 # Calculation of different liquid flows

For this, we will use the drawing of a column as represented in Figure 4.10.

Decanted slurry is of the same composition as the slurry located above the lateral outlet. Accordingly, we can outlet the porosity of this slurry: If we provide ourselves with flow WS of crystals together with the elutriation flow rate density GE, we can immediately deduce cross-section AE of the column. The liquid flow accompanying the crystals is: Now, let us place ourselves at a given location above the lateral outlet.

If the liquid were immobile, the crystals’ fall velocity relative to the workshop would be, according to Richardson and Zaki’s law: Уя8п : fall velocity limit of a particle in the dispersion (m.s-1).

However, the liquid rises with an empty vat velocity VL, which would slow the crystals, which drop to velocity VC relative to the workshop. In addition, the flow density of the crystals is:  Figure 4.10. Schematic diagram of an elutriation column

so: In this expression, everything is known except VL, which can be calculated as follows: The flow rate entering the crystallizer is: We can now calculate the liquid flow rate QF fed at the bottom of the column: Note.-

We will show that crystals are more compacted under the lateral outlet than above it.

The ratio ?'/ ? is placed relative to 1 in the same manner as: It should suffice to show that QLP is less than VC AE.

Indeed:

so:  which is evident.

The lower part, in which crystals are immobile and compressed, is of no interest here. It is therefore recommended to place the liquid injection grid directly above the lateral tube.

Example.- We calculate: so ф = 0.6 m

so Note.-

Flow rate density GE has been taken as equal to 4 kg.m-2.s-1 for particles whose size is of the order of millimeters, but we must adopt a lower value for significantly smaller crystals to avoid a negative value of VL, which would mean that the column is a simple sedimentation column without any elutriation. 