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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
Summary
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.
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.
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