Analysis on the deflection of thin membrane with a droplet according to the surface tension and elasticity

Abstract

Thin membranes that may be exposed to water droplet deposition have been used in various industrial and research fields. Deflection of these membranes by water droplets may greatly affect their characteristics. Therefore, it is important to predict deflection of these thin membranes by water droplets. Here, the contact angle effect of a sessile drop was analyzed by a combination of deformation and surface energy; the deflection of elastomer thin membranes was investigated by experiment and simulation. Circular thin membranes were fabricated comprising various materials (i.e., expanded polytetrafluoroethylene, polytetrafluoroethylene, and polyethylene). Modal characteristics for thin membranes mounted on a ring fixture were measured when all edge points were clamped. Based on the measured fundamental frequency, initial tension was determined in accordance with circular thin membrane vibration theory. A numerical model was derived to describe the water droplet profile and membrane deflection by thermodynamics and mechanical energy. Contact angles and profiles were measured for three types of thin membrane and for various water droplet sizes, using a high-speed camera. Deflections were measured using a laser sensor with water droplets of various sizes and various contact angles, along with various ethanol concentrations on the thin membrane. Experimental results were consistent with simulation results. The degree of nonlinearity could be ignored for thin membranes with water droplet volume of ≤ 200 $\mu L$. Maximum deflection of various thin membranes and various contact angles could be predicted using compensation factors. Maximum deflection of the thin membrane could be sufficiently predicted when considering the contact angle effect.