Flow pattern transition driven by the combined Marangoni effect and rotation of crucible and crystal in a Czochralski configuration

Abstract In order to understand the flow pattern transition driven by the combined Marangoni effect and rotation of crucible and crystal, a series of unsteady three-dimensional numerical simulations were conducted for this complex flow in a Czochralski configuration. Results show that the basic flow is axisymmetric and steady at small driving forces. The flow structures are represented as meridian circulations rotating in different directions, which are dependent on the differential rotation rates of the crystal and the crucible. When the thermocapillary Reynolds number exceeds a threshold value, the basic flow undergoes a transition to the three-dimensional oscillatory flow. Without rotation, the three-dimensional thermocapillary flow is characterized by standing waves or by spoke patterns with fluctuations growing and decaying periodically. When the crystal and/or crucible rotate, the oscillatory flow behaves as temperature and velocity fluctuation waves traveling in the azimuthal directions. The direction and velocity of wave propagation, fluctuation amplitude and wave number, which are dependent on the interaction of the thermocapillary, centrifugal and Coriolis forces, are discussed. Furthermore, the critical conditions for the onset of instabilities are determined and the stability diagrams are mapped. For the counter-rotation of the crystal and the crucible, two flow transitions occur with the increase of the thermocapillary Reynolds number, and three state regimes are zoned. The characteristics of the flow instabilities in each state regime are analyzed.