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 t ube, when the bubble is not small with respect to the tube diameter. T ubes rigidly terminated at one end, or open at both ends, are consider ed. The open ends may be open to the atmosphere or in contact with a l arge mass of liquid. The numerical results are compared with a simple approximation in which the bubble consists of a cylindrical mass of ga s filling up the cross section of the tube. It is found that this appr oximation is very good except when the bubble radius is much smaller t han that of the tube. An alternative approximate solution is developed for this case. The viscous energy dissipation in the tube is also est imated and found generally small compared with the thermal damping of the bubble. This work is motivated by the possibility of using gas bub bles as actuators in fluid-handling microdevices. (C) 1998 Acoustical Society of America.