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Isothermal diffusion of water vapor in unsaturated soils based on Fick’s second law

基于Fick 第二定律的非饱和土中汽态水等温扩散研究

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Abstract

In arid regions, water vapor diffusion predominates the total water migration in unsaturated soil, which significantly influences agriculture and engineering applications. With the aim of revealing the diffusion mechanism of water vapor in unsaturated soil, a water vapor migration test device was developed to conduct the water vapor migration indoor test. The test results demonstrate that the characteristics of water vapor diffusion in unsaturated soil conformed to Fick’s second law. A mathematical model for water vapor diffusion under isothermal conditions in unsaturated soil was established based on Fick’s law. Factors including the initial moisture content gradient, initial moisture content distribution, soil type and temperature that affect the water vapor diffusion coefficient were analyzed. The results show that there was good agreement between the moisture content calculated by the mathematical model and obtained by the indoor experiment. The vapor diffusion coefficient increased with increasing initial moisture content gradient and temperature. When the initial moisture content gradient is constant, the vapor diffusion coefficient increases with the increase of matrix suction ratio in dry and wet soil section. The effect of soil type on the water vapor diffusion coefficient was complex, as both the moisture content and soil particle sizes affected the water vapor diffusion.

摘要

干旱地区非饱和土中汽态水扩散是水分迁移的主要组成部分,这对农业和工程应用具有重要影 响。为了揭示非饱和土中汽态水扩散机理,研制了汽态水扩散试验装置,进行了非饱和土汽态水扩散 室内试验。试验结果表明非饱和土中汽态水扩散特性符合Fick 第二定律。基于Fick 定律,建立了等 温条件下非饱和土汽态水扩散的数学模型,分析了初始含水率梯度、初始含水率分布、土体类型和温 度等因素对汽态水扩散系数的影响。结果表明:用所建的数学模型计算的含水率与室内试验结果吻合 较好;.汽态水扩散系数随着初始含水率梯度和温度的增加而增大;在初始含水率梯度一定的条件下, 汽态水系数随着这干土段和湿土段基质吸力比值的增大而增大;含水率和土颗粒粒径均对汽态水扩散 系数有所影响,致使土体类型对汽态水扩散系数的影响比较复杂。

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Abbreviations

θ :

Moisture content

θ s :

Saturated moisture content

θ r :

Residual moisture content

α :

Parameter for the SWCC

n :

Parameter for the SWCC

D :

Water vapor diffusion coefficient

W 0 :

Initial moisture content of the dry soil column

W s1 :

Initial moisture content of the wet soil column

W m :

Initial moisture content gradient

W s2 :

Moisture content of the soil located at 10.5 cm when the time is t

W (x,t) :

Moisture content of the soil at the position x, time t

ρ v :

Water vapor density

ω v :

Molar mass of water vapor

u v :

Partial pressure of water vapor

u v,sat :

Saturated vapor pressure of water

R :

Universal gas constant

T :

Thermodynamic temperature

C(x, t):

Concentration of water vapor at time t and at distance x

ua−uw :

Matrix suction

(ua−uw)0 :

Initial matric suction of the dry soil column

(ua−uw)s :

Matric suction of the soil located at 10.5 cm

(ua−uw)s1 :

Initial matric suction of the wet soil column

(ua−uw)s2 :

Matric suction of the soil located at 10.5 cm, time t

(ua−uw)(x,t) :

Matric suction of soil at the position x and at time t

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Authors and Affiliations

  1. School of Highway, Chang’an University, **’an, 710064, China

    Fei-fei Liu  (刘飞飞), Xue-song Mao  (毛雪松), Jian-xun Zhang  (张建勋), Qian Wu  (吴谦), Ying-ying Li  (**颖颖) & Cheng Xu  (许铖)

  2. Luoyang Rail Transit Group Co., Ltd., Luoyang, 471023, China

    Ying-ying Li  (**颖颖)

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  1. Fei-fei Liu  (刘飞飞)
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Correspondence to Xue-song Mao  (毛雪松).

Additional information

Foundation item: Projects(51878064, 51378072) supported by the National Natural Science Foundation of China; Projects(300102218408, 300102219108) supported by the Fundamental Research Funds for the Central Universities, China

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Liu, Ff., Mao, Xs., Zhang, Jx. et al. Isothermal diffusion of water vapor in unsaturated soils based on Fick’s second law. J. Cent. South Univ. 27, 2017–2031 (2020). https://doi.org/10.1007/s11771-020-4427-6

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