Kinetic growth theories
We will now review the various models that have been proposed for face growth. We will successively study:
- - The diffusion layer surrounding the crystal. This corresponds to a boundary film that must be crossed by molecules before reaching the crystal.
- - The growth of K faces.
As regards to the F faces, we will examine two models:
- - The spiral growth model from a dislocation that itself is a spiral.
- - The “formation and spreading” model that is an improvement on the polynuclear model.
The Chernov model [CHE 61] is a combination of the spiral growth model and the model of diffusion through a diffusion layer. While not examining this model, we will proceed in another manner, following a method that is applicable both to the spiral growth model and to the “formation and spreading” model.
Diffusion layer theory
We assume that the crystal is surrounded by two superimposed molecular layers. The concentration at the interface of two layers is Co: the external layer is the diffusion layer and the internal layer is the integration layer.
1) The diffusion layer is of thickness 8 given by:
d: crystal dimension (m)
Sc: Schmidt number
|l: liquid viscosity (Pa.s )
D : solute diffusivity in the liquid (m2.s-1) p: liquid density (kg.m-3)
Re : Reynolds number
u : velocity of the crystal relative to liquid (m.s-1)
In a fluidized bed:
? : porosity of the fluidized bed U: velocity of the liquid in the empty vat (m.s-1)
For an agitated suspension:
W: mechanical power per unit of suspension mass (W.kg-1).
Molar concentration (kmol.m-3) on the internal face of the diffusion layer is c0. On the external face, it is equal to c«, which is the concentration inside the solution.
The molar flow density through the diffusion layer is: