Permeability of porous materials for liquid and gases

Abstract

It is shown that propagation of liquids and gases through a porous material has a different character, namely, the viscosity characterizes this process for liquids, whereas for gases it is determined by collisions of the gas molecules with the skeleton of the porous material. The analog of the Kozeny-Carman formula in liquids for the Darcy coefficient or the permeability coefficient is represented for gases. The transition between these limiting cases results from the relation between the mean free path of an individual molecule in a liquid or gas λ and the mean free path of this molecule with respect to its scattering on the skeleton of a porous material.

Slow viscous flow of two porous spherical particles translating along the axis of a cylinder

“…Model ap(m) α(m −1 ) R0(m) Brinkman (1949) 2.18 × 10 −9 2.49 × 10 8 1.6 × 10 −7 Happel & Brenner (1983) 2.18 × 10 −9 2.77 × 10 8 1.5 × 10 −7 Carman-Kozeny (Krainov et al 2014) 2.18 × 10 −9 1.31 × 10 8 3.2 × 10 −7 Experiment (Kapur et al 1996) Not applicable 2.26 × 10 8 1.8 × 10 −7…”

“…(3.10) Mika & Childs (2001) have shown the comparison between the theoretical work and experimental data conducted by Kapur et al (1996) and both equations (3.9)-(3.10) give a good prediction of the permeability of the gel. In addition, the permeability can be predicted with Carman-Kozeny formula (Krainov et al 2014)…”

“…Due to kinematic reversibility at low Reynolds number, the coefficients of the two identical particles are 16 X. Yao, C. H. Ng, J. R. A. Teo, Marcos and T. N. Wong Model ap(m) α(m −1 ) R0(m) Brinkman (1949) 2.18 × 10 −9 2.49 × 10 8 4.0 × 10 −7 Happel & Brenner (1983) 2.18 × 10 −9 2.77 × 10 8 3.8 × 10 −7 Carman-Kozeny (Krainov et al 2014) 2.18 × 10 −9 1.31 × 10 8 8.0 × 10 −7 Experiment (Kapur et al 1996) Not applicable 2.26 × 10 8 4.5 × 10 −7…”

The bubble method of water purification

“…It is convenient to use a power ultrasonic source (for example, [34][35][36]) for laboratory generation of air microbubbles in water, where the power ultrasonic wave perturbs the interface of water and air which leads to penetration of air into water, finally in the form of microbubbles. Air microbubbles are formed in water if air passes through a porous material under the action of a heightened pressure [37,38]. In this experiment we use the decompression method for microbubble generation in water [39], where at the beginning water is saturated with air under the high pressure and then the pressure is lowered.…”