Populations of similar objects are frequently characterized by a distribution of certain properties. Typical examples of technical relevance are solid particles, emulsion droplets, molecules or cells in stirred tank reactors. Some important properties required for the characterization of these objects are, for example, their size and shape, their chain length, moisture content or age. In populations of several objects these characteristics are not identical. The corresponding distribution functions change frequently with time and often also depend on the local positions of the objects. For several important processes, a quantitative understanding of systems with distributed properties is of essential importance, e.g. for comminution or precipitation processes to produce fine powders and pigments (as drug components or dyes), for crystallization processes to purify and isolate dissolved components, for the formation of colloidal suspensions or for the drying of solid particles, for characterization of growth and product formation of populations of cells.

Although there are significant differences between the processes mentioned above, population balance models allow for the description of the dynamics of distributions of the different specific properties in a unified manner. Successful applications comprise the modeling of various aspects of crystallization and precipitation processes as well as cellular production processes. Challenges in the field comprise adequate description of the kinetic processes in a multidimensional space of internal coordinates, identification of unknown kinetic parameters, optimal design of experiments, coupling with non-ideal flow fields, efficient simulation strategies, nonlinear model reduction and control.