Granular activated carbon (GAC) has numerous applications due to its ability to adsorb and desorb gas molecules. Recently, it has been shown to exhibit unusually high low frequency sound absorption. This behavior is determined by both the multi-scale nature of the material, i.e., the existence of three scales of heterogeneities, and physical processes specific to micro- and nanometer-size pores, i.e., rarefaction and sorption effects. To account for these processes a model for sound propagation in GAC is developed in this work. A methodology for characterizing GAC which includes optical granulometry, flow resistivity measurements, and the derivation of the inner-particle model parameters from acoustical and non-acoustical measurements is also presented. The model agrees with measurements of normal incidence surface impedance and sound absorption coefficient on three different GAC samples.

1.
H.
Marsh
and
F.
Rodriguez-Reinoso
,
Activated Carbon
(
Elsevier Science & Technology Books
,
Oxford
,
2006
), pp.
1
554
.
2.
D. D.
Do
,
Adsorption Analysis: Equilibria and Kinetics
(
Imperial College Press
,
London
,
1998
), pp.
1
892
.
3.
J. R.
Wright
, “
The virtual loudspeaker cabinet
,”
J. Audio Eng. Soc.
51
(
4
),
244
247
(
2003
).
4.
T. J.
Mellow
,
O.
Umnova
,
K.
Drossos
,
K.
Holland
,
A.
Flewitt
, and
L.
Karkkainen
, “
On the adsorption-desorption relaxation time of carbon in very narrow ducts
,” in
Proceedings of Acoustics 08
, CD-ROM01, Paris, France (
2008
), pp.
795
800
.
5.
F.
Bechwati
,
M.
Avis
,
D.
Bull
,
T. J.
Cox
,
J.
Hargreaves
,
D.
Moser
,
D.
Ross
,
O.
Umnova
, and
R.
Venegas
, “
Low frequency sound propagation in activated carbon
,”
J. Acoust. Soc. Am.
132
(
1
),
239
248
(
2012
).
6.
R.
Venegas
, “
Microstructure influence on acoustical properties of multiscale porous materials
,” Ph.D. dissertation,
University of Salford
, United Kingdom,
2011
.
7.
R.
Venegas
and
O.
Umnova
, “
Acoustic properties of double porosity granular materials
,”
J. Acoust. Soc. Am.
130
(
5
),
2765
2776
(
2011
).
8.
F.
Bechwati
,
T. J.
Cox
, and
O.
Umnova
, “
New semi-empirical model for sound propagation in adsorbing microporous solid (activated carbon)
,” in
Proceedings of 19th International Congress on Acoustics
, PHY-03-012, Madrid, Spain (September 2–7,
2007
).
9.
C.
Shen
,
Rarefied Gas Dynamics, Fundamentals, Simulations and Micro Flows
(
Springer-Verlag
,
Berlin
,
2005
), pp.
1
406
.
10.
J. F.
Allard
and
N.
Atalla
,
Propagation of Sound in Porous Media: Modeling Sound Absorbing Materials
(
John Wiley & Sons
,
New York
,
2009
), Chaps. 2–5.
11.
J. L.
Auriault
,
L.
Borne
, and
R.
Chambon
, “
Dynamics of porous saturated media, checking of the generalized law of Darcy
,”
J. Acoust. Soc. Am.
77
(
5
),
1641
1650
(
1985
).
12.
J. L.
Auriault
,
C.
Boutin
, and
C.
Geindreau
,
Homogenization of Coupled Phenomena in Heterogeneous Media
(
John Wiley & Sons
,
London
,
2009
), pp.
1
472
.
13.
J. C.
Maxwell
, “
On stresses in rarefied gases arising from inequalities of temperature
,”
Philos. Trans. R. Soc. Part 1
170
,
231
256
(
1879
).
14.
D. D.
Do
and
K.
Wang
, “
A new model for the description of adsorption kinetics in heterogeneous activated carbon
,”
Carbon
36
(
10
),
1539
1554
(
1998
).
15.
H. D.
Do
and
D. D.
Do
, “
A new diffusion and flow theory for activated carbon from low pressure to capillary condensation range
,”
Chem. Eng. J.
84
,
295
308
(
2001
).
16.
M.
Suzuki
,
Adsorption Engineering
(
Kodansha Ltd. and Elsevier Science
,
Tokyo
,
1989
), pp.
63
93
.
17.
M.
Von Smoluchowski
, “
Ueber Wärmeleitung in verdünnten Gasen
” (“On conduction of heat by rarefied gases”),
Ann. Phys. Chem.
64
,
101
130
(
1898
).
18.
V. F.
Kozlov
,
A. V.
Fedorov
, and
N. D.
Malmuth
, “
Acoustic properties of rarefied gases inside pores of simple geometries
,”
J. Acoust. Soc. Am.
117
,
3402
3411
(
2005
).
19.
O.
Umnova
,
D.
Tsiklauri
, and
R.
Venegas
, “
Effect of boundary slip on the acoustical properties of microfibrous materials
,”
J. Acoust. Soc. Am.
126
(
4
),
1850
1861
(
2009
).
20.
M.
Nori
and
S.
Brandani
, “
A model for sound propagation between two adsorbing microporous plates
,”
J. Acoust. Soc. Am.
135
(
5
),
2634
2645
(
2014
).
21.
I.
Langmuir
, “
The constitution and fundamental properties of solids and liquids
,”
J. Am. Chem. Soc.
38
(
11
),
2221
2295
(
1916
).
22.
C.
Boutin
,
P.
Royer
, and
J. L.
Auriault
, “
Acoustic absorption of porous surfacing with dual porosity
,”
Int. J. Solids Struct.
35
,
4709
4737
(
1998
).
23.
X.
Olny
and
C.
Boutin
, “
Acoustic wave propagation in double porosity media
,”
J. Acoust. Soc. Am
114
(
1
),
73
89
(
2003
).
24.
J.
Chastanet
,
P.
Royer
, and
J.-L.
Auriault
, “
Acoustics with wall-slip flow of gas saturated porous media
,”
Mech. Res. Commun.
31
,
277
286
(
2004
).
25.
L.-Z.
Zhang
,
Conjugate Heat and Mass Transfer in Heat Mass Exchanger Ducts
(
Elsevier
,
Oxford
,
2014
), p.
36
.
26.
J.
Chastanet
,
P.
Royer
, and
J.-L.
Auriault
, “
Flow of low pressure gas through dual-porosity media
,”
Transp. Porous Media
66
(
3
),
457
479
(
2007
).
27.
C.
Boutin
and
C.
Geindreau
, “
Estimates and bounds of dynamic permeability of granular media
,”
J. Acoust. Soc. Am.
124
(
6
),
3576
3593
(
2008
).
28.
C.
Boutin
and
C.
Geindreau
, “
Periodic homogenization and consistent estimates of transport parameters through sphere and polyhedron packings in the whole porosity range
,”
Phys. Rev. E
82
,
036313
(
2010
).
29.
K. S. W.
Sing
,
D. H.
Everett
,
R. A. W.
Haul
,
L.
Moscon
,
R. A.
Pierotti
,
J.
Rouguerol
, and
T.
Siemieniewska
, “
Reporting physisorption data for gas/solid systems with special reference to the determination of surface area and porosity (Recommendations 1984)
,”
Pure Appl. Chem.
57
(
4
),
603
619
(
1985
).
30.
K.
Chihara
,
M.
Sukuzi
, and
K.
Kawazoe
, “
Adsorption rate on molecular sieving carbon by chromatography
,”
AIChE J.
24
(
2
),
237
245
(
1978
).
31.
Y. H.
Ma
,
W.
Sun
,
M.
Bhandarkar
,
J.
Wang
, and
G. W.
Miller
, “
Adsorption and diffusion of nitrogen, oxygen, argon, and methane in molecular sieve carbon at elevated pressures
,”
Separ. Technol.
1
,
90
98
(
1991
).
32.
T. A.
Nijhuis
,
L. J. P.
van den Broeke
,
M. J. G.
Linders
,
J. M.
van de Graaf
,
F.
Kapteijn
,
M.
Makkee
, and
J. A.
Moulijn
, “
Measurement and modeling of the transient adsorption, desorption and diffusion processes in microporous materials
,”
Chem. Eng. Sci.
54
,
4423
4436
(
1999
).
33.
R. T.
Yang
,
Gas Separation by Adsorption Processes
(
Butterworth Publishers
,
Stoeham
,
1987
),
121
pp.
34.
M.
Evans
,
N.
Hastings
, and
B.
Peacock
,
Statistical Distributions
, 3rd ed. (
John Wiley & Sons
,
New York
,
2000
), pp.
1
221
.
35.
BS EN 29053:1993
, “
Acoustics. Materials for acoustical applications. Determination of airflow resistance
” (
1993
).
36.
DIN 66135-3
, “
Particle characterization—Micropore analysis by gas adsorption—Part 3: Determination of the micropore volume according to Dubinin and Radushkevich
” (
2001
).
37.
C. D.
Smith
and
T. L.
Parrott
, “
Comparison of three methods for measuring acoustic properties of bulk materials
,”
J. Acoust. Soc. Am.
74
(
5
),
1577
1582
(
1983
).
38.
K.
Price
,
R.
Storn
, and
J.
Lampinen
,
Differential Evolution: A Practical Approach to Global Optimization
(
Springer-Verlag
,
Berlin
,
2005
), pp.
1
560
. See also http://www.icsi.berkeley.edu/~storn/code.html (Last viewed May 26, 2016).
39.
S. A.
Al-Muhtaseb
,
F. A. A.
Al-Rub
, and
M.
Al Zarooni
, “
Adsorption equilibria of nitrogen, methane, and ethane on BDH-activated carbon
,”
J. Chem. Eng. Data
52
,
60
65
(
2007
).
40.
R. P.
Ribeiro
,
T. P.
Sauer
,
F. V.
Lopes
,
R. F.
Moreira
,
C. A.
Grande
, and
A. E.
Rodrigues
, “
Adsorption of CO2, CH4, and N2 in activated carbon honeycomb monolith
,”
J. Chem. Eng. Data
53
,
2311
2317
(
2008
).
41.
B.-U.
Choi
,
D.-K.
Choi
,
Y.-W.
Lee
, and
B.-K.
Lee
, “
Adsorption equilibria of methane, ethane, ethylene, nitrogen, and hydrogen onto activated carbon
,”
J. Chem. Eng. Data
48
,
603
607
(
2003
).
42.
ISO 10534-2:2001
, “
Acoustics—Determination of sound absorption coefficient and impedance in impedance tubes—Part 2: Transfer-function method
” (International Organization for Standardization, Geneva, Switzerland,
2001
).
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