Bifurcation of Cylinders for Wetting and Dewetting Models with Striped Geometry
- Rafael López
- SIAM J. Math. Analysis
This contribution is about the dynamics of a. liquid bridge between two fixed pa.rallel plates. We consider a mathematical model and present some results from the doctorial thesis  of the first author. He showed tha.t there is a Poisson bracket a.nd a. corresponding Ha.miltonia.n, so that the model equa.tions are in Ha.miltonian form. The result generalizes previous results of Lewis et al.  on the dynamics of free bounda.ry problems for "free" liquid drops to the case of a drop between two pa.rallel plates, including. especially the effect of capillarity and the angle of contact between the plates and the free fluid surface. Also, we prove tJie existence of special solutions which represent uniformly rotating fluid bridges, and we present specific stability conditions for these solutions. These results extend work of Concus and Finn  and Vogel ,[191 on static capillarity problems (see also Finn ). Using the Hamiltonian structure of the model equations and symmetries of the solutions, the stability conditions can be derived in a systematic way. The ideas that a.re desribed will be useful for other situations involving capillarity and free bounda.ry problems as well.