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/
mwhere,
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/
mε
2where,
v is penetration volume of liquid per unit area (cm), ε is porosity of paper (dimensionless).
v/
t=1/κ·Δ
P/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/cm
2), 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=Δ
Pκη/
nΣ
t=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.
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