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Hyperbolic regions in flows through three-dimensional pore structures.

Jeffrey D Hyman1, C Larrabee Winter2

  • 1University of Arizona, Program in Applied Mathematics, Tucson, Arizona 85721-0089, USA.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|February 4, 2014
PubMed
Summary
This summary is machine-generated.

Finite time Lyapunov exponents reveal distinct flow regions in porous media. These regions, though sparse, are crucial for understanding fluid mixing and dispersion across pore networks.

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Area of Science:

  • Fluid dynamics
  • Computational physics
  • Porous media research

Background:

  • Understanding fluid flow in complex geometries like pore structures is essential for various scientific and engineering fields.
  • Laminar steady-state flow simulations are commonly used to study fluid behavior in such environments.
  • Identifying specific flow characteristics within these structures can reveal insights into transport phenomena.

Purpose of the Study:

  • To utilize finite time Lyapunov exponents (FTLEs) to characterize flow dynamics in 3D pore structures.
  • To identify and analyze expanding, contracting, and hyperbolic flow regions within computational simulations.
  • To understand the distribution and impact of these flow regions on fluid particle trajectories and mixing.

Main Methods:

  • Computational simulations of laminar steady-state fluid flows within realistic 3D pore structures.
  • Application of finite time Lyapunov exponents (FTLEs) to identify flow regions.
  • Analysis of fluid particle trajectories passing through identified flow regions.

Main Results:

  • FTLEs successfully identified expanding, contracting, and hyperbolic regions within the pore structures.
  • These regions, though sparse, were found to be critical pathways for fluid particle trajectories.
  • Nearly all fluid particles traversed multiple hyperbolic regions, indicating widespread in-pore mixing.
  • Two scales of heterogeneity in fluid dynamics were observed: large-scale dispersion and small-scale velocity variations within pores.

Conclusions:

  • Sparse but critical flow regions (expanding, contracting, hyperbolic) govern fluid behavior in porous media.
  • In-pore mixing, driven by hyperbolic regions, is a pervasive phenomenon affecting fluid transport.
  • Porous media exhibit multi-scale heterogeneity influencing fluid dispersion and velocity distributions.