Volume measurement and calculation of sessile droplets on inclined planes and spherical external surfaces

This paper puts forward a novel measurement and calculation method for sessile droplets' volumes on inclined planes and spherical external surfaces. The volume of a droplet on an inclined plane or on a spherical external surface, which has a fictitious inclined plane, is determined by its shape factor (β), the maximum distance (d) of the contour points away from the inclined plane, and the plane inclination angle θinc. Using the circular arc differential method of the Bashforth–Adams equation and the image processing technique, the d and β are obtained or calculated out. The theoretical model and its algorithm are set up to calculate the droplet volume. In addition, we do experiments to validate the accuracy of the theoretical model. The experimental results show good agreement with those calculated by the theoretical model. This work is significant and can be used to measure and control volumes of droplets in microfluidic and biomedical technologies.