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Fluid Deformation in Random Steady Three Dimensional Flow.

Daniel R Lester1, Marco Dentz2, Tanguy Le Borgne3

  • 1School of Engineering, RMIT University, 3000 Melbourne, Australia.

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Summary
This summary is machine-generated.

This study introduces a new model for fluid deformation in steady random flows, revealing how flow structure impacts mixing and dispersion. The findings clarify fluid dynamics in complex media like porous materials.

Keywords:
Fluid deformationporous mediasteady flowstochastic modelling

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Area of Science:

  • Fluid dynamics
  • Statistical mechanics
  • Transport phenomena

Background:

  • Fluid deformation by velocity gradients is crucial for mixing and reactions.
  • Turbulent flow deformation is well-studied, but steady random flow deformation is less understood.
  • Steady random flows, like those in porous media, exhibit anisotropic fluid deformation.

Purpose of the Study:

  • To develop a novel model for fluid deformation in steady, random 3D flows.
  • To analyze fluid deformation in complex flow structures, such as heterogeneous porous media.
  • To investigate the implications for mixing and dispersion in such flows.

Main Methods:

  • Derivation of an *ab initio* coupled continuous time random walk (CTRW) model.
  • Application of a streamline coordinate transform to simplify velocity gradient and deformation tensors.
  • Analysis of fluid deformation in various model flows, including chaotic and non-chaotic scenarios.

Main Results:

  • The coupled CTRW model reveals a simple deformation structure in the streamline coordinate frame.
  • Fluid deformation in chaotic flows depends on Lyapunov and power-law exponents of the velocity PDF.
  • Non-chaotic flows show algebraic deformation linked to shear event intermittency.

Conclusions:

  • The study provides a new framework for understanding fluid deformation in steady random flows.
  • The findings highlight the distinct anisotropic nature of deformation in these flows compared to turbulent flows.
  • This research offers insights into longitudinal and transverse mixing and dispersion in complex media.