Vibrations of sessile drops of soft hydrogels

Sessile drops of soft hydrogels were vibrated vertically by subjecting them to a mechanically-induced Gaussian white noise. Power spectra of the surface fluctuation of the gel allowed identification of its resonant frequency that decreases with their mass, but increases with its shear modulus (μ)(μ). The principal resonant frequencies of the spheroidal modes of the gel of shear moduli ranging from 55 Pa to 290 Pa were closest to the lowest Rayleigh mode of vibration of a drop of pure water. These observations coupled with the fact that the resonance frequency varies inversely as the mass with an exponent close to 0.5 suggest that they primarily correspond to the capillary (or a pseudo-capillary) mode of drop vibration. The contact angles of the gel drops also increase with the modulus of the gel. When the resonance frequencies are plotted against a fundamental frequency scale (γ/ρP2h)0.5(γ/ρP2h)0.5 (expressed in terms of its surface tension (γ)(γ), density (ρ)(ρ), perimeter (P)(P) and mean thickness (h)(h)) all the data collapse nicely on a single plot provided that the latter is shifted by a shear modulus dependent factor (1+μh/2γ). We believe that this method has the potential to measure directly the surface tension of soft elastic gels.