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 language | English (US) |
|---|---|
| Article number | 057001 |
| Journal | Physical Review E - Statistical, Nonlinear, and Soft Matter Physics |
| Volume | 88 |
| Issue number | 5 |
| DOIs | |
| State | Published - Nov 21 2013 |
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ASJC Scopus subject areas
- Statistical and Nonlinear Physics
- Statistics and Probability
- Condensed Matter Physics
Cite this
Comment on "hydrodynamics of fractal continuum flow" and "map of fluid flow in fractal porous medium into fractal continuum flow". / Li, Jun; Ostoja-Starzewski, Martin.
In: Physical Review E - Statistical, Nonlinear, and Soft Matter Physics, Vol. 88, No. 5, 057001, 21.11.2013.Research output: Contribution to journal › Review article
}
TY - JOUR
T1 - Comment on "hydrodynamics of fractal continuum flow" and "map of fluid flow in fractal porous medium into fractal continuum flow"
AU - Li, Jun
AU - Ostoja-Starzewski, Martin
PY - 2013/11/21
Y1 - 2013/11/21
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.
UR - http://www.scopus.com/inward/record.url?scp=84889254399&partnerID=8YFLogxK
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U2 - 10.1103/PhysRevE.88.057001
DO - 10.1103/PhysRevE.88.057001
M3 - Review article
AN - SCOPUS:84889254399
VL - 88
JO - Physical Review E
JF - Physical Review E
SN - 2470-0045
IS - 5
M1 - 057001
ER -