The natural frequency of oscillation of gas bubbles in tubes

A numerical study is presented of the natural frequency of the volume oscillations of gas bubbles in a liquid contained in a finite-length tube, when the bubble is not small with respect to the tube diameter. Tubes rigidly terminated at one end, or open at both ends, are considered. The open ends may be open to the atmosphere or in contact with a large mass of liquid. The numerical results are compared with a simple approximation in which the bubble consists of a cylindrical mass of gas filling up the cross section of the tube. It is found that this approximation is very good except when the bubble radius is much smaller than that of the tube. An alternative approximate solution is developed for this case. The viscous energy dissipation in the tube is also estimated and found generally small compared with the thermal damping of the bubble. This work is motivated by the possibility of using gas bubbles as actuators in fluid-handling microdevices.