construction of maximum tortuosity of single fluid path in grid-based 2-d system (5×20) and 3-d...
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International Conference on Energy Sciences (ICES) 25-7 July 2016, Bandung, Indonesia 1
Construction of Maximum Tortuosity of Single Fluid Path in Grid-based 2-d
System (5×20) and 3-d system (5×20×3)
S. Viridi1, F. D. E. Latief2, S. N. Khotimah3
Physics Department, Institut Teknologi BandungJalan Ganesha 10, Bandung 40132, [email protected], [email protected], [email protected]
International Conference on Energy Sciences (ICES) 25-7 July 2016, Bandung, Indonesia 2
Outline
• Introduction• Model• Results and discussion• Summary
International Conference on Energy Sciences (ICES) 25-7 July 2016, Bandung, Indonesia 3
Introduction
Porosity
• Porosity ϕ is fraction of void space VV in material with total volume VT
International Conference on Energy Sciences (ICES) 25-7 July 2016, Bandung, Indonesia 4
R. Hilfer, Phys. Rev. B 45 7115 (1992)
VT
VV
Tortuosity• Hydraulic tortuosity T is ratio of averaged fluid
path λavg and geometrical distance L between two points
International Conference on Energy Sciences (ICES) 25-7 July 2016, Bandung, Indonesia 5
M. Matyka, A. Khalili, Z. Koza, Phys. Rev E 78 026306 (2008)
LT avg
L
λavg
Specific surface area
• Specific surface area S is defined as
with N is number of channels per cross-sectional area and lavg is average peripheral length of each pore, which could be simply circumference of a pore
International Conference on Energy Sciences (ICES) 25-7 July 2016, Bandung, Indonesia 6
F.A. Schwertz, J. Am. Ceram. Soc. 32 390 (1949)
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Model
L
W
H
• Imitating CDI-likeconstruction
Model
International Conference on Energy Sciences (ICES) 25-7 July 2016, Bandung, Indonesia 8
.A. Hemmatifar, M. Stadermann, J.G. Santiago, J. Phys. Chem. C 119 24681 (2015)
capacitive deionization (CDI)
Model: Simplification
International Conference on Energy Sciences (ICES) 25-7 July 2016, Bandung, Indonesia 9
Model: Connected grids
• It should be perpendicular connected
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International Conference on Energy Sciences (ICES) 25-7 July 2016, Bandung, Indonesia 11
Results and discussion
Some microstates
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Thermodynamics probability
• Thermodynamics probability for certain porosity ϕ
with the term 2NL is from side walls
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.
Thermodynamics prob.. (cont.)
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Averaged tortuosity
• Assume W = 1 for all tortuosity T smaller then Tmax
where path with Tmax is found visually and intuitively
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WT
dTW
TT 11 max
1avgmax
Averaged tortuosity (cont.)
International Conference on Energy Sciences (ICES) 25-7 July 2016, Bandung, Indonesia 16
ϕ = 0.28, WT > 1
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ϕ = 0.28, WT > 1 (cont.)
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ϕ = 0.28, WT > 1 (cont.)
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ϕ = 0.28, not connected voids
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ϕ = 0.28, 3-d system (5×20×3)
• It can be understood that porosity between 0.253 and 0.280 will have the same value of Tmax, since the 8 unconnected voids do not give any contribution to Tmax
International Conference on Energy Sciences (ICES) 25-7 July 2016, Bandung, Indonesia 21
International Conference on Energy Sciences (ICES) 25-7 July 2016, Bandung, Indonesia 22
Summary
Summary
• System for modeling tortuosity of single channel fluid path has been developed
• Thermodynamics probability of a certain porosity value to produce a tortuous channel is very small, in order of 10-17
• The postulate only is not sufficient to predict how such channel can be formed in nature, other mechanism is required
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.
Acknowledgements
• Part of this work is supported by RIK ITB with contract number 006q/I1.C01/PL/2016
• This presentation is supported by ICES 2016 Committee and Faculty of Mathematics and Natural Sciences, Institut Teknologi Bandung
International Conference on Energy Sciences (ICES) 25-7 July 2016, Bandung, Indonesia 24
International Conference on Energy Sciences (ICES) 25-7 July 2016, Bandung, Indonesia 25
Thank you