Thermodynamic analysis of steady wetting state of droplet on single microstructure surface

A three dimension thermodynamic model is used to investigate the steady wetting state of droplet on a single microstructure surface based on the lowest principle of droplet free energy. The cone, frustum (upright and inverted) and sphere in micro-scale are selected as studied structures. The results show that both the intrinsic contact angle and morphology parameters of microstructure surface affect the wetting depth and normalized Helmholtz free energy (NFE) of droplet. The wetting maps for minimum points of NFE of droplet on cone and frustum surfaces with respect to intrinsic contact angle and morphology parameters have been presented. These wetting maps provide a guidance for fabricating microstructures that is used to enhance droplet adhesion. The effect of three phase contact line tension on droplet NFE has been studied. Results indicate that the line tension slightly increases the droplet NFE and that causes the decrease of droplet wetting stability. The absolute differences between F-tau* (NFE with line tension) and F* (NFE without line tension) are small both for 1 mu L and 1 nL droplets. But the relative differences, (F-tau*-F*)/F*, of 1 nL droplet are significantly larger than that of 1 mu L droplet. Therefore, for a droplet with small volume, the line tension effect on droplet free energy is relatively large and that results in the increase of instability of droplet wetting state.