Tortuosity of 2-d and 3-d small system are constructed using grid based system. Thermodynamics postulate shows that possiblility of a microstate with tortuous channel is very small, in order of 10^{-17}. This means other mechanism is required why nature can provide some structures.

1. 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 Bandung
Jalan Ganesha 10, Bandung 40132, Indonesia
1
dudung@fi.itb.ac.id, 2
fourier@fi.itb.ac.id, 3
nurul@fi.itb.ac.id

2. International Conference on
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25-7 July 2016, Bandung, Indonesia 2
Outline
• Introduction
• Model
• Results and discussion
• Summary

3. International Conference on
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25-7 July 2016, Bandung, Indonesia 3
Introduction

4. Porosity
• Porosity ϕ is fraction of void space VV in
material with total volume VT
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25-7 July 2016, Bandung, Indonesia 4
R. Hilfer, Phys. Rev. B 45 7115 (1992)
φ =
VV
VT
VT
VV

5. Tortuosity
• Hydraulic tortuosity T is ratio of averaged fluid
path λavg and geometrical distance L between
two points
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25-7 July 2016, Bandung, Indonesia 5
M. Matyka, A. Khalili, Z. Koza, Phys. Rev E 78 026306 (2008)
L
T
avg
λ
=
L
λavg

6. 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
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25-7 July 2016, Bandung, Indonesia 6
S =
Nlavg
1−φ
F.A. Schwertz, J. Am. Ceram. Soc. 32 390 (1949)

7. International Conference on
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25-7 July 2016, Bandung, Indonesia 7
Model

8. L
W
H
• Imitating CDI-like
construction
Model
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25-7 July 2016, Bandung, Indonesia 8
.
A. Hemmatifar, M. Stadermann, J.G. Santiago, J. Phys. Chem. C 119 24681 (2015)
capacitive
deionization
(CDI)

9. Model: Simplification
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10. Model: Connected grids
• It should be perpendicular connected
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Results and discussion

12. Some microstates
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13. Thermodynamics probability
• Thermodynamics probability for certain
porosity ϕ
with the term 2NL is from side walls
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25-7 July 2016, Bandung, Indonesia 13
.
Wφ =
N − 2NL( )!
Nϕ( )! N − 2NL − Nϕ( )!

14. Thermodynamics prob.. (cont.)
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15. 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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25-7 July 2016, Bandung, Indonesia 15
φφ W
T
dT
W
T
T 11 max
1
avg
max −
=≈ ∫

16. Averaged tortuosity (cont.)
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17. ϕ = 0.28, WT > 1
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18. ϕ = 0.28, WT > 1 (cont.)
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19. ϕ = 0.28, WT > 1 (cont.)
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20. ϕ = 0.28, not connected voids
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21. 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
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Summary

23. 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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.

24. 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
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Thank you