Direct Measurement of the Surface Tension of a Soft Elastic Hydrogel: Exploration of Elasto-Capillary Instability in Adhesion

Elasto-capillarity plays an important role in a variety of surface phenomena. In an attempt to investigate the role of elasto-capillarity in the adhesion of ultra-soft gels, it was found that an adhesively stressed thin film of a soft hydrogel confined between two rigid flat substrates auto-roughens with its dominant wavelength () exhibiting pronounced dependence on the film thickness (H). A linear stability analysis confirmed that this long wavelength instability (~7H) is due to an elasto-capillary effect, the implementation of which required direct measurements of the surface tension and the elasticity of the gel. A novel method is introduced to estimate the surface tension () of the gel from the fundamental spherical harmonic of its hemispherical cap that is excited by an external noise. The resonance vibration frequency of the hemispherical gel cap's free surface was found to vary with its volume as  , being very close to that of water in magnitude and character, i.e., . Analogous to the Stokes' experiment in liquids which is performed to measure the viscosity, a static Stokes' braking experiment in the soft hydrogel is found to give an estimation of the shear modulus. This was achieved by submerging a high density steel ball inside the gel which balances its excess weight with the accumulated strain induced elastic force. The shear modulus () of the gel was also determined from its resonant shear mode in a confined geometry comprising a thin gel slab sandwiched between two glass plates. From the independently determined values of the surface tension and the shear modulus of the gel, a large elasto-capillary length (≈ 1.8 mm) ascertains the role of elasto-capillarity in the adhesion induced pattern formation with such gels. Experimental results are in accord with a linear stability analysis that predicts that the rescaled wavelength  is linear with H. Some new results related to the role of the finite dilation of a material in interfacial pattern formation that may have non-trivial consequences in the adhesive delamination of very thin and/or soft elastic films via self-generated cracks were also found.