Crystal Population Balance: Birth and Growth Need Separate Rate Terms

Define the Phase or Process Boundary

COMSOL's size-based population documentation describes number density per particle-size interval and separate nucleation and growth terms. Growth moves particles in size space; nucleation adds a population source. Bin population and interval-normalized density are different outputs.

Review a Hypothetical Comparison

Suppose fictional bins 5 µm and 10 µm wide each contain 50 particles per cubic meter. Their interval-normalized densities are 10 and 5 particles/(m³·µm), respectively, despite equal populations. Now move 20 particles from the smaller bin into the larger by an assigned growth-only event: counts become 30 and 70, total 100 unchanged. Adding 20 newly born particles to the smaller bin gives 50 and 70, total 120. Treating the transferred 20 as 20 new births would double count the modelled event.

Keep the Evidence with the Decision

Record interval edges, density units and whether an output is integrated over a bin. Check a total-number balance separately from a solid-volume balance, because growth can conserve number while increasing solid volume. Identify particles crossing the represented size-domain boundary and any aggregation, breakage or transport terms omitted from the model.

This is a bookkeeping example, not a discretization recipe or identified kinetic model. The chosen bins and rates are invented and do not resolve a real crystallizer distribution.

Which population quantity changes through particle creation and which changes through size-space transport?

This blank worksheet is for your own project. It contains no H M machine trial result.

Customer Questions

Primary References

These references support the technical principles discussed in this guide. The worked examples and review questions are educational.

• COMSOL's size-based population documentation
• Reference from hmpharmamachines.com