Resonant properties of sessile droplets; contact angle dependence of the resonant frequency and width in glycerol/water mixtures

Abstract

A simple optical deflection technique was used to monitor the vibrations of small (microlitre) sessile droplets of glycerol/water mixtures when a puff of air was used to apply an impulse to the drops. A photodiode was used to detect time dependent variations in the intensity of laser light that was reflected from the droplets. The intensity variations obtained from droplets with masses in the range 0.0005–0.03 g were Fourier transformed to obtain information about the resonant properties (frequency and width of the resonance). These experiments were performed on a range of different substrates where the three phase contact angle formed by the droplets varied between 38 ± 2° and 160 ± 4°. This was repeated for droplets with glycerol compositions ranging from 10% to 75%. The measured resonant frequency values were found to be in good agreement with a recently developed 1-D theory of vibrations in sessile droplets which considers standing wave states around the meridonal profile length of the droplet. The widths of the resonances were also compared with modified theories which predict the influence of substrate effects, surface contamination effects and bulk viscous effects on the damping of capillary waves at the free surface of the droplets. These experiments indicate that the dominant source of damping in sessile liquid droplet is due to bulk viscous effects but that for small contact angles damping due to the droplet/substrate interaction becomes more important.