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The equilibrium contact angle of a droplet resting on a solid substrate canreveal essential properties of the solid's surface. However, when the motion ofa droplet on a surface shows significant hysteresis, it is generally acceptedthat the solid's equilibrium properties cannot be determined. Here, we describea method to measure surface tensions of soft solids with strong wettinghysteresis. With independent knowledge of the surface tension of the wettingfluid and the linear-elastic response of the solid, the solid deformationsunder the contact line and the contact angle of a single droplet togetherreveal the difference in surface tension of the solid against the liquid andvapor phases. If the solid's elastic properties are unknown, then this surfacetension difference can be determined from the change in substrate deformationswith contact angle. These results reveal an alternate equilibrium contactangle, equivalent to the classic form of Young-Dupr\'{e}, but with surfacetensions in place of surface energies. We motivate and apply this approach withexperiments on gelatin, a common hydrogel.

Measuring surface tensions of soft solids with huge contact-angle hysteresis