Desktop version

Home arrow Environment arrow Crystallization and Crystallizers

Balance of population with attrition

The frequency of impacts between the impeller and the parent crystals is proportional to the number of these crystals coming into contact with the impeller:

Q: recirculation flow in the vat (m3.s-1)

c: number of particles per cubic meter of the suspension (m-3)

By applying probability p, so that an impact is followed by attrition:

The apparition of fragments between La and La + ALa in dimension is given by:

m(La): frequency of the number of fragments issued by a single impact (m-1)

The attrition parameters are ultimately:

- frequency of the number of fragments of size L:

- growth decreases with the size of crystals, as attrition is equivalent to a negative growth proportional to the square of the crystal dimension:

A crystallizer’s general balance of attrition for continuous crystallization is written as:

In addition, for batch crystallization:

Continuous homogenous crystallizer with attrition

By bringing together the fragments resulting from attrition and crystals coming from primary nucleation or seeding into a single equation, we obtain:

where Lmin is the minimum size (that of seeds) and, if L nears Lmin, the second term is dominant and strongly positive.

However, for low values of L, the derivative is cancelled where:

It then becomes negative.

Lmax is the maximum size allowed and, if L nears this value, the derivative of Ln(n) is cancelled for:

For example, if:

We should then have:

Finally, variations of Ln (n) will appear as in Figure 4.1.

Ln (n) variations with the crystal size

Figure 4.1. Ln (n) variations with the crystal size

< Prev   CONTENTS   Source   Next >

Related topics