Cusp development in free boundaries, and two-dimensional slow viscous flows
Sam Howison, Stephen M. Richardson · European Journal of Applied Mathematics · 1995
We consider a family of problems involving two-dimensional Stokes flows with a time dependent free boundary for which exact analytic solutions can be found; the fluid initially occupies some bounded, simply-connected domain and is withdrawn from a fixed point within that domain. If we suppose there to be no surface tension acting, we find that cusps develop in the free surface before all the fluid has been extracted, and the mathematical solution ceases to be physically relevant after these have appeared. However, if we include a non-zero surface tension in the theory, no matter how small this may be, the cusp development is inhibited and the solution allows all the fluid to be removed.