# Classification zone

We will provide the elements in order to simulate the operation of a classification zone.

1) Sedimentation rate. We will use the following values: s: volume fraction of the liquid

vl: maximum drop velocity of an isolated particle (m.s^{-1})

d: minimum dimension of a crystal p: viscosity of the liquid phase (Pa.s )

Ap: difference in solid and liquid densities (kg.m^{-3}) g: acceleration due to gravity (9.81 m.s^{-2})

The sedimentation rate is:

We calculate:

- 0.2 < Re < 1 n = 4.4/Re
^{0 023} - 1 < Re < 500 n = 4.4/Re
^{0 0982}

Re > 500 n = 2.39

The rate calculated this way only applies to spherical particles. For angular particles such as crystals, this rate must be divided by 2.

2) Rate and residence time within a section. We divide the classification zone into *n sections of current index j rising from 1 to n from the bottom to the top of the classification zone.* The bands’ widths are all equal to Az . If v_{0 }is the rate in an empty vat measured upwards and positively, and if vij is the sedimentation rate of class i particles of diameter d_{iJ} in section j, the absolute rate of the particle relative to the workshop is:

With:

v_{aij} > 0, the particle enters section j + 1

v_{aij} < 0, the particle enters section j - 1

The retention time within a section is: At,, = Az / v„,,

^{ij aij}

3) Growth of crystals within section j. If d_{ije} is the size of particles entering section j (and coming from sections j + 1 and j - 1), the crystal size exiting the section is:

In sections j - 1 and j + 1 into which the particles from index i would have entered, we can calculate: V_{a}, _{i}, _{j+1} or V_{a}, _{i}, _{j-1}

4) The main purpose of the calculation is knowing the cutoff diameter of the classification zone, that is, the size of particle d_{i}^{*}o entering at the base so that, after growth, at the summit we have z = nAz.

To this end, we have a liquid fraction s that is constant and equal to the value of supply at the base of the zone. We also have constant supersaturation and growth.

The cancellation of absolute rate vain gives a cutoff diameter of d^{*}in . Going back in time, we recognize the value d^{*}io from the diameter of the same particle at the entry of the classification zone.

If d_{io} < d*_{o} the particle is carried with the “clean” liquor.

If d_{io} > d*_{o} the particle remains in the crystallizer body.