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Taylor dispersion with absorbing boundaries: a stochastic approach.

Rudro R Biswas¹, Pabitra N Sen

¹Department of Physics, Harvard University, Cambridge, Massachusetts 02138, USA. rrbiswas@physics.harvard.edu

Physical Review Letters

|May 16, 2007

Summary

We present a new stochastic method to understand Taylor dispersion near absorbing boundaries. This approach reveals how absorption affects particle movement, enhancing effective velocity and skewness while reducing dispersion.

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Area of Science:

Fluid dynamics
Statistical mechanics
Transport phenomena

Background:

Taylor dispersion describes particle spreading in fluid flow.
Absorbing boundaries introduce complexities not fully captured by standard models.
Stochastic methods offer a powerful framework for analyzing complex transport.

Purpose of the Study:

To develop an exact stochastic formulation for Taylor dispersion with absorbing boundaries.
To derive closed-form expressions for particle displacement moments.
To analyze the impact of absorption on dispersion dynamics.

Main Methods:

Exact stochastic formulation applied to Taylor dispersion.
Derivation of moments of convective displacement using transverse diffusion eigenmodes.
Calculation of longitudinal cumulants and skewness for parallel plate flow.

Main Results:

Closed-form expressions for displacement moments obtained.
Cumulants grow linearly with time, leading to a long-time Gaussian distribution.
Effective velocity and skewness are enhanced by absorption.
Taylor dispersion is suppressed due to boundary absorption.

Conclusions:

The stochastic method provides a clear picture of Taylor dispersion with absorbing boundaries.
Absorption significantly alters dispersion characteristics, enhancing velocity and skewness.
The findings are demonstrated for parallel plate fluid flow, with implications for various transport processes.