Consider a batch granulator in which coalescence is the primary mechanism of

growth. By very careful control of the nucleation process, we produce nuclei

granules that are essentially uniform in size at $0\mathrm{.}2mm.$ These then grow by

coalescence.

Assuming a size$-$independent and constant kernel, write down the population

balance in terms of the number size distribution with respect to volume $n(v)$

and the moments form of the size distribution. Solve the moments form of the

population balance and sketch how the following parameters of the

distribution vary with time: $N(t),V(t)\frac{,}{b}ar(v),n(v)vsv.$ Be as quantitative as possible.

Repeat this analysis for a well$-$mixed continuous granulator operating at

steady state.

Now a size$-$independent, constant kernel is probably not a really good model.

Consider this alternative model. There is no successful coalescence until liquid

is squeezed to the surface of the granules. There is a finite time $($say $2$min

after nucleation$)$ for this to happen. After this time, our "ball bearing and

honey" model is true; i$.$e$.,$ granule collision events are successful provided the

mean size of granules in the collision is less than some critical size for

this system$).$ Now reconsider the batch granulator. Sketch the way you expect

$N(t),V(t)\frac{,}{b}ar(v),n(v)vsv$ to vary with time. $($This can be a qualitative analysis.$)$

If I make the binder viscosity $10$ times as large, how do your expectations

change?