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The Diffusion of Passive Tracers in Laminar Shear Flow

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Published on: May 1, 2018

Effective diffusivity in transient state.

Zbisław Tabor¹, Paweł Nowak, Małgorzata Krzak

¹Cracow University of Technology, Warszawska 24, 31-155 Krakow, Poland. tabor.zbislaw@gmail.com

The Journal of Chemical Physics

|August 24, 2013

Summary

This summary is machine-generated.

This study investigates diffusion in finite composite media under transient conditions. Numerical modeling reveals that the effective diffusion coefficient can differ from predictions of the Kalnin-Kotomin model for stationary diffusion.

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Area of Science:

Materials Science
Chemical Engineering
Physical Chemistry

Background:

The Kalnin-Kotomin model, an extension of the Maxwell-Garnett formula, is commonly used to predict effective diffusivity in polymer composites.
This model accurately describes stationary diffusion in infinite media but has limitations for transient diffusion in finite systems.

Purpose of the Study:

To investigate diffusion in finite composite media under transient conditions.
To numerically model the diffusion process and estimate the effective diffusion coefficient in the transient state.
To develop an analytical model explaining deviations from the stationary diffusion predictions.

Main Methods:

Numerical modeling of diffusion processes in composite media.
Estimation of the effective diffusion coefficient under transient conditions.
Development of an analytical model to account for transient effects.

Main Results:

The effective diffusion coefficient in finite systems under transient conditions can differ from predictions based on the Kalnin-Kotomin model.
Numerical simulations provide estimates for the transient effective diffusion coefficient.
An analytical model is proposed to explain these transient deviations.

Conclusions:

The Kalnin-Kotomin model's predictions for effective diffusivity may not hold for finite systems under transient diffusion.
Transient diffusion in composite materials requires specialized modeling beyond stationary state assumptions.
The proposed analytical model offers insights into the behavior of diffusion in finite, transient composite systems.