José S. Andrade Jr. Universidade Federal do Ceará Departamento de Física Flow and heat transport in irregular channels Collaborators: Ascânio Dias Araújo (UFC) Raimundo N. Costa Filho (UFC) Murilo P. Almeida (UFC) Marcel Filoche (Ecole Polytechnique, France) Bernard Sapoval (Ecole Polytechnique, France)
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José S. Andrade Jr. Universidade Federal do Ceará Departamento de Física Flow and heat transport in irregular channels Collaborators: Ascânio Dias Araújo.
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José S. Andrade Jr.
Universidade Federal do CearáDepartamento de Física
Flow and heat transport in irregular channels
Collaborators:
Ascânio Dias Araújo (UFC)
Raimundo N. Costa Filho (UFC)
Murilo P. Almeida (UFC)
Marcel Filoche (Ecole Polytechnique, France)
Bernard Sapoval (Ecole Polytechnique, France)
Screening EffectsScreening Effects
Sapoval, Phys. Rev. Lett. (1994)Filoche and Sapoval, Phys. Rev. Lett. (2000)Andrade, Filoche and Sapoval, Chem. Eng. Sci. (2001)
temperature heat flux
Laplacian system
Makarov TheoremMakarov Theorem
Makarov theorem (1985): “The information dimension of the harmonic measure is equal to 1 in d=2.”
Meaning: The set where the activity takes place has a dimension equal to 1. The length of the active zone is proportional to the system size.
2) Laplace equation
1) Dirichlet BC
Diffusion Cell:
.1 withLLa
Makarov TheoremMakarov Theoremsubstrate
“alive” interface
active interface
SLL pa /
is the “screening efficiency”1S
L
LLS p /
pL
Makarov TheoremMakarov Theorem
1
1
2
PL
iiaL ),1( Pat LL
Active Length Square Koch Curve
02 C
0C
SCC
./ jii qq
pa LL equal partition of fluxes
1aL
with
strongly “localized”
),/1( iLpi
The value La=22.9 is compatible with the prediction of the Makarov theorem, La ≈ L=27.
Screening in flow through fractal Screening in flow through fractal channels channels Laplace & Stokes
Screening in flow through fractal Screening in flow through fractal channels channels
Laplace & Stokes
LS
highly heterogeneous!!
Evertsz & Mandelbrot,J. Phys. A (1992)
Andrade, Araújo, Filoche & Sapovalaccepted PRL (2007)