Vibrations of Sessile Drops of Soft Hydrogels

TL;DR

This study investigates the vibrational behavior of soft hydrogel drops, revealing how their resonant frequencies depend on mass and shear modulus, and identifying a capillary-like vibration mode influenced by wetting properties.

Contribution

It introduces a detailed analysis of vibrational modes in soft hydrogel drops and uncovers a universal scaling law involving shear modulus, mass, and wetting effects.

Findings

Resonant frequency decreases with mass and increases with shear modulus.

Vibrational modes resemble the lowest Rayleigh mode of water drops.

A universal frequency scaling law incorporating shear modulus and wetting angle is proposed.

Abstract

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. 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 square root of the mass in all cases 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 corrected for the wetting angles, and plotted against the fundamental frequency scale (gamma/mu)^0.5, all the data collapse nicely on a single plot provided that the latter is shifted by a shear modulus dependent factor (1+mu.L/gamma). A length scale L, independent of both the modulus and the mass of the drop emerges from such a fit.