ABSTRACT
An alternative derivation of Young’s equation follows the same route as the derivation of the Laplace equation using a notional change of the location of the dividing surface. Consider the surface free energy of the system depicted in Fig. 4. Around the line of three-phase contact a cylinder is drawn with length L and radius R, and implicitly we assume that R and L approach
infinity. The contribution to the surface free energy associated with the three surfaces reads in this geometry
Fs=σsvRL+σslRL+σlvRL. (9)
If the location of the dividing surface is now shifted by a distance ∆ (dashed line in Fig. 4), the notional change in surface free energy associated with the notional change in surface area is given by
(10)
Again, from the requirement that [dFs]=0, we recover Young’s law. Even though alternative and more rigorous derivations of Young’s law have appeared
in the literature [1, 3, 7-11], the validity of Young’s law has been a continued subject of scrutiny [12-17]. Young’s equation has been questioned as a general rule [12, 13] and in the presence of a gravitational field [12-15]. Its validity has been investigated using integral relations and arguments have been given for the introduction of a microscopic contact angle [16, 17]. As we will discuss in Section III, it is now recognized that for very small liquid droplets on a substrate, Young’s law indeed has to be modified to account for the presence of the line tension of the triple line [18-21]. For macroscopically large droplets and for macroscopically large distances from the triple line, however, the contact angle is given by Young’s law.
