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Analyzing Mixing Inhomogeneity in a Microfluidic Device by Microscale Schlieren Technique
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Information-Optimal Mixing at Low Reynolds Number.

Luca Cocconi1, Yihong Shi1, Andrej Vilfan2

  • 1Max Planck Institute for Dynamics and Self-Organization, 37077 Göttingen, Germany.

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|August 4, 2025
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Summary
This summary is machine-generated.

Researchers developed a new method to measure mixing efficiency using mutual information. This approach reveals universal, time-reversal symmetric optimal protocols for mixing in low Reynolds number systems.

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Area of Science:

  • Physics
  • Statistical Mechanics
  • Fluid Dynamics

Background:

  • Mixing efficiency is crucial in microfluidics and soft matter.
  • Low Reynolds number flows are governed by Stokes equation, exhibiting kinematic reversibility.
  • Quantifying mixing efficiency often requires assumptions or specific system knowledge.

Purpose of the Study:

  • To introduce a universal, assumption-free measure of mixing efficiency.
  • To determine optimal control protocols for mixing in planar shear flows.
  • To establish the minimum energetic cost of information erasure in nonequilibrium systems.

Main Methods:

  • Utilizing mutual information between particle positions before and after mixing.
  • Deriving a compact expression for mutual information as a functional of the shearing protocol.
  • Solving the extremization problem for optimal control under shear and dissipation constraints.

Main Results:

  • Mutual information provides a universal measure of mixing efficiency, accounting for Stokes equation reversibility.
  • Optimal mixing protocols are derived and found to be universal and time-reversal symmetric.
  • A minimum energetic cost for information erasure in drift-diffusive systems is established.

Conclusions:

  • Mutual information is a powerful tool for quantifying mixing in low Reynolds number flows.
  • Optimal mixing strategies are inherently time-reversal symmetric and universal.
  • This work provides fundamental insights into the thermodynamics of information in nonequilibrium systems.