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Related Experiment Videos

Aggregation of inertial particles in random flows.

B Mehlig1, M Wilkinson, K Duncan

  • 1Department of Physics, Göteborg University, 41296 Göteborg, Sweden.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|December 31, 2005
PubMed
Summary

Particles suspended in turbulent fluid aggregate when their trajectories coalesce. This study details a method to calculate the Lyapunov exponent, predicting particle aggregation in three-dimensional flows based on particle inertia and fluid velocity field characteristics.

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Area of Science:

  • Fluid Dynamics
  • Statistical Physics
  • Turbulence

Background:

  • Particle aggregation in randomly moving fluids is governed by the Lyapunov exponent of particle trajectories.
  • A negative Lyapunov exponent indicates trajectory coalescence and subsequent particle aggregation.
  • Understanding this phenomenon is crucial for various applications, including atmospheric science and industrial processes.

Purpose of the Study:

  • To provide a detailed account of a method for calculating the Lyapunov exponent of suspended particles.
  • To analyze the stochastic differential equation governing the random variable evolution in the short correlation time limit (Langevin equation).
  • To derive an asymptotic perturbation expansion for the Lyapunov exponent in three-dimensional flows.

Main Methods:

Related Experiment Videos

  • Expressing the Lyapunov exponent as the expectation value of a random variable under a stochastic differential equation.
  • Analyzing the Langevin equation in the limit of short velocity field correlation times.
  • Deriving an asymptotic perturbation expansion using dimensionless measures of particle inertia (epsilon) and velocity field components (Gamma).

    • Main Results:

    • A detailed method for calculating the Lyapunov exponent is presented.
    • An asymptotic perturbation expansion for the Lyapunov exponent is derived for 3D flows.
    • The phase diagram in the epsilon-Gamma plane is determined, illustrating aggregation regimes.

    Conclusions:

    • The study provides a robust framework for predicting particle aggregation in turbulent fluids.
    • The derived expansion and phase diagram offer valuable insights into the interplay between particle inertia and fluid dynamics.
    • This work contributes to a deeper understanding of particle transport and mixing in complex flow systems.