Comment on "hydrodynamics of fractal continuum flow" and "map of fluid flow in fractal porous medium into fractal continuum flow"

Research output: Contribution to journalReview article

Abstract

In two recent papers, the authors proposed fractal continuum hydrodynamics and its application to model fluid flows in fractally permeable reservoirs. While in general providing a certain advancement of continuum mechanics modeling of fractal media to fluid flows, some results and statements to previous works need clarification. We first show that the nonlocal character those authors alleged in our paper actually does not exist; instead, all those works are in the same general representation of derivative operators differing by specific forms of the line coefficient c1. Next, the claimed generalization of the volumetric coefficient c3 is, in fact, equivalent to previously proposed product measures when considering together the separate decomposition of c3 on each coordinate. Furthermore, the modified Jacobian proposed in the two commented papers does not relate the volume element between the current and initial configurations, which henceforth leads to a correction of the Reynolds' transport theorem. Finally, we point out that the asymmetry of the Cauchy stress tensor resulting from the conservation of the angular momentum must not be ignored; this aspect motivates a more complete formulation of fractal continuum models within a micropolar framework.

Original languageEnglish (US)
Article number057001
JournalPhysical Review E - Statistical, Nonlinear, and Soft Matter Physics
Volume88
Issue number5
DOIs
StatePublished - Nov 21 2013

Fingerprint

continuum flow
fluid flow
Porous Media
Fluid Flow
Fractal
Hydrodynamics
fractals
Continuum
hydrodynamics
continuums
Product Measure
Micropolar
continuum mechanics
Continuum Mechanics
Continuum Model
Stress Tensor
stress tensors
Coefficient
coefficients
Angular Momentum

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Statistics and Probability
  • Condensed Matter Physics

Cite this

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title = "Comment on {"}hydrodynamics of fractal continuum flow{"} and {"}map of fluid flow in fractal porous medium into fractal continuum flow{"}",
abstract = "In two recent papers, the authors proposed fractal continuum hydrodynamics and its application to model fluid flows in fractally permeable reservoirs. While in general providing a certain advancement of continuum mechanics modeling of fractal media to fluid flows, some results and statements to previous works need clarification. We first show that the nonlocal character those authors alleged in our paper actually does not exist; instead, all those works are in the same general representation of derivative operators differing by specific forms of the line coefficient c1. Next, the claimed generalization of the volumetric coefficient c3 is, in fact, equivalent to previously proposed product measures when considering together the separate decomposition of c3 on each coordinate. Furthermore, the modified Jacobian proposed in the two commented papers does not relate the volume element between the current and initial configurations, which henceforth leads to a correction of the Reynolds' transport theorem. Finally, we point out that the asymmetry of the Cauchy stress tensor resulting from the conservation of the angular momentum must not be ignored; this aspect motivates a more complete formulation of fractal continuum models within a micropolar framework.",
author = "Jun Li and Martin Ostoja-Starzewski",
year = "2013",
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N2 - In two recent papers, the authors proposed fractal continuum hydrodynamics and its application to model fluid flows in fractally permeable reservoirs. While in general providing a certain advancement of continuum mechanics modeling of fractal media to fluid flows, some results and statements to previous works need clarification. We first show that the nonlocal character those authors alleged in our paper actually does not exist; instead, all those works are in the same general representation of derivative operators differing by specific forms of the line coefficient c1. Next, the claimed generalization of the volumetric coefficient c3 is, in fact, equivalent to previously proposed product measures when considering together the separate decomposition of c3 on each coordinate. Furthermore, the modified Jacobian proposed in the two commented papers does not relate the volume element between the current and initial configurations, which henceforth leads to a correction of the Reynolds' transport theorem. Finally, we point out that the asymmetry of the Cauchy stress tensor resulting from the conservation of the angular momentum must not be ignored; this aspect motivates a more complete formulation of fractal continuum models within a micropolar framework.

AB - In two recent papers, the authors proposed fractal continuum hydrodynamics and its application to model fluid flows in fractally permeable reservoirs. While in general providing a certain advancement of continuum mechanics modeling of fractal media to fluid flows, some results and statements to previous works need clarification. We first show that the nonlocal character those authors alleged in our paper actually does not exist; instead, all those works are in the same general representation of derivative operators differing by specific forms of the line coefficient c1. Next, the claimed generalization of the volumetric coefficient c3 is, in fact, equivalent to previously proposed product measures when considering together the separate decomposition of c3 on each coordinate. Furthermore, the modified Jacobian proposed in the two commented papers does not relate the volume element between the current and initial configurations, which henceforth leads to a correction of the Reynolds' transport theorem. Finally, we point out that the asymmetry of the Cauchy stress tensor resulting from the conservation of the angular momentum must not be ignored; this aspect motivates a more complete formulation of fractal continuum models within a micropolar framework.

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