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Emergence of long-range non-equilibrium correlations in free liquid diffusion
Marco Bussoletti1, Mirko Gallo1, Amir Jafari2
1Department of Mechanical and Aerospace Engineering, Sapienza University of Rome, via Eudossiana 18, 00184 Rome, Italy.
This study reveals how non-equilibrium long-range correlations in concentration fluctuations dynamically emerge during solute diffusion. It uncovers new regimes of spatial decay for these correlations, offering experimental predictions.
Area of Science:
- Physical Chemistry
- Fluid Dynamics
- Statistical Mechanics
Background:
- Non-equilibrium long-range correlations in concentration fluctuations are experimentally known in free diffusion.
- The dynamic mechanisms establishing these correlations remain poorly understood.
Purpose of the Study:
- To investigate the dynamic establishment of non-equilibrium long-range correlations in concentration fluctuations.
- To analyze these correlations in the Donev, Fai, and Vanden-Eijnden (DFV) model derived from fluctuating hydrodynamics.
Main Methods:
- Utilized methods from turbulence theory.
- Employed analytical and numerical approaches.
- Modeled free diffusion of a solute in a solvent with an initial planar interface.
Main Results:
- Identified a quasi-steady regime with self-similar time decay of concentration correlations at long times.
- Discovered two correlation regimes: ∝r for r ≲ (Dt)¹/² and a new ∝1/r decay for r ≳ (Dt)¹/².
- Observed transient growth ∝t driving the quasi-steady regime, confirming DFV predictions and extending them.
Conclusions:
- Provided new insights into the dynamic emergence of non-equilibrium long-range correlations.
- Established a theoretical framework for understanding these complex fluctuations.
- Offered novel, experimentally testable predictions for concentration fluctuation behavior.
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