The relative importance of the Rayleigh and Reynolds numbers is defined by the ratio A=Ra/Re², often called the Archimedes number. When the parameter is far away from unity, Ra (for A>>1) or Re (for A<<1) alone will control the flow. For the ratio A close to unity, one can expect an interaction between the buoyant and rotational force fields. It is reasonable to expect that the critical value of the Archimedes number that defines transition from buoyancy to rotation-controlled flow regimes is geometry dependent. Two and three-dimensional geometries are expected to yield different critical values. In the absence of definite information, A=1 is used in the following discussion as a critical value.

For the experiments conducted in the present work, the Rayleigh number based on the smallest crystal diameter is 10⁴, while based on the largest crystal diameter it is in excess of 10⁶. The corresponding Reynolds numbers range from 0 (no rotation) to 8 (smallest crystal) to 110 (largest crystal). These changes occur primarily because of an increase in the crystal size, but also due to an increase in the concentration difference available in a higher ramp rate experiment. For a small rotating crystal, one can calculate the ratio A=156, while for a large rotating crystal, A=82. Clearly, A>>1 in all the experiments discussed above, and fluid motion is controlled by buoyancy, thus ensuring large-scale circulation in the crystal growth chamber. Rotation plays an important role locally in equalizing solutal concentrations and maintaining stable growth conditions.

The directional nature of gravity imparts certain peculiar properties to the buoyancy field. Specifically, the strength of convection patterns over the horizontal faces of the crystal depends on whether the face is aligned or opposed to the gravity vector. The downward facing surface is stabilized by gravity, experiences weak convection and has the smallest concentration gradients (as seen in Figure 5.22(a)) (Lecture 31). At a later point of time, convection in the bulk of the solution drives fluid flow over the lower surface as well, thus increasing the concentration gradients. A second consequence of weak convection is that the influence of rotation is felt strongly even at small time leading to a rapid increase in concentration gradients. This result is once again to be observed in Figure 5.22(a) (Lecture 31).