Asymptotic analysis of contact line dynamics of spreading/retracting drops on spherical surfaces

We investigate the spreading and retraction of a small sessile drop on a sphere governed by capillary and viscous forces. The lubrication equation established in spherical coordinates is solved analytically and numerically. The Navier slip model is adopted to overcome the singularity at the contact line. An asymptotic matching method is employed to study the contact line movement. The results show that the spreading process is always faster than the retraction process for a given drop volume. The position and speed of the contact line can be well-predicted using the asymptotic theory during the whole process of spreading and the late stage of retraction, while the theory becomes invalid at the early time of retraction because the macroscopic interface is significantly perturbed by the moving contact line.