Population Balance Equations - SPL-ethz/CAT GitHub Wiki

The population balance (PB) framework is concerned with modeling systems composed of a continuous or discrete number of entities interacting with their environment, generally assumed to be a continuous phase; typically the entities in question are particles, such as in the case of crystals.

A particle is distinguished by its internal and external coordinates. The internal coordinates of the particle provide properties chosen to represent the entity while the external coordinates usually describe the physical location of the center of mass of the entity. The joint space of internal and external coordinates is referred to as the particle state space.

Essential to the formulation of population balance is the assumption that there exists a number density of particles at every point in the particle state space. The population balance equation (PBE), a(n) (integro-)partial differential equation, can then be seen as the equation describing the evolution of this number density function with time.

In crystallization, the PBE is typically coupled with the corresponding material balance to take into account e.g. the consumption of solute due to growing crystals. The set of equations is then solved together with initial and boundary conditions through numerical methods, as analytical solutions exist merely for the simplest of cases.

PBEs find application in a number of fields that deal with particulate systems, these include

• chemical engineering
• process engineering
• biotechnology/bioengineering

More information can be found in [1] and [2].

> [1] Ramkrishna, D. & Singh, M. R. (2014). Population Balance Modeling: Current Status and Future Prospects. Annual review of chemical and biomolecular engineering,(0)
[2] Ramkrishna, D. (2000). Population Balances. Academic Press