Bubble shapes in rotating two-phase fluid systems: A thermodynamic approach

A method is reported for predicting the shape of the phase boundary in two-phase isothermal constant-volume constant-mass rotating fluid systems. In contrast to previous methods that have employed the continuum concept of pressure, the proposed method uses the thermodynamic concept. The latter requires, in addition to the usual condition of a force balance existing at the boundary, that the equilibrium phase boundary shape be such that there is no net mass flux. The latter condition is imposed by requiring that the chemical potentials in the different phases be equal at the phase boundary. A non-dimensional parameter is defined that allows one to determine when the effects of a gravitational held acting at 90 degrees to the axis of rotation may be neglected. Experiments have been performed under conditions where this restriction is satisfied. With known values of the experimentally controllable variables, the proposed method has been used to predict the length of the vapour phase. To within the experimental error, the predicted lengths are found to be in agreement with the measurements. If, however, a gravitational field of a sufficient magnitude is imposed the vapour phase has been found to become unstable and to break into two or more separate bubbles. Using the variable-gravity environment of an aircraft following a parabolic flight path, this instability has been investigated. By approximating the gravitational effects, the theoretical description has been extended and a method proposed to determine the conditions under which the phase boundary becomes unstable. If the angle of action of the net viscous shear force on the bubble were known, a prediction of the breakup could be made entirely in terms of experimentally controllable parameters. Using arguments for the value of this angle, bounds on the breakup condition are compared with experimental results.