Thermally driven pumps and diodes in multistage assemblies consisting of microchannels with converging, diverging and uniform rectangular cross sections

Tatsios, Giorgos; Valougeorgis, Dimitris; Rojas-Cárdenas, Marcos; Baldas, Lucien; Barrot-Lattes, Christine; Colin, Stéphane

doi:10.1007/s10404-020-02357-z

Cited by 8 publications

(4 citation statements)

References 57 publications

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“…Using the variational principle described in Refs. [34,35], one can prove that the functional J( h) attains its stationary (minimum) value when h = h(x, c) solves Equation (9) with the boundary conditions (10). If we let h = h, Equation (13) reduces to:…”

Section: The Variational Approach To Plane Poiseuille and Thermal-cre...mentioning

confidence: 99%

“…In the last decades, the property of the TPD generation, due to a temperature gradient applied to a surface, started to be used for the development of microdevices like micro gas sensors [5,6], micropumps without moving parts and lubricant fluids [7][8][9][10] and micro gas chromatography columns [11][12][13]. The information about the TPD can also be used to calculate several physical quantities as the Eucken factor, the rotational collision number [14] and the heat conductivities of polar and non-polar polyatomic gases [15].…”

Section: Introductionmentioning

confidence: 99%

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Extraction of Tangential Momentum and Normal Energy Accommodation Coefficients by Comparing Variational Solutions of the Boltzmann Equation with Experiments on Thermal Creep Gas Flow in Microchannels

Missoni

Yamaguchi

Graur

et al. 2021

Fluids

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In the present paper, we provide an analytical expression for the first- and second-order thermal slip coefficients, σ1,T and σ2,T, by means of a variational technique that applies to the integrodifferential form of the Boltzmann equation based on the true linearized collision operator for hard-sphere molecules. The Cercignani-Lampis scattering kernel of the gas-surface interaction has been considered in order to take into account the influence of the accommodation coefficients (αt, αn) on the slip parameters. Comparing our theoretical results with recent experimental data on the mass flow rate and the slip coefficient for five noble gases (helium, neon, argon, krypton, and xenon), we found out that there is a continuous set of values for the pair (αt, αn) which leads to the same thermal slip parameters. To uniquely determine the accommodation coefficients, we took into account a further series of measurements carried out with the same experimental apparatus, where the thermal molecular pressure exponent γ has been also evaluated. Therefore, the new method proposed in the present work for extracting the accommodation coefficients relies on two steps. First of all, since γ mainly depends on αt, we fix the tangential momentum accommodation coefficient in such a way as to obtain a fair agreement between theoretical and experimental results. Then, among the multiple pairs of variational solutions for (αt, αn), giving the same thermal slip coefficients (chosen to closely approximate the measurements), we select the unique pair with the previously determined value of αt. The analysis carried out in the present work confirms that both accommodation coefficients increase by increasing the molecular weight of the considered gases, as already highlighted in the literature.

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Section: The Variational Approach To Plane Poiseuille and Thermal-cre...mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Extraction of Tangential Momentum and Normal Energy Accommodation Coefficients by Comparing Variational Solutions of the Boltzmann Equation with Experiments on Thermal Creep Gas Flow in Microchannels

Missoni

Yamaguchi

Graur

et al. 2021

Fluids

View full text Add to dashboard Cite

show abstract

“…Milićev and Stevanović [109] recently provided an analytical solution for the steady pressure driven flow of viscous compressible isothermal gas through constant or slowly-varying cross-section microchannels and Quesada et al [110] computationally studied the phenomenon of thermal transpiration-which was explained in the 'introduction' section-in multi-stage Knudsen pumps. In this paper, it is suggested that due to the broad applications of thermal pumps in industry and recent advances in the microfabrication technology, there is room to investigate alternative pump designs.…”

Section: Converging or Diverging Channelsmentioning

confidence: 99%

A review of rarefied gas flow in irregular micro/nanochannels

Taassob

Bordbar

Kheirandish

et al. 2021

J. Micromech. Microeng.

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In today’s complex micro–electro–mechanical systems (MEMS), investigation of flow through irregular micro/nanochannels, such as bended channels, variable cross-sectional area channels, and those with rough surfaces, can contribute considerably to efficient designing of the microdevices and to gain a better understanding of the flow structure in these geometries. The present paper reviews the prominent studies published in literature on rarefied gas flow through these types of complex geometries. The main focus of the study is to explore the physical aspects of the findings and the analyses provided in support of the results. Finally, the areas in which a gap exists in literature and could be subjects of future studies are introduced.

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“…Furthermore, the temperature gradients can be adjusted by changing input power so as to control the gas flow rate [12,13]. In order to observe thermal creep flow phenomena in the numerical simulations, the two extremities of the channel are assumed as isothermal walls at different temperatures, and the temperatures of the channel walls are linearly distributed [16,18,30].…”

Section: Introductionmentioning

confidence: 99%

Numerical Investigation into the Flow Characteristics of Gas Mixtures in Knudsen Pump with Variable Soft Sphere Model

Wang

Han

et al. 2020

Micromachines

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In Knudsen pumps with geometric configuration of rectangle, gas flows are induced by temperature gradients along channel walls. In this paper, the direct simulation Monte Carlo (DSMC) method is used to investigate numerically the flow characteristics of H2–N2 mixtures in the Knudsen pump. The variable soft sphere (VSS) model is applied to depict molecular diffusion in the gas mixtures, and the results obtained are compared with those calculated from a variable hard sphere (VHS) model. It is demonstrated that pressure is crucial to affecting the variation of gas flow pattern, but the gas concentration in H2–N2 mixtures and the collision model do not change the flow pattern significantly. On the other hand, the velocity of H2 is larger than that of N2. The velocities of H2 and N2 increase if the concentration of H2 rises in the gas mixtures. The results of velocity and mass flow rate obtained from VSS and VHS models are different. Finally, a linear relation between the decrease of mass flow rate and the increase of H2 concentration is proposed to predict the mass flow rate in H2–N2 mixtures.

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Thermally driven pumps and diodes in multistage assemblies consisting of microchannels with converging, diverging and uniform rectangular cross sections

Cited by 8 publications

References 57 publications

Extraction of Tangential Momentum and Normal Energy Accommodation Coefficients by Comparing Variational Solutions of the Boltzmann Equation with Experiments on Thermal Creep Gas Flow in Microchannels

Extraction of Tangential Momentum and Normal Energy Accommodation Coefficients by Comparing Variational Solutions of the Boltzmann Equation with Experiments on Thermal Creep Gas Flow in Microchannels

A review of rarefied gas flow in irregular micro/nanochannels

Numerical Investigation into the Flow Characteristics of Gas Mixtures in Knudsen Pump with Variable Soft Sphere Model

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