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Investigating the Three-dimensional Flow Separation Induced by a Model Vocal Fold Polyp
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Published on: February 3, 2014

Fluid flow through Apollonian packings.

Rafael S Oliveira1, José S Andrade, Roberto F S Andrade

  • 1Instituto de Física, Universidade Federal da Bahia, 40210-210 Salvador, Brazil.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|May 21, 2010
PubMed
Summary
This summary is machine-generated.

This study models fluid flow through an inhomogeneous medium using Apollonian packing. The Kozeny-Carman relation holds when apparent porosity and a formation factor are considered, validating Darcy

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Area of Science:

  • Fluid dynamics
  • Porous media physics
  • Geometrical modeling

Background:

  • Inhomogeneous media present challenges for fluid flow modeling.
  • Apollonian packing (AP) offers a unique geometric model for such media.
  • Understanding Darcy's law validity in complex geometries is crucial.

Purpose of the Study:

  • To investigate Newtonian fluid flow in a 2D channel with AP obstacles.
  • To determine the validity region of Darcy's law under varying conditions.
  • To establish the relationship between flow patterns, permeability, and porosity.

Main Methods:

  • Simulating fluid flow through channels with scaled AP obstacle geometries.
  • Analyzing flow patterns and permeability across different Apollonian packing generations.
  • Evaluating Darcy's law validity as a function of channel Reynolds number and scaling factor 's'.

Main Results:

  • Established the dependency of flow patterns and permeability on porosity.
  • Identified the region of validity for Darcy's law.
  • Demonstrated that the Kozeny-Carman relation is satisfied under specific conditions.

Conclusions:

  • The Kozeny-Carman scaling relation is applicable to AP-modeled inhomogeneous media.
  • Apparent porosity and an 's'-dependent formation factor are key considerations.
  • This work provides insights into fluid flow in complex, geometrically defined porous structures.