Shapes of liquid drops obtained using symbolic computation

The first aim of this paper is to show how two free boundary problems arising from fluid mechanics can be solved with a domain perturbation method. The second aim is to analyse the range of validity of the series solutions. The analysis will aim at identifying the location and the nature of the singularities characterizing these series. After expansion, the equations obtained are linear, but at each stage the length of the expressions grows exponentially. Herein we implement techniques for the automatic generation of hierarchical expression sequences and we present several tools for reducing the combinatorial blow-up of the expressions arising in these two problems.