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I am having a problem understanding Young's
equation, an equation relating the connecting
angle of an air-water interface (in a air-water-
solid interace) with the interfacial tensions.
The equations seems counter-intuitive, and seems
to violate the principle of least action.

I am reviewing a text (Quantitative Hydrogeology, 
de Marsily) that discusses wetting/non-wetting
fluids in a air-water-solid interface. In a 
diagram (Fig. 2.12, p 28) of the interface, the
solid boundary is horizonal, with the water forming
a droplet on top. This is probably a common diagram
shown in any soil physics or physical chemistry text. 

The angle of the air-water interface is measured 
through the water. If the angle < 90 deg. the fluid
is "wetting". This is easy to see; as the angle 
approaches 0 deg., the drop spreads out over the
entire surface. Similarly, if the angle > 90 deg. 
the fluid is "non-wetting". As the angle approaches
180 deg., the droplet beads up to where only a point
is touching the solid. Again, easy to visualize.

 However:

 Young's Equation:


   cos(theta)= (sigma_s_a - sigma_s_w)/sigma_a_w

where  

  theta = the connecting angle

  sigma_s_a = interfacial energy between the solid-air
              (the energy required to separate a unit
               area of air-solid interface)

  sigma_s_w = interfacial energy between the solid-water

  sigma_a_w = interfacial energy between the air-water

Suppose (using J/m**2 or any convenient units)

  sigma_s_a = 1, sigma_s_w = 2 , sigma_a_w = 1

Since it take twice the amount of energy to peel
a unit area of solid-water apart compared to
solid-air, or air-solid, it would seem that the
system would seek to minimize its energy by
spreading the water over the entire surface
(theta-0). However, these values give theta=180,
where the water is only touching at a single
point. This seems a much higher energy state.

What is wrong with my reasoning. Thank you
for any help on this.

--- Bart Killam,  SAS Institute Inc.