Marangoni Convection in a Gravity-Free Silicon Float Zone.

摘要

The onset of Marangoni convection in the float zone of liquid silicon is studied from a state at rest in the absence of gravity. This time-dependent flow problem is solved numerically with the aid of the Navier-Stokes equations for an axisymmetric flow with nonlinear free surface conditions. On this free surface the temperature gradient is generated by heat transfer and radiation from a heater, which is symmetrically located between the two walls of the float zone. After a certain time, the flow is asymmetrically disturbed by moving the heater for a short time away from its symmetric position and back. Three different Marangoni numbers (based on the temperature difference between heater and melting point of silicon) are computed: 10,400, 30,225, and 50,050. The results show that for Ma = 10,400 the flow is steady and stable. For the two higher Marangoni numbers, however, the disturbed flows become unstable, and persistent oscillatory modes of 0.22 Hz for Ma = 30,225 and 0.27 Hz for Ma = 50,050 develop. Silicon float zone, Marangoni convection.