The capillary component of the potential Ψ, the partial specific Gibbs free energy associated with the solid–liquid interactions, is taken to depend on the liquid–vapor interface mean curvature; and the adsorptive component to depend on the normal distance of the interface from the solid. The equilibrium condition that it is a surface of constant Ψ then yields the differential equation of the interface. Simple methods of solution are developed for two‐dimensional (spaces between parallel plates, wedge‐shaped pores, spaces between circular cylinders) and axisymmetrical (circular tubes, spaces between spheres) configurations. Illustrative examples are given for capillary condensation of water vapor ( relative humidity 0.70–0.98) at 300 K in the space between parallel plates; in wedge‐shaped pores with semiangles π/12, π/6, and π/4; and in circular tubes. We find values of ‖Ψ‖ between plates and in tubes which are, respectively, 60% and 44% greater than the values given by the Kelvin equation; and we find for wedges very much greater condensation for a given Ψ than the Kelvin equation predicts. These examples suggest, further, that the expedient of allowing for adsorption by modifying the radius of curvature in the Kelvin equation by an assumed constant film thickness is inadequate. The extension of the approach to include gravity is indicated.

1.
N. E.
Edlefsen
 and
A. B. C.
Anderson
,
Hilgardia
15
,
31
(
1943
).
Google Scholar
Crossref
Search ADS
 
2.
Edlefsen and Anderson called it the “free energy,” Δf.
3.
J. R. Philip, Proceedings of the Symposium on Sorption of Water by Porous Materials (CSIRO, Melbourne, 1956), p. 37.
4.
E. Buckingham, U.S. Dept. Agr. Bur. Soils Bull. 38 (1907).
5.
See, for example, the following reviews:
J. R.
 
Philip
,
Spec. Rep. Highway Res. Board, Washington
 
40
,
147
(
1958
);
Google Scholar
 
J. R.
 
Philip
,
Ann. Rev. Fluid Mech.
 
2
,
177
(
1970
);
Google Scholar
Crossref
Search ADS
 
J. R. Philip, in Applied Mechanics, edited by E. Becker and G. K. Mikhailov (Springer, Berlin, 1973), p. 279.
6.
B. V.
Deryaguin
,
J. Phys. Chem.
3
,
29
(
1932
).
Google Scholar
 
7.
B. V. Deryaguin, Proceedings of the Second International Congress on Surface Activity (Butterworths, London, 1957), p. 153.
8.
A. G. Foster, J. Chem. Soc. 1952, 1806.
9.
See, for example, V. Ponec, Z. Knor, and S. Černý, Adsorption on Solids (Butterworths, London, 1974), p. 402.
10.
For definiteness we refer to the “liquid‐vapor interface.” Read “liquid‐air interface” for systems where air is present.
11.
J. F.
Padday
,
Special Discuss. Faraday Soc.
1
,
64
(
1970
).
Google Scholar
Crossref
Search ADS
 
12.
Cf.
W. A.
Steele
 and
G. D.
Halsey
, Jr.,
J. Phys. Chem.
59
,
57
(
1955
), a reference drawn to my attention by a referee. As W. E. Stewart, University of Wisconsin, observed to me recently, treating F as F(v) is a boundary layer approximation: as in fluid mechanics, it leads to useful simplifications, though its limitations must be recognized.
Google Scholar
Crossref
Search ADS
 
13.
Strictly, ρ is the excess density of the liquid over that of the vapor or over that of the air (where air is present).
14.
With appropriate choice of λ, Eq. (33) represents correctly the order of magnitude of experimental observations on v throughout the h range discussed; and we are therefore justified in using it below to estimate the order of magnitude of errors in the Kelvin equation and in the prevalent correction to it.
15.
See reviews such as
A.
 
Sheludko
,
Adv. Colloid Interface Sci.
 
1
,
391
(
1967
);
Google Scholar
Crossref
Search ADS
 
J. Clifford, in Water, a Comprehensive Treatise, edited by F. Franks (Plenum, New York, 1975), Vol. 5, p. 75.
This content is only available via PDF.
© 1977 American Institute of Physics.
1977
American Institute of Physics
You do not currently have access to this content.