Abstract
Concerning fluid flow in porous structure of uniand multi-ply paper, equations of liquid penetration, gas permeation, etc. were obtained, using Kozeny-Carman's equation, etc.
Main results, concerning flow to thickness direction, are as follows :
1. uni-ply
(1) liquid penetration
t=κ/2·η/σ cos θ·l2/m
where, t is penetration time of liquid (s), k is Kozeny-Carman's constant (dimensionless), η is viscosity of liquid (P), σ is surface tension of liquid (dyn/cm), θ is contact angle between pore wall of paper and liquid (rad), l is penetration distance of liquid (cm), m is hydraulic radius of pore of paper (cm).
t=κ/2·η/σ cos θ·v2/mε2
where, v is penetration volume of liquid per unit area (cm), ε is porosity of paper (dimensionless).
v/t=1/κ·ΔP/η·m2ε{1+Z(λ/m)}/L
(2) gas permeation where, v is permeation volume of gas per unit area (cm), t is permeation time of gas (s), ΔP is pressure difference (dyn/cm2), ηis viscosity of gas (P), Z is constant (dimensionless), λ is mean free path of gas molecules (cm), L is thickness of paper (cm).
2. multi-ply equations are obtained, from the following basic equation of liquid permeation.
v/t=ΔPκη/nΣt=1(Li/mi2ε)
where, v is permeation volume of liquid per unit area (cm), t is permeation time of liquid (s).
Each suffix indicates number of ply.
