Dynamic Behavior of Microbial Populations in Stirred Bioreactors Simulated with Euler−Lagrange Methods: Traveling along the Lifelines of Single Cells

In the present work, an Euler−Lagrange approach has been applied to characterize the behavior of a heterogeneous cell population in a stirred-tank bioreactor with nonideal mixing. It allows one to describe population behavior as the outcome of the interaction between the intracellular state of its individual cells and the turbulent flow field in the reactor. The modeling approach and the numerical method employed are based on an Euler−Lagrange formulation of the system combined with a fractional-step method to allow for a stable, accurate, and numerically efficient solution of the underlying equations. This strategy permits one to account for the heterogeneity present in real reactors in both the fluid and cellular phases, respectively. Three examples are used to illustrate the application of this approach. The suggested method is easily transferable to similar problems requiring a segregated and high-dimensional description of the internal structure of the corpuscular phase, which usually precludes the application of population balance equations.