A FRACTAL MODEL FOR GAS DIFFUSION IN DRY AND WET FIBROUS MEDIA WITH TORTUOUS CONVERGING–DIVERGING CAPILLARY BUNDLE

Jun Gao, Boqi Xiao, Biliang Tu, Fengye Chen and Yonghui Liu
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Jun Gao: School of Mechanical and Electrical Engineering, Wuhan Institute of Technology, Wuhan 430205, P. R. China†School of Mechanical and Electrical Engineering, Wuhan Business University, Wuhan 430056, P. R. China
Boqi Xiao: School of Mechanical and Electrical Engineering, Wuhan Institute of Technology, Wuhan 430205, P. R. China
Biliang Tu: School of Mechanical and Electrical Engineering, Wuhan Institute of Technology, Wuhan 430205, P. R. China
Fengye Chen: School of Mechanical and Electrical Engineering, Wuhan Institute of Technology, Wuhan 430205, P. R. China
Yonghui Liu: School of Mechanical and Electrical Engineering, Wuhan Institute of Technology, Wuhan 430205, P. R. China

FRACTALS (fractals), 2022, vol. 30, issue 09, 1-10

Abstract: In this paper, a fractal model is proposed for gas diffusion in dry and wet fibrous media with tortuous converging–diverging capillary bundle on the basis of the fractal theory. The proposed theoretical model for the normalized gas diffusivity (NGD) can be expressed as an explicit functional relation of porosity, φ, fluid saturation, s, fractal dimensions, Dt and Df, the minimum average radius, R¯min, the maximum average radius, R¯max, the straight capillary length of a unit cell L0 as well as fluctuation amplitude a. The predictions of the proposed model have been compared with the existing experimental data and the available model predictions, and a good agreement can be observed. The effect of various parameters on the NGD is studied alone. It is observed that the NGD decreases with an increase in the fluctuation amplitude. Also, it is seen that the NGD decreases with an increase in the tortuosity fractal dimension. Moreover, it is found that the NGD in wet fibrous media decreases with an increase in the fluid saturation. The present model has no empirical constant and each parameter contains clear physical meaning. These may better reveal the physical mechanisms of gas diffusion in fibrous media.

Keywords: Converging–diverging Capillary Bundle; Fractal; Gas Diffusivity; Fibrous Media (search for similar items in EconPapers)
Date: 2022
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DOI: 10.1142/S0218348X22501766

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