Gravity-capillary oscillations of an edgewise constrained meniscus in a cylindrical duct

The linear free vibration of the meniscus of a bulk inviscid fluid in a cylindrical duct, with a fixed line of contact between the meniscus and the lateral walls, is considered. Gravity along the duct axis is accounted for. The problem is reduced to one of finding eigenvalues and eigenvectors of a linear operator on L2 (0,1) whose components, in a standard basis of L2 (0,1) are analytically evaluated. Numerical approximate results are obtained and compared with results available in the literature. Moreover, the influence of the main non-dimensional parameters on the vibration frequencies and modes is studied.