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Gas Filled Membrane Pores – Fundamentals and Applications
Published in Anil K. Pabby, S. Ranil Wickramasinghe, Kamalesh K. Sirkar, Ana-Maria Sastre, Hollow Fiber Membrane Contactors, 2020
A. Sengupta, S. Ranil Wickramasinghe
Self-diffusivity is a measure of the translational mobility of individual molecules. Under thermodynamic equilibrium, a molecule is tagged, and its trajectory followed over a long time. In the case of diffusive motion, and a medium having no long-range correlations, the squared displacement of the molecule from its original position will grow linearly with time as suggested by Einstein’s equation. To reduce statistical errors in simulations, the self-diffusivity of a species is defined from ensemble averaging Einstein’s equation over a large enough number of molecules. Knudsen diffusion is applicable only to gases, since the mean free path for molecules in the liquid state is too small and near the diameter of the molecule itself. Figure 14.10 illustrates the different diffusion mechanisms.
2 Permeation and Separation
Published in Zeinab Abbas Jawad, 2 Sequestration and Separation, 2019
Thiam Leng Chew, Tiffany Yit Siew Ng, Yin Fong Yeong
Knudsen diffusion happens through the pores in the porous inorganic membrane having diameter, dp, smaller than the mean free path, λ, of the gas molecules in the gas phase (Park 2013). When the Knudsen number (λ/d) is greater than one, the collision frequency between the molecules inside the narrow pore channels with the wall is much higher than the collision frequency between gas molecules themselves. Under the scenario where Knudsen diffusion is predominant, the diffusion rate of different gas molecules is inversely proportional to the square root of the molecular weights of the gas molecules. In another way, lower molecular weight gas molecules can diffuse faster than those with higher molecular weight. If the Knudsen number is relatively small, both collisions between gas molecules themselves, and between gas molecules and pore walls will be rate determined (Shekhawat et al. 2003).
K
Published in Carl W. Hall, Laws and Models, 2018
Keywords: capillary, flow, gas, molecular flow, rate KNUDSEN, Martin Hans Christian, 1871-1949, Danish physicist Sources: NUC; Thewlis, J. 1961-1964. KNUDSEN NUMBER, Kn OR NKn A dimensionless group applicable to low-pressure gas flow or rarefied gas flow that relates the mean free path of gaseous diffusion, such as in drying, to the characteristic dimension: Kn = /L where = length of mean free path L = characteristic length dimension There is also a Knudsen number that relates bulk diffusion and Knudsen diffusion as well as a separate representation of Knudsen number for diffusion. Keywords: diffusion, gas, low pressure, mean free path KNUDSEN, Martin Hans Christian, 1878-1943, Danish physicist Sources: Bolz, R. E. and Tuve, G. L. 1970; Eckert, E. R. G. and Drake, R. M. 1972; Jerrard, H. G. and McNeill, D. B. 1972; NUC; Parker, S. P. 1992; Perry, R. H. 1967; Potter, J. H. 1967; Rohsenow, W. M. and Hartnett, J. P. 1973.
Thermal Insulation Performance of Monolithic Silica Aerogel with Gas Permeation Effect at Pressure Gradients and Large Temperature Differences
Published in Nanoscale and Microscale Thermophysical Engineering, 2023
Hao-Qiang Pang, Sheng-Nan Zhang, Ting-Hui Fan, Xu Zhang, Tian-Yuan Liu, Yan-Feng Gao
In Figure 9(b) of the gas permeability model with ρ = 82, 280 kg·m−3, and ≈28 nm, the magnitude of Kg equals 10−14~10−15 m2 at P = 104~105 Pa. The Kg model and the experimental data [72] show an excellent agreement, with the largest deviation being no more than 5%. Our model decreases sharply with increasing pressure at P = 103~105 Pa because the mean free path of gas molecules decreases, and the Knudsen diffusion effect is reduced [35]. The apparent Kg converges on Darcy’s permeability when P > 106 Pa [35]. As the porosity increases, the mean pore size becomes more prominent, and thus the gas permeability increases, meaning the gas pressure significantly affects the gas flow in aerogels with high porosity.
Determination of Water Vapor Transmission Properties of Sandstones in the Yungang Grottoes
Published in International Journal of Architectural Heritage, 2022
Yue Zhang, Yi Zheng, Jizhong Huang
If the mean free path of the diffusing molecules is significantly smaller than the pore size (NK≤0.01), the collisions between vapor molecules are remarkable. Under this circumstance, the diffusion process within the gas-filled pores is controlled by molecular diffusion. The molecular diffusion coefficient Dm, independent of the pore size, is governed by the temperature, pressure and chemical composition of the gas phase. On the contrary, when the pore size is significantly smaller than the mean free path (NK≥10), Knudsen diffusion occurs which is a process dominated by collisions of the diffusing molecules with the pore walls. In this case, the diffusion coefficient which is indicated as Dk can be estimated from the equation below:
Coalbed methane characterization and modeling: review and outlook
Published in Energy Sources, Part A: Recovery, Utilization, and Environmental Effects, 2020
The coal matrices have pores of microscale. Gas diffusion through micropores is composed of three diffusion mechanisms. First, Knudsen diffusion where gas molecules flow from higher to lower concentration when the pressure gradient is negligible and the mean free path of the gas molecules is greater than the pore diameter (Collins 1991; Zhao 1991). It is driven by the molecule-wall collisions since molecules collide more with the flow path walls than with each other (Shi and Durucan 2003a; Thorstenson and Pollock 1989). Consequently, the resistance to gas flow is primarily caused by the collisions with the pore walls rather than with each other (Pillalamarry, Harpalani, and Liu 2011). Second, surface diffusion where gas flows through a physically adsorbed layer (Shi and Durucan 2003a). It happens when the adsorbed gas molecules move along the adsorbent surface as liquid (Collins 1991). It could be negligible compared to Knudsen diffusion at room temperature and it is normally ignored for CBM production (Pillalamarry, Harpalani, and Liu 2011). Third, bulk diffusion where fluid-fluid collisions dominate (Shi and Durucan 2003a). Unlike Knudsen diffusion, it happens at higher pressures (Collins 1991) where the mean free path of the gas molecules is smaller than the pore diameter. In contrary to the Knudsen diffusion, the resistance to flow is primarily caused by fluid-fluid collisions, not the fluid-wall collisions.