Page 317 - Geology and Geochemistry of Oil and Gas

278 APPENDIX A

A.2.1. Interfacial Tension and Contact Angle

On considering an element of an interface having double curvature (R 1 and
R 2 ), the sum of the force components normal to the element is equal to zero
(see Fig. A.4). The pressure difference ( p 2 – p 1 ) is balanced by the interfacial tension
forces:
ðp p Þdydx ¼ 2sdy sin y 2 þ 2sdx sin y 1 (A.2)
2
1
If the contact angles (y 1 and y 2 ) are small, then the following simplifications may
be made:
(A.3)
sin y 1 ¼ dy=2R 1
and
(A.4)
sin y 2 ¼ dx=2R 2
Therefore, Eq. A.3 becomes

1 1
p p ¼ s þ (A.5)
2
1
R 2 R 1
For a capillary tube (see Fig. A.5)
R 1 ¼ R 2 ¼ R (A.6)
cos y ¼ d=2R (A.7)
and

p ¼ p þ gh (A.8)
2
1

Fig. A.4. Surface tension forces acting on a small element on the surface having double curvature
(p 2 ¼ p 1 þ g h ) (see Binder, 1962; Vennard, 1961). r 1 ¼ R 1 and r 2 ¼ R 2 (radii of curvature).