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Multiscale Modeling of Porous Media
Published in Peng Xu, Agus P. Sasmito, Arun S. Mujumdar, Heat and Mass Transfer in Drying of Porous Media, 2020
Peng Xu, Arun S. Mujumdar, Agus P. Sasmito, Boming Yu
where λ is the pore diameter. The Knudsen number, which is defined as the ratio of the gas molecule's mean free path to the diameter Kn=l/λ, can be used as an indicator to evaluate the effect of Knudsen diffusion.
Molecular Collisions
Published in Igor Bello, Vacuum and Ultravacuum, 2017
The regions of pressure dependence, for example, damping oscillations of a torsion disc pendulum, can be estimated taking into account the values of the Knudsen number. The boundaries between different regimes of damping the disc oscillations are not sudden, which can be illustrated on a simple example. At conditions where Kn = 1, that is, L = D, there is a large fraction of molecules (~30%) that makes direct wall-to-wall collisions, while the remaining molecular portion (70%) makes volume collisions. To reduce the portion of molecules making the volume collisions to 1%, the Knudsen number has to be reduced from L/D = 1 to L/D ≈ 4.6 as determined from the equation for distribution of molecules according to free molecular paths (n/n0 = e−L/D = e−4.6 ≈ 0.01). The Knudsen number has often been used as a criterion to categorize the gas flow regimes to (1) low-vacuum or continuum regime when the Knudsen number Kn < 0.01, (2) slip flow regime when 0.01 < Kn < 0.1, (3) transition flow regime when 0.1 < Kn < 4, and (4) free molecular (or just molecular) regime when Kn > 4.
Fundamentals of Microscale Convection
Published in C. B. Sobhan, G. P. Peterson, Microscale and Nanoscale Heat Transfer, 2008
The most established criterion to decide whether the analytical approach to a fluid flow problem could be the continuum approach or a discrete calculation method is the magnitude of the Knudsen number (Zohar 2006). The Knudsen number is defined as the ratio between the molecular mean free path of the fluid under consideration and the characteristic length scale for the flow domain. The Knudsen number is given by () Kn=ΛL
Free vibration and instability analysis of a viscoelastic micro-shell conveying viscous fluid based on modified couple stress theory in thermal environment
Published in Mechanics Based Design of Structures and Machines, 2022
Kaveh Rashvand, Akbar Alibeigloo, Mehran Safarpour
In order to classify the various fluid flow regime, the influence of Knudsen number () is taken into account which defined as the ratio of the mean-free-path of the molecules to a characteristic length scale. The radius of the micro/nano-shell is assumed as the characteristic length scale. According to the value of the Knudsen number, four fluid flow regimes are defined as: continuum flow regime (), slip flow regime (), transition flow regime () and free molecular flow regime () (Ghorbanpour Arani et al. 2014). In the micro/nano-shell, Knudsen number may be larger than 0.01 means in the range of slip flow regime. Therefore, the assumption of no-slip conditions is not validated, and the axial fluid velocity should be modified by the velocity correction factor (VCF) as follow (Ghorbanpour Arani et al. 2014) in which VCF can be obtained as follows
Aerodynamic characteristics of the evacuated tube maglev train considering the suspension gap
Published in International Journal of Rail Transportation, 2022
Peng Zhou, Deng Qin, Jiye Zhang, Tian Li
According to Knudsen number, the flow can be divided into four types consisting of continuous flow (0< Kn<0.01), slip flow (0.01≤ Kn<0.1), transition flow (0.1≤ Kn<10) and free molecular flow (Kn≥0.1).To judge the flow type induced by ETMT, the suspension gap can usually be taken as the characteristic length. As the ambient pressure and temperature remain unchanged, the Knudsen number decreases with the suspension gap increasing and vice versa. Under the initial environment with the temperature of 300 K and pressure of 0.01 atm, if Knudsen number is just 0.01, the corresponding characteristic length is 0.075 mm, far less than the suspension gap of 25 mm. Based on the initial Knudsen number in such a state, the flow caused by ETMT can be considered as continuous flow.
Study of Shock Structures Using the Unified Gas-Kinetic Wave-Particle Method with Various BGK Models
Published in International Journal of Computational Fluid Dynamics, 2022
Guochao Fan, Wenwen Zhao, Zhongzheng Jiang, Weifang Chen
The Knudsen number (Kn), defined as the ratio of the molecular mean free path to the object characteristic length, is used to preliminarily evaluate the degree of gas rarefaction and distinguish the flow regime from continuum flow to free molecular flow correspondingly. As Kn increases, beyond the hydrodynamic scale, the widely used Navier–Stokes equations with linear constitutive relations become incompetent in those non-equilibrium flows due to the breakdown of continuum assumption. For example, Navier–Stokes equations cannot correctly reproduce the behaviour of shock thickness for increasing Mach number (Gilbarg and Paolucci 1953). As the foundation of gas-kinetic theory, however, the Boltzmann equation is capable of describing the non-equilibrium processes from continuum flow to free molecular flow. After this kinetic equation is formed, the crucial problem in academia is how to solve it accurately and efficiently.