Penny-Shaped Trapped Drops

The first term in equation (9.32) is the interface contribution corresponding to the surface energy that must be expended to form a wet zone of radius 7 ., starting from a dry rubber/solid interface. The second term is the elastic energy associated with a typical deformation (H/R) induced by the drop in the elastomer. The deformation extends over a depth of the order of the radius R of the drop (the deformation is localized within a volume 

Minimizing the energy while keeping the volume Q constant Q a HR ) yields 

For R=l im and ho = 10 nm, we get H = 100 nm. The drop is therefore quite flat, resembling a penny. If we manage to measure the thickness H and radius R of the wedged-in drop, we can deduce the spreading parameter S by way of the relation 

The prefactor in equation (9.36) is taken from a paper by I. Sneddon, who calculated the energy [equation (9.32)] exactly. 

---