A highly accurate dynamic contact angle algorithm for drops on inclined surface based on ellipse-fitting.

To improve the accuracy in the calculation of dynamic contact angle for drops on the inclined surface, a significant number of numerical drop profiles on the inclined surface with different inclination angles, drop volumes, and contact angles are generated based on the finite difference method, a least-squares ellipse-fitting algorithm is used to calculate the dynamic contact angle. The influences of the above three factors are systematically investigated. The results reveal that the dynamic contact angle errors, including the errors of the left and right contact angles, evaluated by the ellipse-fitting algorithm tend to increase with inclination angle/drop volume/contact angle. If the drop volume and the solid substrate are fixed, the errors of the left and right contact angles increase with inclination angle. After performing a tremendous amount of computation, the critical dimensionless drop volumes corresponding to the critical contact angle error are obtained. Based on the values of the critical volumes, a highly accurate dynamic contact angle algorithm is proposed and fully validated. Within nearly the whole hydrophobicity range, it can decrease the dynamic contact angle error in the inclined plane method to less than a certain value even for different types of liquids.