance for optimizing oil reservoir extraction strategies.

Turbulent flow field in maglev centrifugal blood pumps of CH-VAD and HeartMate III: secondary flow and its effects on pump performance.

Secondary flow path is one of the crucial aspects during the design of centrifugal blood pumps. Small clearance size increases stress level and blood damage, while large clearance size can improve blood washout and reduce stress level. Nonetheless, large clearance also leads to strong secondary flows, causing further blood damage. Maglev blood pumps rely on magnetic force to achieve rotor suspension and allow more design freedom of clearance size. This study aims to characterize turbulent flow field and secondary flow as well as its effects on the primary flow and pump performance, in two representative commercial maglev blood pumps of CH-VAD and HeartMate III, which feature distinct designs of secondary flow path. The narrow and long secondary flow path of CH-VAD resulted in low secondary flow rates and low disturbance to the primary flow. The flow loss and blood damage potential of the CH-VAD mainly occurred at the secondary flow path, as well as the blade clearances. By contrast, the wide clearances in HeartMate III induced significant disturbance to the primary flow, resulting in large incidence angle, strong secondary flows and high flow loss. At higher flow rates, the incidence angle was even larger, causing larger separation, leading to a significant decrease of efficiency and steeper performance curve compared with CH-VAD. This study shows that maglev bearings do not guarantee good blood compatibility, and more attention should be paid to the influence of secondary flows on pump performance when designing centrifugal blood pumps.

Groundwater recharge sources and mechanisms in the Ethiopian central Afar rift: Insights from isotopic and hydrogeochemical tracers.

Groundwater flow and recharge mechanisms in the central Afar rift and the associated western marginal grabens and Northwestern Plateau (NWP) are poorly understood because of the complex geology and spatial heterogeneity in the aquifer systems. The major aquifers in the region include the Oligocene and Pliocene to recent volcanics and recent alluvio-lacustrine sediments. We employed hydrogeochemical, stable isotopes of water (18O and 2H), and geological structures insights to identify groundwater recharge sources and mechanisms, aiming to develop a representative conceptual groundwater flow model. Water samples from groundwater and surface water were collected based on lithological/aquifer variation and geomorphological setup for isotope and hydrochemical analysis. Findings reveal distinct isotopic differences between the deep (>350 m) and shallow groundwater systems of the Afar rift, with deep systems showing relative isotopic depletion, indicating varying recharge sources. The deep groundwater exhibited a similar isotopic signature to that of the marginal grabens and NWP. The distribution of major ion chemistry and electric conductivity (EC) of groundwaters from the western plateau to the Afar rift show significant spatial variability. However, in some corridors of western parts of the rift, there is a clear geochemical evolution along the flow paths inferring groundwater flow continuity between aquifers. The results revealed the existence of preferential deep groundwater recharge from the NWP through the highly fractured linking zones, interacting fault zones in between the marginal grabens, to the deeper volcanic aquifers of the central Afar rift. The proposed groundwater flow model of this study illustrates the deep groundwater flow from the NWP to the Afar rift is primarily directed by the orientations of the faulted marginal grabens and the highly fractured interacting zones. This model is pivotal for understanding groundwater dynamics in similar continental rift environments, offering insights for effective groundwater management.

Vibration energy transfer in forced laminated composite box structure

This study investigates the dynamics of laminated composite box structures from the viewpoint of energy flow transmission. Using a substructure-based technique, the power flow and dynamic responses are defined and obtained. The relationship between natural frequencies and the fiber orientations is explored. The influence of excitation frequencies, fiber angles, and boundary conditions on power flow and energy transmission paths (ETPs) is examined. The fiber orientations of box structure and boundary conditions are shown to have a substantial impact on ETPs and the positions of sinks. By modifying fiber angles, vibration suppression of box structure can be achieved.

Ultrasensitive, Highly Stable, and Stretchable Strain Sensor Using Gated Liquid Metal Channel

AbstractDeveloping stretchable strain sensors with high sensitivity and stability is crucial for various applications such as prosthetic hands, human health monitoring, and human‐machine interactions. However, achieving these qualities simultaneously remains challenging. Here, an inherently stretchable strain sensor is presented that integrates ultrahigh sensitivity and robust stability, enabling stretch, press, or bend sensing capabilities. This sensor employs a softer elastomeric channel filled with liquid metal (LM) as the conductive path. A stiffer elastomer convex integrated into the channel serves as a strain‐manipulated gate, controlling opening gap of electrical current flow path. During deformation, the softer elastomer undergoes cross sectional reduction due to the Poisson effect, while the stiffer convex gate retains its geometry. This heterogeneous deformation behavior leads to significant contraction or closure of the LM channel, resulting in increased resistance and a remarkable enhancement in sensitivity by more than two orders of magnitude. The all‐soft design maintains exceptional stability even under extended or repetitive substantial deformations. With the ability to monitor subtle and large human body movements, detect grip actions of soft grippers reliably, and monitor the gradual and extended growth process of plants, this sensor holds significant potential for advancements in flexible electronics.

Delayed diagnosis of ocular graft-versus-host disease after allogeneic hematopoietic stem cell transplantation

PurposeTo investigate the delayed diagnosis of chronic ocular graft-versus-host disease (coGVHD) after allogeneic hematopoietic stem cell transplantation (alloHCT), and further analyze potential confounding factors. MethodsThis cross-sectional study included 118 patients newly diagnosed as coGVHD after alloHCT at Zhongshan Ophthalmic Center, Sun Yat-sen University. All participants finished the flow path of medical history taking, detailed ophthalmological examination and questionnaire-based survey. coGVHD was diagnosed and graded by International Chronic Ocular GVHD Consensus Group (ICOGCG) criteria. Lag time of diagnosis was defined as interval between noting of ocular symptoms and confirmed diagnosis of coGVHD (TN-D). We further compared the clinical parameters between groups categorized by the median TN-D as medium and long delay groups. ResultsThe median TN-D was 6.3 [IQR 2.8–14.5] months. Most coGVHD patients underwent delayed diagnosis of coGVHD longer than 3 months (70 %, 83 of 118), with 90 of 118 diagnosed as severe coGVHD (76 %). The long delay group exhibited higher ICOGCG scores (10 [IQR 9–10.5] vs. 9 [IQR 8–10], P = 0.039) and more pronounced ocular signs, including conjunctival injection, meibomian gland loss, fibrotic tarsal conjunctiva, symblepharon, and corneal complications (all P < 0.05). Delayed diagnosis was strikingly correlated with seeking ophthalmic medical care twice or more prior to diagnosis (adjusted OR = 5.42, 95%CI: 1.40–21.06, P = 0.015) and accurate knowledge of ocular discomfort symptoms in coGVHD (adjusted OR = 0.29, 95%CI: 0.08–1.00, P = 0.050). ConclusionsDelayed diagnosis of coGVHD, associated with disease severity, was common among alloHCT recipients in southern China. Improving patient education and the awareness of ophthalmologists may facilitate early diagnosis of coGVHD.

Development of a simple calculation method for the conductance of rarefied gas flow in cylindrical pipe applicable to divertor exhaust investigation of nuclear fusion reactor

ABSTRACT A gas pressure distribution calculation method for viscous laminar and intermediate flows is developed. By introducing the pseudo-conductance for viscous laminar flow, linearized equations describing pressure distribution are obtained. In intermediate flow, the pressure distribution is iteratively obtained. The validity of the method is confirmed by demonstrating a pressure in a long-tube flow path with various flow rates. The result smoothly connects theoretical curves of molecular flow and viscous laminar flow between two regions. Then, the calculation method is applied to an actual device and is compared to the measurement. The comparison between the calculation and measurement shows the qualitative agreement and reveals the requirement for a more detailed implementation of the actual conditions.