Computations of form and stability of rotating drops with finite elements

We consider the numerical computation of equilibrium shapes of rotating drops and their bifurcations, depending on the angular velocity. The drops are subject to centrifugal forces and surface tension alone. We present a path-tracking algorithm which is based on the discretisation of a continuously formulated Newton's iteration. Our algorithm uses parametric finite elements and avoids artificial symmetry assumptions. The results of our numerical experiments extend those published by Brown & Scriven (1980, The shape and stability of rotating liquid drops. Proc. R. Soc. Lond. Ser. A, 371, 331-357) and cover drops of spheroidal as well as annular shape.