Abstract
The mechanical behavior of void water in the general capillary system, which was difficult of hydrostatical analysis, is studied from the standpoint of thermodynamics. The following basic equation of thermodynamical equilibrium in the system is derived.
diS=-{σGL(dAGL+dASG cos α)+mgdz}/T, (i)
where
diS: entropy production,
σLG: interfacial tension of liquid-gas interface,
AGL: area of gas-liquid interface,
ASG: area of solid-gas interface,
α: contact angle,
m: mass of void water,
g: gravitational acceleration,
z: mean height of capillary raise,
T: absolute temperature.
As an application of eq. (i), the mean height of capillary raise or capillary constant for the spherical particle layer and the irregular particle layer are analyzed under the condition of reversibility, and the following equations are obtained:
For the spherical particle layer
z=6(1-e)σGL cos α/eρgdp (ii)
or
K=6(1-e)/e (iii)
For the irregular particle layer
z=(1-e)σGL cos α/e(1/νρp)ρg (iv)
or
K=1-e/e
where
z: mean height of capillary raise,
e: void ratio,
ρ: density of void water,
dp: diameter of particle,
ν: specific area,
ρp: density of particle,
and capillary constants for the spherical and the irregular particle layer are denoted by Ks and Ki respectively, i. e.,
Ks≡ρgdpz/σGL cos α
Ki≡ρgz(1/νρp)/σGL cos α
It was shown further that eqs. (ii), (iii), (iv) and (v) provide either the upper or the lower limit for the actual irreversible process according as a direction of the movement of void water.
The eqs. (iii) and (v) are compared with the experimental values. As shown in Figs. 4 and 5 the validity of the present analysis are demonstrated.
