Suppose a trivial case without an external force field then the problem is iso-perimetric where dual and primal are equal: the problem to find the minimum perimeter with the largest volume is the same as the problem to find the minimum volume with the largest perimeter. In reality, the dual and the primal are not equal because of the external field that affects the internal repulsive/attractive forces between the water molecules.
I feel this very hard iso-volumetric problem i.e. the volume can be assumed to be constant when the water-drop moves. According to Wolfram, quartic surfaces such as the piriform are not fully categorized.
I am very grateful for references that tries to formulate this problem as a DP problem.