Experimental and numerical analysis on the equilibrium shape of sessile droplets on elastic thin membranes

Abstract

The equilibrium shape of sessile droplets on elastic thin membranes is determined by the balance among three types of surface tensions at the interface, namely vapor-liquid, liquid-solid, and solid-vapor. We studied the cross-sectional contour of the membrane equilibrium state and sessile drops by focusing on the global characteristics of the deformation, both numerically and experimentally. To determine the initial tension, which is required for numerical analysis, we carried out a modal test. A laser Doppler vibrometer (LDV) was used to measure the velocity of the membrane vibration on a table isolated from external forces. With the measured the first and second modal frequencies, the initial tension of the membrane was derived using a circular membrane vibration equation by solving a first kind of Bessel function. Furthermore, a high-resolution reflective displacement sensor and micro linear actuator with micrometer accuracy were used to measure the cross-section deformation of the membrane on the sessile drop, and the droplet contact radius in the experimental environment. The membrane sample was assembled on a thin, light aluminum ring with a resonance frequency of about 700 Hz, and three different diameters were employed. Using this technique, we investigated the trend in membrane deformation due to the increase in the weight of the water droplets and the surface tension, which is an intrinsic property of the membrane. In addition, we found that the experimental results related to the contact radius and contour of a water drop agreed with the simulation data well.