Euler-Lagrange models interactions

Detailed mathematical models capturing the variation in both the extracellular environment and the metabolism of a segregated biophase promise to aid significantly in describing the behavior of cell populations in bioreactors. This requires a combination of both approaches outlined above in other words, an Euler-Lagrange simulation. For the first time, this interaction between the intracellular state of the individual cells of the population and the turbulent flow field in the bioreactor was tackled by Lapin et al. [69-71]. 

Blei, S. (2005). On the interaction of non-uniform particles during the spray drying process Experiments and modelling with the Euler-Lagrange approach. PhD Dissertation, Martin-Luther-Universitat Halle-Wittenberg. 

For his reason, the main body of this chapter deals with fluid-particle interaction and addresses such questions as what is the fluid mechanical basis of it, for which canonical cases do we have rehable data and correlations, how does the most general correlation of the general case look hke, what are the effects of turbulence in the carrier phase and of neighboring particles in a swarm, how is the fluid—particle interaction treated in the various CFD approaches (point-particle tracking, two-fluid models), and what is the effect of aU the variations of the interaction force applied by so many investigators on the computational results, particularly with respect to the mesoscale structures of interest These issues have been addressed in great detail in the context of both Euler—Lagrange and Euler-Euler simulations. (Other important effect, such as particle—particle coUisions, coalescence and... 

Inhomogeneous or multiphase reaction systems are characterised by the presence of macroscopic (in relation to the molecular level) inhomogeneities. Numerical calculations of the hydrodynamics of such flows are extremely complicated. There are two opposite approaches to their characterisation [63, 64] the Euler approach, with consideration of the interfacial interaction (interpenetrating continuums model) and the Lagrange approach, of integration by discrete particle trajectories (droplets, bubbles, and so on). The presence of a substantial amount of discrete particles in real systems makes the Lagrange approach inapplicable to study motion in multicomponent systems. Under the Euler approach, a two-phase flow is described... 

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