Resolving the tension between droplets and solids. 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...

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