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Hagen-Poiseuille flow describes a viscous fluid's steady, incompressible flow through a cylindrical tube with a constant radius R. This flow profile is often applied to understand fluid transport in narrow channels, such as capillaries. It serves as a foundational example of laminar flow. In this model, cylindrical coordinates (r,θ,z) are used to describe the radial (r), angular (θ), and axial (z) dimensions within the tube. For Hagen-Poiseuille flow, the velocity profile is purely...
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Couette flow represents the flow of fluid between two parallel plates, with one plate fixed and the other moving with a constant velocity. This configuration allows for a simplified analysis using the Navier-Stokes equations, which govern fluid motion under conditions of viscosity and incompressibility. For Couette flow, the assumptions include a steady, laminar, incompressible flow with a zero-pressure gradient in the flow direction. This flow type is beneficial for understanding shear-driven...
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Fluid flow analysis is critical in many scientific and engineering disciplines, and two principal approaches are used to describe this flow: the Eulerian and Lagrangian methods. These methods offer different perspectives on monitoring and analyzing the motion of fluids, each with distinct advantages depending on the scenario.
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Anomalous diffusion for inertial particles under gravity in parallel flows.

Marco Martins Afonso1

  • 1Laboratoire de Mécanique, Modélisation et Procédés Propres, CNRS UMR 7340, Aix-Marseille Université, Ecole Centrale Marseille, 38 rue Frédéric Joliot-Curie, 13451 Marseille cedex 13, France.

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This study explores diffusion for inertial particles in parallel flows, considering fluid kinetic-energy spectrum effects. Results extend tracer studies to particles with gravity and Brownian motion.

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Area of Science:

  • Physics of Fluids
  • Particle Transport Phenomena
  • Statistical Mechanics

Background:

  • Understanding particle diffusion in fluid flows is crucial for various applications.
  • The kinetic-energy spectrum of turbulent flows, particularly its infrared behavior, influences particle dynamics.
  • Long-range spatiotemporal correlations in fluid flows can lead to anomalous diffusion.

Purpose of the Study:

  • To investigate the transition between normal and anomalous effective diffusion for inertial particles.
  • To analyze the influence of the fluid kinetic-energy spectrum's power-law behavior on particle diffusion.
  • To extend existing diffusion models to include effects like gravity and Brownian motion for inertial particles.

Main Methods:

  • Modeling the infrared behavior of the fluid kinetic-energy spectrum as a power law with two parameters.
  • Analyzing particle diffusion in the limit of weak relative inertia.
  • Considering both steady and time-dependent parallel flows.
  • Investigating scenarios with vanishing and finite particle sedimentation.

Main Results:

  • Derived bounds for normal and anomalous effective diffusion of inertial particles.
  • Demonstrated that the results are applicable to particles of any mass density.
  • Showed extension of well-known results for passive tracers to inertial particles under gravity and Brownian diffusion.

Conclusions:

  • The study provides a comprehensive framework for understanding diffusion regimes of inertial particles.
  • The findings are relevant for diverse particle-laden flow systems, from atmospheric science to industrial processes.
  • The model successfully incorporates key physical parameters influencing particle dispersion.