Aris-Taylor dispersion in tubes with dead ends

Area of Science:

• Physics
• Physical Chemistry
• Fluid Dynamics

Background:

• Brownian particle transport in confined geometries is crucial for understanding various physical and biological processes.
• Previous models often simplify particle interactions with boundaries, assuming Markovian behavior.
• Cylindrical tubes with dead ends present a complex system where particle dynamics deviate from simple models.

Purpose of the Study:

• To analyze the transport of Brownian particles in a cylindrical tube with dead ends under laminar flow.
• To develop a theoretical framework for effective transport parameters considering non-Markovian binding dynamics.
• To investigate the influence of flow velocity and geometric parameters on particle diffusion and velocity.

Main Methods:

• Derivation of general expressions for effective transport parameters in the case of non-Markovian binding.
• Application of known results for particle lifetime moments in dead ends to find specific effective velocity and diffusivity.
• Comparison of theoretical predictions with results from Brownian dynamics simulations.

Main Results:

• The study establishes a theoretical framework for particle transport with non-Markovian binding, applicable to dead-end geometries.
• Effective velocity and diffusivity were determined as functions of flow velocity and tube geometry.
• Theoretical predictions demonstrated excellent agreement with Brownian dynamics simulation results.

Conclusions:

• The developed theory accurately describes Brownian particle transport in tubes with dead ends, accounting for non-Markovian escape dynamics.
• The findings highlight the importance of considering non-Markovian processes in modeling particle transport in complex microfluidic environments.
• The study validates the theoretical approach through robust comparison with numerical simulations.