Streaming generated in a liquid bridge due to nonlinear oscillations driven by the vibration of an endwall

It has been observed that streaming can be generated in a liquid bridge supported by two endwalls, with one wall vibrating to excite its capillary oscillations [Anilkumar et al, J. Appl. Phys. 73, 4165 (1993); Mollot et al., J. Fluid Mech. 255, 411 (1993)]. The finding has been applied to suppress thermocapillary convection in crystal growth using the float zone technique [Grugel ct al., J. Cryst. Growth 142, 209 (1994)]. In this work we shall explain the mechanism that drives the streaming, for low streaming velocities, in terms of an ''acceleration shear'' of the free surface of the liquid column. The results compare favorably with experiments with long columns. We have found that for a low viscosity liquid, the streaming pattern changes sign when the oscillation is adjusted from one side of a resonant peak to the other. This allows for more flexibility in the application of the streaming to counteract thermocapillary convection, during crystal growth in a float zone. We have also found that for low viscosities, the streaming velocity is inversely proportional to viscosity. (C) 1996 American Institute of Physics.