COMPETING MECHANSIMS IN CONVECTION

The relative importance of buoyant convection over rotation is discussed in the present section in fundamental terms. Essentially, the increase in crystal size takes place owing to the deposition of excess salt in the solution on the crystal faces. The speed at which the deposition occurs is proportional to the gradients in solutal concentration prevailing in this region. The gradients in turn depend on the pattern of fluid motion in the crystal growth chamber. The influence of fluid motion on concentration gradients can be explained in terms of solutal boundary-layers (diffusion boundary-layers) adjacent to the crystal faces. The boundary-layer thickness decreases as the fluid velocity increases. Clearly vigorous convective motion will increase concentration gradients, ultimately leading to a rapid increase in crystal size.

The conditions under which flow is intensified can be understood in terms of the forces acting on the fluid particles. For the solution contained in the beaker, the external force arises from buoyancy (in a gravitational field), while inertia forces related to linear and rotational acceleration are also present. The motion, in all situations is retarded by fluid viscosity. The forces are conveniently explained in terms of the dimensionless parameters Ra, the Rayleigh number and Re, the Reynolds number. Rayleigh number denotes the ratio of energy available in a buoyancy field and energy required to overcome viscous forces. Reynolds number is a ratio of rotational and viscous forces.

Here, is acceleration due to gravity and is the volumetric expansion coefficient of the solution with respect to salt concentration . Further is the concentration difference between the saturated and super-saturated solution, the crystal thickness in the vertical direction, the kinematic viscosity and the mass diffusivity . The symbol is the crystal rotational speed. In the present set of experiments, the linear dimension increases with time, till the excess solute in the vicinity of the crystal is fully utilized.