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Analyzing Mixing Inhomogeneity in a Microfluidic Device by Microscale Schlieren Technique

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Published on: June 12, 2015

Concentration fluctuations in fluid mixtures.

Robert M Mazo¹

¹Department of Chemistry and Institute of Theoretical Science, University of Oregon, Eugene, Oregon 07403, USA. mazo@uoregon.edu

The Journal of Chemical Physics

|December 3, 2008

Summary

Kirkwood-Buff theory simplifies solution component fluctuations using a lower-dimensional subspace when B matrix eigenvalues differ significantly. This approach, demonstrated with water-urea and water-trifluoroethanol solutions, often provides acceptable accuracy.

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Area of Science:

Physical Chemistry
Solution Theory
Thermodynamics

Background:

The Kirkwood-Buff (KB) theory provides a framework for understanding solution properties through integrals related to number fluctuations.
The B matrix within KB theory captures interspecies correlations and number fluctuations in multicomponent solutions.
Analyzing these fluctuations is crucial for predicting thermodynamic properties and molecular-level behavior.

Purpose of the Study:

To develop a simplified approach for describing number fluctuations in solutions based on the B matrix of Kirkwood-Buff theory.
To investigate the applicability of dimensionality reduction in composition space for analyzing these fluctuations.
To assess the trade-off between simplification and accuracy in the proposed method.

Main Methods:

Analysis of the B matrix eigenvalues from Kirkwood-Buff theory.
Restriction of the description of fluctuations to a lower-dimensional subspace of composition space.
Application and validation of the method using experimental or simulated data for binary solutions.

Main Results:

A simplified description of number fluctuations is achievable when the eigenvalues of the B matrix are widely different in magnitude.
This simplification involves projecting the fluctuations onto a lower-dimensional subspace, leading to a controlled loss of accuracy.
The method was successfully illustrated using water-urea and water-2,2,2-trifluoroethanol solutions.

Conclusions:

The dimensionality reduction approach offers a computationally efficient and often accurate method for analyzing solution fluctuations.
In the studied systems (water-urea and water-trifluoroethanol), component fluctuations are strongly coupled by maintaining a near-constant void space.
This finding highlights the importance of void space in governing the collective behavior of solution components.