2. MULTIPRODUCT SEPARATION IN APPARATUS ASSEMBLED FROM IDENTICAL BLOCKS

Multiproduct apparatuses with identical blocks, operating in general technological regimes, may produce powders of different grain size composition. This has been confirmed with sufficient reliability by experiments.

In this case, for the main parameters characterising the operation of apparatus, we may write the relationship

Here k _j and ? _j can change from block to block, and it is only important that their product remains constant. Taking this into account, the continued fraction, consisting of n elements may be written in the form:

This expression may be simplified taking into account that the dependence is a recurrent function.

We introduce the following notations:

and consequently

Therefore,

and

From this we obtain a recurrent equation.

This equation may be solved introducing the so-called characteristic equation

The roots of this equation are the dependences

and consequently

i.e.

(XI-16)

The unknown parameters C ₁ and C ₂ are determined from the following considerations. At x ₁ = 1, C ₁ + C ₂ = 1, i.e. C ₁ = 1 - C ₂.

For

and consequently

(XI-17)

Substituting (XII-16) into (XII-17) gives:

Carrying out appropriate transformations taking into account that

we obtain

(XII-18)

Expression (XII-18) shows that the following relationship is always valid:

(XII-19)

This is also clear on the intuitive level because if it is assumed that k = 0.9 then ? < 0.1 and then the product corresponds to...