ON THE BIFURCATION AND STABILITY OF RIGIDLY ROTATING INVISCID LIQUID BRIDGES

We consider a mathematical model that describes the motion of an ideal fluid of finite volume that forms a bridge between two fixed parallel plates. Most importantly, this model includes capillarity effects at the plates and surface tension at the free surface of the liquid bridg e. We point out that the liquid can stick to the plates due to the inn er pressure even in the absence of adhesion forces. We use both the Ha miltonian structure and the symmetry group of this model to perform a bifurcation and stability analysis for relative equilibrium solutions. Starting from rigidly rotating, circularly cylindrical fluid bridges, which exist for arbitrary values of the angular velocity and vanishin g adhesion forces, we find various symmetry-breaking bifurcations and prove corresponding stability results. Either the angular velocity or the angular momentum can be used as a bifurcation parameter. This anal ysis reduces to find critical points and corresponding definiteness pr operties of a potential function involving the respective bifurcation parameter.