In 1805 Thomas Young derived the relationship between the static forces of a liquid droplet at rest on a solid substrate. As shown in the schematic, the droplet’s contact angle, θ, can be determined by balancing the horizontal solid–liquid and solid–vapor forces and the horizontal component of the liquid–vapor force, determined by the surface tension, γ/v (see PHYSICS TODAY, February 2007, page 84). However, for more than two centuries, theories yielded unrealistic singularities for stress and strain at the three-phase contact line. That’s because Young’s equation does not account for the vertical, out-of-plane force pulling on the solid substrate, which naturally should be balanced by the substrate’s elastic response. Now, researchers at Yale University and at consumer products manufacturer Unilever have experimentally and theoretically resolved the out-of-plane contributions. Using a confocal fluorescence microscope, the researchers, led by Yale’s Eric Dufresne, laced a 20-micron-thick film of silicone gel with fluorescent beads and measured the deformation due to a water droplet. At equilibrium, a one-micron-high ridge, illustrated in the inset, formed in the gel at the contact line. When the researchers factored the gel’s surface tension and thickness into a linear elastic model, they arrived at a nonsingular theoretical solution for stress that closely fit their experimental data. Their model, however, underestimates the deformations in the solid-liquid contact plane, which they believe are caused by pinning or viscous drag. (E. Jerison et al., Phys. Rev. Lett., in press.)—Jermey N. A. Matthews
