construction of maximum tortuosity of single fluid path in grid-based 2-d system (5×20) and 3-d...

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]


Outline

• Introduction• Model• Results and discussion• Summary


Introduction

Porosity

• Porosity ϕ is fraction of void space VV in material with total volume VT


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


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


F.A. Schwertz, J. Am. Ceram. Soc. 32 390 (1949)


Model

L

W

H

• Imitating CDI-likeconstruction

Model


.A. Hemmatifar, M. Stadermann, J.G. Santiago, J. Phys. Chem. C 119 24681 (2015)

capacitive deionization (CDI)

Model: Simplification


Model: Connected grids

• It should be perpendicular connected



Results and discussion

Some microstates


Thermodynamics probability

• Thermodynamics probability for certain porosity ϕ

with the term 2NL is from side walls


.

Thermodynamics prob.. (cont.)


Averaged tortuosity

• Assume W = 1 for all tortuosity T smaller then Tmax

where path with Tmax is found visually and intuitively


WT

dTW

TT 11 max

1avgmax

Averaged tortuosity (cont.)


ϕ = 0.28, WT > 1


ϕ = 0.28, WT > 1 (cont.)


ϕ = 0.28, not connected voids


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



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


.

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



Thank you

construction of maximum tortuosity of single fluid path in grid-based 2-d system (5×20) and 3-d...

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