Population systems comprise a number of single elements, which can be distinguished by certain properties. There is a large variety of this type of systems. Intuitively one might e.g. think of a human population of a country. The individual persons differ from each other by their age. The future development of the age structure depends on birth, death rates and migration rates.

Chemical engineering processes with disperse phases can also be modeled as population systems. Disperse phases are e.g. suspensions or emulsions, where particles or droplets, respectively, are embedded in a continuous fluid. A straightforward property of the particles or droplets is their size. In analogy to the evolution of the human population mentioned above, one is interested in the dynamics of the size distribution of the dispersed phase. As the physico-chemical, biological or sociological phenomena acting on these different types of populations are rather different, it is remarkable that they all can be treated with the same mathematical tools.

The development and use of these mathematical tools for predictive modeling, analysis and optimization of population dynamics processes is the main objective of the research group.

The current focus of the group is on crystal suspensions. The physico-chemical phenomena during crystallization are quite diverse. For predictive modeling these phenomena need to be modeled on different physical scales in order to achieve sufficient accuracy. To reflect this, different methods ranging from molecular dynamics simulations via Monte-Carlo techniques to deterministic population balance models shall be employed in the group. Only an integrating framework for these modeling and simulation techniques will improve the predictive power of population dynamic models as it is eventually needed for tailored product design and process design.

The junior research group Population Dynamics is embedded in the Physical and Chemical Process Engineering Group aand was instantiated in summer 2007. The group is still in its start-up phase. Hence, we are still looking for highly qualified co-workers (PostDoc, PhD, diploma thesis, student assistant) with a background in chemical engineering, physics, applied mathematics, or related fields. Even if there is no explicit job opening of the group on the Jobs-Webpage do not hesitate to send your application (preferably by email) directly to Heiko Briesen.

Crystal aggregates appear in complex geometrical structures. For deterministic population balance modeling usually assumptions about the aggregate geometry are made. Thus, these models can not predict the aggregate geometry. As a detailed characterization of the aggregate morphology requires a very large number of variables, the applicability of deterministic population balance modeling for modeling of complex geometries is limited.

In the project Monte-Carlo techniques are used to reflect the full 3-dimensional structure of the crystal aggregates. However, the fully detailed geometrical characterization is still infeasible for practical use even for Monte-Carlo techniques. Hence, reduced characterizations of the aggregate structure will be developed, which allow the prediction of aggregate morphology at moderate computational cost. The models will be validated with own experimental investigations.

Figure: Detailed representation of crystal aggregates (left). Corresponding reduced characterization by means of point mass systems (right).

If crystals collide with sufficient kinetic energy with a stirrer, crystal attrition arises. At collision small crystal fragments are formed which act as secondary nuclei in the process. The interplay between crystal growth and secondary nucleation often determines the behavior of industrial crystallizers. The understanding of attrition is therefore imperative for tailored process and product design.

Various experimental studies show that attrition depends not only on the size of the crystals but also on their shape. The objective of this project is to mechanistically model this shape dependent attrition behavior. Also the shape change due to attrition shall be properly reflected and experimentally validated.

Figure: Characterization of crystals according to their size and shape (shape factor Ψ) (left). 2-dimensional number density distribution Φ representing size- and shape-dependent attrition behavior in a population balance model.

The understanding of colloidal aggregates under process conditions is still poor. Experimental results show that even moderate shear leads to restructuring of colloidal aggregates.

In the projects that restructuring behavior in a shear field is investigated by means of models. Models will be formulated at different degrees of detail. The objective of the project is to develop a model, which represents the restructuring dynamics with sufficient accuracy. This model then shall be integrated in an appropriate population balance formulation.

The project is conducted in cooperation with the Chair of Computational Analysis of Technical Systems, RWTH Aachen (Prof. M. Behr) and is funded within the DFG Priority Program 1273 "Colloidal processing".

Figure: Colloidal aggregate in a shear field.