Measuring Surface Tensions of Soft Solids with Huge Contact-Angle Hysteresis

Abstract

The equilibrium contact angle of a droplet resting on a solid substrate can reveal essential properties of the solid’s surface. However, when the motion of a droplet on a surface shows significant hysteresis, it is generally accepted that the solid’s equilibrium properties cannot be determined. Here, we describe a method to measure surface tensions of soft solids with strong wetting hysteresis. With independent knowledge of the surface tension of the wetting fluid and the linear-elastic response of the solid, the solid deformations under the contact line and the contact angle of a single droplet together reveal the difference in surface tension of the solid against the liquid and vapor phases If the solid’s elastic properties are unknown, then this surface tension difference can be determined from the change in substrate deformations with contact angle. These results reveal an alternate equilibrium contact angle, equivalent to the classic form of Young-Dupré, but with surface tensions in place of surface energies. We motivate and apply this approach with experiments on gelatin, a common hydrogel.

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Plain Language Summary

Surface properties of solids are most commonly measured by placing a droplet on the solid and measuring the angle at which the droplet surface contacts the solid surface. This contact angle can reveal the key value that controls surface properties: the surface energy. The technique is widely applied in both science and industry and works well for rough measurements, but it can cause huge measurement uncertainty on most surfaces. Here, we showcase a novel technique that overcomes this age-old problem to accurately measure the surface properties of soft solids with wetting experiments.

Much of the uncertainty in droplet-based measurements comes from contact-angle hysteresis—various surface properties and droplet behaviors cause the value of the angle to lag behind changes to the experimental setup. Our workaround involves measuring tiny deformations of the solid directly under the contact line of the droplet and relating these to the forces acting at the surface of the solid. Essentially, this is achieved by measuring the angle at which the surface tension forces in the droplet are in horizontal force balance. While this requires knowledge of the droplet surface tension, the properties of the underlying surface can be unknown. We demonstrate this approach with droplets on gelatin surfaces.

Our technique enables the measurement of surface-tension differences and “depinning forces” on soft solids, even in the presence of huge contact-angle hysteresis. This approach should be broadly applicable in measuring surface properties of soft materials.