Berlin 2015 – scientific programme
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DY: Fachverband Dynamik und Statistische Physik
DY 32: Focus Session: Statistics of fully developed turbulence
DY 32.8: Talk
Wednesday, March 18, 2015, 17:30–17:45, BH-N 243
The stochastic description of non-Brownian particles in shear flow by a colored-noise Fokker-Planck equation — •Laura Lukassen1,2 and Martin Oberlack1,2 — 1Chair of Fluid Dynamics, TU Darmstadt — 2Graduate School of Excellence Computational Engineering, TU Darmstadt
As described in literature, non-Brownian particles in shear flow show a diffusive behavior due to hydrodynamic interactions, namely shear-induced diffusion. The stochastic description by means of a Fokker-Planck equation is of major interest for non-Brownian particles in shear-induced diffusion. In contrast to Brownian diffusion, there is no separation of time scales in the context of shear-induced diffusion. The configuration of non-Brownian particles changes on the same time scale as the hydrodynamic velocity. This fact violates the Markov process assumption in pure position space. In order to assure the Markov process assumption, we derived a new Fokker-Planck equation in coupled position-velocity space (Lukassen, Oberlack, Phys. Rev. E 89, 2014). Under certain conditions, this new coupled Fokker-Planck approach can be reduced to a modified equation in pure position space. The new modified position space description exhibits additional correction terms when compared to other position space Fokker-Planck equations in that context known from literature. Our extended approach shall enable a better stochastic description of non-Brownian particle flows.
The work of L. Lukassen is supported by the "Excellence Initiative" of the German Federal and State Governments and the Graduate School of Computational Engineering at TU Darmstadt.