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Analyzing Mixing Inhomogeneity in a Microfluidic Device by Microscale Schlieren Technique

Analyzing Mixing Inhomogeneity in a Microfluidic Device by Microscale Schlieren Technique

Published on: June 12, 2015

Multipoint concentration statistics for transport in stratified random velocity fields.

Marco Dentz¹, Jesus Carrera, Diogo Bolster

¹Institute of Environmental Assessment and Water Research (IDAEA-CSIC), 08034 Barcelona, Spain. marco.dentz@idaea.csic.es

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics

|November 13, 2009

Summary

This study analyzes superdiffusive transport in random velocity fields, providing analytical expressions for concentration moments. Results show concentration uncertainty increases exponentially, highlighting practical concerns for early and late arrivals.

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Area of Science:

Physics
Fluid Dynamics
Statistical Mechanics

Background:

Superdiffusive transport describes particle movement faster than Brownian motion.
Understanding concentration statistics is crucial for predicting contaminant dispersal and mixing processes.
Random, stratified velocity fields are common in geophysical and astrophysical flows.

Purpose of the Study:

To derive explicit analytical expressions for multipoint concentration statistics in superdiffusive transport.
To quantify concentration uncertainty using concentration variance.
To characterize the influence of Lagrangian velocity correlations on concentration moments.

Main Methods:

Utilized a Lagrangian approach to track particle trajectories.
Derived analytical expressions for multipoint concentration moments.
Analyzed one- and two-particle velocity correlations.

Main Results:

Developed a full characterization of multipoint concentration statistics.
Found that concentration variance increases exponentially with time and distance from the center of mass.
Identified that Lagrangian mean velocity and velocity correlations fully determine concentration moments.

Conclusions:

The derived analytical expressions offer a robust framework for studying superdiffusive transport.
Exponential increase in concentration uncertainty poses practical challenges for predicting arrival times and concentrations.
Small concentration values are highly uncertain, impacting the interpretation of early and late-arriving plumes.