Dispersion coefficients from a field-theoretic renormalization of fluid mechanics

Area of Science:

• Fluid dynamics
• Statistical physics

Background:

• Subtle correlations in fluid scattering by obstacles may cause dispersion coefficients to diverge at long times for high Péclet numbers.
• This contrasts with finite predictions from mean-field theories.

Purpose of the Study:

• To develop a theoretical framework that accurately describes fluid mechanics with relevant fluctuations.
• To investigate the behavior of the dispersion coefficient under conditions of high Péclet numbers and low disorder.

Main Methods:

• A novel master equation was formulated to model fluid mechanics, incorporating critical fluctuations.
• A renormalization group procedure was applied to analyze the effects of these fluctuations.

Main Results:

• The study found a finite dispersion coefficient for fluids with low volume fractions of disorder at high Péclet numbers.
• This result challenges previous theoretical predictions of diverging dispersion coefficients.

Conclusions:

• The developed master equation and renormalization group approach provide a more accurate description of fluid dispersion in disordered media.
• Physical fluctuations play a crucial role in determining the dispersion coefficient, leading to finite values even at high Péclet numbers.