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A Non-inertial Model for Particle Aggregation Under Turbulence.

Franco Flandoli1, Ruojun Huang2

  • 1Scuola Normale Superiore di Pisa, Piazza Dei Cavalieri 7, 56126 Pisa, Italy.

Journal of Statistical Physics
|March 28, 2025
PubMed
Summary
This summary is machine-generated.

This study derives a formula for particle collision rates in turbulent environments. The findings simplify to the Saffman-Turner formula under specific conditions, aiding in understanding aggregation dynamics.

Keywords:
Cell equationParticle coalescenceSaffman–Turner formulaScaling limitTurbulent fluid

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Area of Science:

  • Fluid dynamics
  • Statistical physics
  • Turbulence theory

Background:

  • Particle aggregation is crucial in various natural and industrial processes.
  • Understanding collision rates in turbulent flows is complex.
  • Existing models often rely on simplifying assumptions.

Purpose of the Study:

  • To develop an abstract model for particle aggregation.
  • To derive a general formula for the mean collision rate.
  • To investigate the relationship between the abstract model and existing theories.

Main Methods:

  • Utilizing an abstract non-inertial model of aggregation.
  • Incorporating Gaussian white noise with prescribed space-covariance.
  • Analyzing the limit of infinitesimal relaxation time and approximating Gaussian noise.

Main Results:

  • A formula for the mean collision rate (R) was derived.
  • The formula relates collision rate to particle number density and velocity field increments.
  • Under specific assumptions (Kolmogorov time scale, dissipative range), the Saffman-Turner formula is recovered.

Conclusions:

  • The derived formula provides a generalized framework for collision rate calculations.
  • The study bridges abstract modeling with established physical formulas.
  • This work offers insights into particle interactions in turbulent media.