An Efficient Stochastic-Based Approach For Determination of Effective Diffusion Coefficient in Poiseuille Flow

AN EFFICIENT STOCHASTIC-BASED APPROACH FOR DETERMINATION OF EFFECTIVE DIFFUSION COEFFICIENT IN POISEUILLE FLOW

PARVIN GOLBAYANI¹, MOTOYA MACHIDA², J.R.SANDERS¹, PEDRO E. ARCE^[1]

¹Department of Chemical Engineering, Tennessee Technological University, Cookeville, Tennessee

²Department of Mathematics, Tennessee Technological University, Cookeville, Tennessee

ABSTRACT

Taylor- Aris dispersion between two parallel plates with Poiseuille flow has been calculated, generally, by up-scaling the species-continuity equation using, for example, area averaging approach. In contrast, in this study, a stochastic-based method, to calculate Tylor-Aris dispersion, is explained where the process is modeled by stochastic differential equation (SDE). This is based on an exact solution of SDE with the hydrodynamic biased force (drag force) as the biased agent. The analysis involves the analytical solution of the equation of motion of a Brownian particle by using a Langevin equation as opposed to its counterpart, the Fokker-Plank equation. Results of this investigation are consistent with Taylor- Aris dispersion limit based on continuum mechanics. This, to the best of our knowledge, would be the first effort to determine biased diffusion coefficients directly from fundamental principles and without a scaling-based approach.  The approach is the same that the one used in determine diffusion coefficients by using a Brownian motion-based methodology. Generalization to other regimes (beyond) the Taylor-Aris limit will be also illustrated. Numerous applications in bioseparation, mixing, and other similar ones are relevant to this effort.

 

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See more of this Session: Poster Session: Fluid Mechanics (Area 1j)
See more of this Group/Topical: Engineering Sciences and Fundamentals