NUMERICAL SIMULATIONS OF THE TRANSLATIONAL AND SHAPE OSCILLATIONS OF A LIQUID-DROP IN AN ACOUSTIC FIELD

In this work, the boundary element method combined with the fourth ord er Runge-Kutta scheme as time integrator is used to simulate the dynam ics of an acoustically levitated axisymmetric liquid drop. For a given set of dimensionless parameters-wavenumber, Bond number, and acoustic Bond number-the drop dynamics in an acoustic field is studied in term s of the shape oscillation and the translational motion of the drop. T he shape oscillation of the drop is characterized by using the equator ial radius and its rate of change as two phase variables. Fixed points on this phase plane represent the static equilibrium shapes. The tran slational motion is characterized by using the position and the veloci ty of the drop centroid as two phase variables. The fixed points on th is phase plane represent the equilibrium positions of the drop in the acoustic field. It is found that fixed points corresponding to both tr anslational and shape oscillations undergo saddle-node bifurcations wi th the acoustic Bond number as a parameter. These saddle-node bifurcat ions define an upper and a lower limit on the acoustic Bond number tha t can be used in acoustic levitation. We also investigate the coupling effect between the translational oscillation and the shape oscillatio n. It is found that owing to the order-of-magnitude difference between the period of translational oscillation and that of shape oscillation the coupling effect is only significant at the boundary of the trappi ng region. (C) 1997 American Institute of Physics.