Corners, Cusps, and Pearls in Running Drops

Small drops sliding down a partially wetting substrate bifurcate between different shapes depending on their capillary number $\mathrm{Ca}$. At low $\mathrm{Ca}$, they are delimited by a rounded, smooth contact line. At intermediate values they develop a corner at the trailing edge, the angle of which evolves from flat to 60° with increasing velocity. Further up, they exhibit a cusped tail that emits smaller drops (“pearls”). These bifurcations may be qualitatively and quantitatively recovered by considering the dynamic contact angle along the contact line.