Equilibrium Shapes, Stability and Dynamical Behaviour of Liquid Captive Menisci under Gravitational, Centrifugal and Electrical Fields
A linear analysis of the free oscillations of captive drops or bubbles surrounded by an immiscible liquid or gas undergoing rotation in the presence of gravity has been carried out. Using spectral analytical methods, the natural frequencies corresponding to the symmetric and non-symmetric vibration modes have been calculated for any combination of the Bond and Weber numbers. The method uses normal mode decomposition and Green’s function to reduce the linearized Navier-Stokes equations and boundary conditions to an eigenvalue problem. Both the Green’s function and normal velocities at the interface are expanded in the orthogonal functional space generated by the Sturm-Liouville problem associated with the homogeneous part of the interface equation. The effect on the vibration modes of the density and geometrical parameters of the captive drop and the surrounding medium has been analysed. The case ω = 0 which determines the stability boundaries has also been considered. It is shown that the elliptic vibration spectrum presents two different and unexpected features depending on the Weber number range and the geometrical parameters. Finally, experimental results for the no-rotation case have been obtained and they show a good agreement with the calculated frequencies.
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