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Brownian particle diffusion in generalized polynomial shear flows.

Nan Wang1, Yuval Dagan1

  • 1Faculty of Aerospace Engineering, <a href="https://ror.org/03qryx823">Technion-Israel Institute of Technology</a>, Haifa 3200003, Israel.

Physical Review. E
|September 19, 2024
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Summary
This summary is machine-generated.

This study introduces a new mathematical framework to calculate Brownian particle diffusion in shear flows. It accurately predicts particle mean-square displacement across all timescales, offering a more precise analytical approach.

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Area of Science:

  • Physics
  • Physical Chemistry
  • Fluid Dynamics

Background:

  • Brownian motion is fundamental to understanding particle diffusion.
  • Calculating diffusion in complex flows like shear flows presents significant challenges.
  • Existing theories often fail to capture particle behavior across all timescales.

Purpose of the Study:

  • To develop a mathematical framework for calculating Brownian particle diffusion in generalized shear flows.
  • To resolve particle mean-square displacement (MSD) at all timescales.
  • To provide a more accurate analytical approach for diffusion processes in shear flows.

Main Methods:

  • Solving Langevin equations using stochastic calculus.
  • Developing a mathematical formulation for polynomial velocity profiles in 2D parallel shear flows.
  • Analyzing particle diffusion in Couette, plane Poiseuille, and hyperbolic tangent flows.

Main Results:

  • The particle MSD's polynomial order at long timescales is n+2, where n is the velocity profile's polynomial order.
  • The framework resolves particle diffusion at all timescales, including particle relaxation timescales.
  • Three distinct diffusion stages observed for Couette and Poiseuille flows; four for hyperbolic tangent flow.

Conclusions:

  • The proposed framework offers a comprehensive method for analyzing Brownian particle diffusion in shear flows.
  • The study reveals distinct diffusion stages governed by different physical mechanisms.
  • This work enables higher temporal and spatial resolution for diffusion studies in shear flows.