Biomedical Engineering Reference
In-Depth Information
Figure 3.77
Example of minimal surface: one surface formed by the interface of a liquid attached
to a vertical rod (Surface Evolver calculation).
where
E
SG
,1
is the surface energy of the solid surface in contact with the gas. Then,
we have
(
)
òò
(3.99)
E
=
γ
S
+
γ γ
-
dA E
+
LG LG
SL
SG
SG
,0
S
SL
The last term on the right-hand side of (3.99) does not depend on the drop
shape. Thus, we have to minimize
(3.100)
E
=
γ
S
+ òò
γ γ
-
dA
(
)
LG LG
SL
SG
S
SL
Taking into account Young's law, the energy to be minimized is [50]
òò
E
=
γ
S
-
γ
cos
θ
dA
(3.101)
LG LG
LG
S
SL
As mentioned earlier, the parameters intervening in (3.101) are
q
and
g
LG
. Thanks
to Young's equation, we do not need the surface tension of the solid with the liquid
or the gas. This is a real simplification that
q
and
g
LG
are difficult to measure.
References
[1] Israelachvili, J.,
Intermolecular and Surface Forces
, New York: Academic Press, 1992.
[2] Table of surface tension for chemical fluids, http://www.surface-tension.de/.
[3] Navascués, G., “Liquid Surfaces: Theory of Surface Tension,”
Rep. Prog. Phys
., Vol. 42,
1979, pp. 1133-1183.
[4] Guggenheim, E. A., “The Principle of Corresponding States,”
J. Chem. Phys
., Vol. 13,
1945, pp. 253-261.
[5] Pasandideh-Fard, M., et al., “The Generalized Laplace Equation of Capillarity. I. Thermo-
dynamic and Hydrostatic Considerations of the Fundamental Equation for Interfaces,”
Advances in Colloid and Interface Science
, Vol. 63, 1996, pp. 151-178.
