An efficient stochastic-based approach for biased Brownian motion: Fundamental theory and selected applications

Advancement in separation technologies can lead to improvement of present clinical diagnostics applications and it can also provide new insights to researchers working in bioseparations, drug delivery, and environmental proteomics. Therefore, the main focus of this research is on the use of stochastic-based approach to obtain transient (both short and long time limits) effective diffusion coefficients which play an important role in separation science. An exact analytical solution of the transient dispersion in three regimes with respect to the time is obtained by the stochastic approach such regimes include the following: Diffusive Regime (for small times), Anomalous Regime (for intermediate times) and Taylor-Aris Regime (for long times) in both Poiseuille and Couette flows. This, to the best of our knowledge, would be the first effort to determine such coefficient by employing the fundamental principles of stochastic calculus. The analysis involves the solution of the equation of motion of a Brownian particle by using a Langevin equation. Results of this study at long times are consistent with Taylor- Aris dispersion based on the continuum mechanics approach in these flow profiles. In addition, for the case of Couette flow, an area averaging approach is used not only for the validation but also for the comparison to the stochastic approach.;In this research, determination of the separation time of two proteins, Lysozyme (LYZ, MW: 14.4 KDa) and Cytochrome c (CYC, MW: 11.7 KDa) in the presence of biased forces such as biased electrical field force have been studied as selected examples. Results include the valuation of parameters to inform device design by practitioners. In summary, this project offers a very efficient path to obtain vital information to guide both experiments and new research relevant to those topics mentioned above.