Rafael López

Capillary liquid channels in cylindrical support surfaces 

A simple situation in capillary theory is that of depositing an amount of  liquid on a cylindrical support under ideal conditions on the materials and absence of gravity.  After a study of the eigenvalues of the Jacobi operator, it is investigated when planar strips and sections of circular cylinders are stable in cylindrical symmetric support surfaces. The Plateau-Rayleigh instability phenomenon is studied finding the critical value h such that rectangular pieces of planar strips or circular cylinders of length greater than h are necessarily unstable. It is also studied when new morphologies of capillary surfaces can emerge from given circular cylinders. Using the method of bifurcation by simple eigenvalues, we establish conditions on the support surface that prove that  when 0 is a simple eigenvalue of the Jacobi operator,  there is bifurcation from  explicit circular cylinders.