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Related Experiment Video

Updated: Jun 20, 2026

An Inverse Analysis Approach to the Characterization of Chemical Transport in Paints

An Inverse Analysis Approach to the Characterization of Chemical Transport in Paints

Published on: August 29, 2014

Resolving the inconsistency between classical diffusion and adsorption.

G L Aranovich¹, M D Donohue

¹Department of Chemical & Biomolecular Engineering, The Johns Hopkins University, Baltimore, Maryland 21218, USA.

Langmuir : the ACS Journal of Surfaces and Colloids

|August 27, 2009

Summary

Classical diffusion models fail to predict fluid adsorption near surfaces. A new diffusion equation, by relaxing the mean-free-path limit, accurately models surface adsorption phenomena.

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Area of Science:

Physical Chemistry
Fluid Dynamics
Surface Science

Background:

Classical diffusion models, based on Fick's law, assume a zero mean-free-path (lambda --> 0).
This simplification reduces independent parameters and length scales, causing a loss of information about surface phenomena.
Consequently, classical diffusion predictions conflict with observed fluid density profiles near surfaces.

Purpose of the Study:

To analyze the inconsistency between classical diffusion models and fluid adsorption behavior.
To propose a new diffusion equation that reconciles adsorption phenomena with diffusion theory.
To develop solutions for the new equation that are consistent with surface density profiles.

Main Methods:

Analysis of the classical diffusion model's limitations, particularly the lambda --> 0 limit.
Development of a new diffusion equation by using an exact finite-difference functional for the flux term.
Solving and analyzing the proposed finite-difference diffusion equation.

Main Results:

The classical diffusion model's failure to account for adsorption is attributed to the lambda --> 0 limit.
The proposed finite-difference diffusion equation successfully incorporates the mean-free-path length scale.
Solutions to the new equation allow for boundary conditions that align with density profiles of fluids near surfaces.

Conclusions:

Relaxing the lambda --> 0 assumption in diffusion models is crucial for accurately describing surface adsorption.
The novel finite-difference diffusion equation provides a more accurate framework for studying fluid behavior near interfaces.
This work resolves a long-standing conflict between diffusion theory and experimental observations of adsorption.