This paper presents a numerical study to characterize the effect of loss of blowing agents on the thermal insulation properties of polystyrene foams. In this study, a transient cell-to-cell diffusion model is developed to predict the loss of the blowing agents. The Mie theory is used to quantify the radiative conductivity. A cubic-series-parallel approach in analogy with electric circuits is employed to acquire the thermal conductivity of the gas-polymer matrix. The effects of foam morphology and blowing agent type on the loss of blowing agents and the resulting thermal insulation properties of polystyrene foams are examined.

1.
Suh
,
K. W.
, 2006, “
Blowing Agent
,”
Encyclopedia of Chemical Processing
, Vol.
1
,
S.
Lee
, ed.,
CRC Press
,
Boca Raton, FL
, pp.
237
250
.
2.
Park
,
C. B.
,
Behravesh
,
A. H.
, and
Venter
,
R. D.
, 1998, “
Low-Density, Microcellular Foam Processing in Extrusion Using CO2
,”
Polym. Eng. Sci.
0032-3888,
38
(
11
), pp.
1812
1823
.
3.
Naguib
,
H. E.
,
Park
,
C. B.
, and
Reichelt
,
N.
, 2004, “
Fundamental Foaming Mechanisms Governing Volume Expansion of Extruded PP Foams
,”
J. Appl. Polym. Sci.
0021-8995,
91
(
4
), pp.
2661
2668
.
4.
Xu
,
X.
,
Park
,
C. B.
,
Xu
,
D.
, and
Pop-Iliev
,
R.
, 2003, “
Effect of the Die Geometry on Cell Nucleation of PS Foams Blown With CO2
,”
Polym. Eng. Sci.
0032-3888,
43
(
7
), pp.
1378
1390
.
5.
Vo
,
C. V.
, and
Paquet
,
A. N.
, 2004, “
An Evaluation of the Thermal Conductivity of Extruded Polystyrene Foam Blown with HFC-134a or HCFC-142b
,”
J. Cell. Plast.
0021-955X,
40
(
3
), pp.
205
228
.
6.
Skochdopole
,
R. E.
, 1961, “
The Thermal Conductivity of Foamed Plastics
,”
Chem. Eng. Prog.
0360-7275,
57
, pp.
55
59
.
7.
Booth
,
J. R.
, 1993, “
An Evaluation of the Dow Thermal Performance Prediction Model for a Database of XPS∕CFC-12 Aged Resistivity and Physical Properties
,”
J. Thermal Insul., Bldg. Envelops
,
17
, pp.
154
170
.
8.
Biedermann
,
A.
,
Kudoke
,
C.
, and
Merten
,
A.
, 2001, “
Analysis of Heat Transfer Mechanisms in Polyurethane Rigid Foam
,”
J. Cell. Plast.
0021-955X,
37
(
6
), pp.
467
483
.
9.
Wu
,
J. W.
,
Sung
,
W. F.
, and
Chu
,
H. S.
, 1999, “
Thermal Conductivity of Polyurethane Foams
,”
Int. J. Heat Mass Transfer
0017-9310,
42
, pp.
2211
2217
.
10.
Ostrogorsky
,
A. G.
,
Glicksman
,
L. R.
, and
Reitz
,
D. W.
, 1986, “
Aging of Polyurethane Foams
,”
Int. J. Heat Mass Transfer
0017-9310,
29
(
8
), pp.
1169
1176
.
11.
Leach
,
A. G.
, 1993, “
The Thermal Conductivity of Foams I: Models for Heat Transfer
,”
J. Phys. D: Appl. Phys.
0022-3727,
26
, pp.
733
739
.
12.
Caps
,
R.
,
Heinemann
,
U.
,
Fricke
,
J.
, and
Keller
,
K.
, 1997, “
Thermal Conductivity of Polyamide Foams
,”
Int. J. Heat Mass Transfer
0017-9310,
40
(
2
), pp.
269
280
.
13.
Tseng
,
C. J.
,
Ramaguch
,
M.
, and
Ohmori
,
T.
, 1997, “
Thermal Conductivity of Polyurethane Foams From Room Temperature to 20K
,”
Cryogenics
0011-2275,
37
(
6
), pp.
305
312
.
14.
Wong
,
C. M.
, and
Hung
,
M. L.
, 2008, “
Polystyrene Foams as Core Materials Used in Vacuum Insulation Panel
,”
J. Cell. Plast.
0021-955X,
44
(
3
), pp.
239
259
.
15.
Coquard
,
R.
, and
Baillis
,
D.
, 2006, “
Modeling of Heat Transfer in Low-density EPS Foams
,”
ASME J. Heat Transfer
0022-1481,
128
(
6
), pp.
538
549
.
16.
Glicksman
,
L. R.
,
Schuetz
,
M.
, and
Sinofsky
,
M.
, 1987, “
Radiation Heat Transfer in Foam Insulation
,”
Int. J. Heat Mass Transfer
0017-9310,
30
(
1
), pp.
187
197
.
17.
Kuhn
,
J.
,
Ebert
,
H. P.
,
Arduini-schuster
,
M. C.
,
Buttner
,
D.
, and
Fricke
,
J.
, 1992, “
Thermal Transport in Polystyrene and Polyurethane Foam Insulations
,”
Int. J. Heat Mass Transfer
0017-9310,
35
(
7
), pp.
1795
1801
.
18.
Doermann
,
D.
, and
Sacadura
,
J. F.
, 1996, “
Heat Transfer in Open Cell Foam Insulation
,”
ASME J. Heat Transfer
0022-1481,
118
(
1
), pp.
88
93
.
19.
Yang
,
C. T.
, and
Lee
,
S. T.
, 2003, “
Dimensional Stability Analysis of Foams Based on LDPE and Ethylene-styrene Interpolymer Blends
,”
J. Cell. Plast.
0021-955X,
39
(
1
), pp.
59
69
.
20.
Pilon
,
L.
,
Fedorov
,
A. G.
, and
Viskanta
,
R.
, 2000, “
Gas Diffusion in Closed Foams
,”
J. Cell. Plast.
0021-955X,
36
(
6
), pp.
451
474
.
21.
Briscoe
,
B. J.
, and
Savvas
,
T.
, 1998, “
Gas Diffusion in Dense Poly(ethylene) Foams
,”
Adv. Polym. Technol.
0730-6679,
17
, pp.
87
106
.
22.
Alsoy
,
S.
, 1999, “
Modeling of Diffusion in Closed Cell Polymeric Foams
,”
J. Cell. Plast.
0021-955X,
35
(
3
), pp.
247
271
.
23.
Booth
,
J. R.
,
Graves
,
R. S.
, and
Yarbrough
,
D. W.
, 1995, “
Aging of Thin-slices of PIR Foams Manufactured With Alternative Blowing Agents
,”
J. Thermal Insul., Bldg. Envelops
,
19
(
2
), pp.
118
131
.
24.
Bhattacharjee
,
D.
,
Irwin
,
P. W.
,
Booth
,
J. R.
, and
Grimes
,
J. T.
, 1994, “
The Acceleration of Foam Aging by Thin Slicing—Some Interpretations and Limitations
,”
J. Thermal Insul., Bldg. Envelops
,
17
(
3
), pp.
219
237
.
25.
Shankland
,
I. R.
, 1995, “
Blowing Agent Emission Calculations for a Refrigerator
,”
J. Cell. Plast.
0021-955X,
31
(
3
), pp.
227
243
.
26.
Tant
,
M. R.
, and
Wilkes
,
G. L.
, 1981, “
Physical Aging Studies of Semicrystalline Poly (ethylene Terephthalate)
,”
J. Appl. Polym. Sci.
0021-8995,
26
, pp.
2813
2825
.
27.
Ruiz-Herrero
,
J. L.
,
Rodríguez-pérez
,
M. A.
, and
de Saja
,
J. A.
, 2005, “
Effective Diffusion Coefficient for the Gas Contained in Closed Cell Polyethylene-Based Foams, Subjected to Compressive Creep Tests
,”
Polymer
0032-3861,
46
, pp.
3105
3110
.
28.
Quoc
,
P. N.
,
Zitha
,
P. L. J.
, and
Currie
,
P. K.
, 2002, “
Effect of Foam Films on Gas Diffusion
,”
J. Colloid Interface Sci.
0021-9797,
248
(
2
), pp.
467
476
.
29.
Griffiths
,
P. C.
,
Tipples
,
C. N.
,
Stilbs
,
P.
, and
McCormick
,
B. H.
, 1998, “
Restricted Diffusion of a “Gas” in a Solid Foam
,”
Langmuir
0743-7463,
14
(
22
), pp.
6603
6605
.
30.
Takeno
,
K.
,
Ichinose
,
T.
, and
Tokuda
,
K.
, 1996, “
Effects of High Expansion Foam Dispersed onto Leaked LNG on the Atmospheric Diffusion of Vaporized Gas
,”
J. Loss Prev. Process Ind.
0950-4230,
9
(
2
), pp.
125
133
.
31.
Hanssen
,
J. E.
, 1993, “
Foam as a Gas-Blocking Agent in Petroleum Reservoirs II: Mechanisms of Gas Blockage by Foam
,”
J. Pet. Sci. Eng.
0920-4105,
10
(
2
), pp.
135
156
.
32.
Gandel’sman
,
M. I.
,
Matveyenko
,
R. V.
, and
Budtov
,
V. P.
, 1987, “
Diffusion in Porous Strained Polymer Media
,”
Polym. Sci. U.S.S.R.
0032-3950,
29
(
6
), pp.
1212
1218
.
33.
Varady
,
M. J.
, and
Fedorov
,
A. G.
, 2002, “
Combined Radiation and Conduction in Glass Foams
,”
ASME J. Heat Transfer
0022-1481,
124
(
6
), pp.
1103
1109
.
34.
Krishnan
,
S.
,
Murthy
,
J. Y.
, and
Garimella
,
S. V.
, 2006, “
Direct Simulation of Transport in Open-cell Metal Foam
,”
ASME J. Heat Transfer
0022-1481,
128
(
8
), pp.
793
799
.
35.
Ghosh
,
I.
, 2008, “
Heat-Transfer Analysis of High Porosity Open-Cell Metal Foam
,”
ASME J. Heat Transfer
0022-1481,
130
(
3
), p.
034501
.
36.
Chen
,
C.
and
Jaluria
,
Y.
, 2007, “
Modeling of Radiation Heat Transfer in the Drawing of an Optical Fiber With Multilayer Structure
,”
ASME J. Heat Transfer
0022-1481,
129
(
3
), pp.
342
352
.
37.
Liu
,
L. H.
, and
Liu
,
L. J.
, 2007, “
Discontinuous Finite Element Approach for Transient Radiative Transfer Equation
,”
ASME J. Heat Transfer
0022-1481,
129
(
8
), pp.
1069
1074
.
38.
An
,
W.
,
Ruan
,
L. M.
,
Tan
,
H. P.
, and
Qi
,
H.
, 2006, “
Least-Squares Finite Element Analysis for Transient Radiative Transfer in Absorbing and Scattering Media
,”
ASME J. Heat Transfer
0022-1481,
128
(
5
), pp.
499
503
.
39.
Giaretto
,
V.
,
Miraldi
,
E.
, and
Ruscica
,
G.
, 1995∕1996, “
Simultaneous Estimations of Radiative and Conductive Properties in Lightweight Insulation Materials
,”
High Temp. - High Press.
0018-1544,
27∕28
, pp.
191
204
.
40.
Çengel
,
Y. A.
, 1977,
Heat Transfer-a Practical Approach
, 2nd ed.,
McGraw-Hill
,
New York
.
41.
Placido
,
E.
,
Arduini-Schuster
,
M. C.
, and
Kuhn
,
J.
, 2005, “
Thermal Properties Predictive Model for Insulating Foams
,”
Infrared Phys. Technol.
1350-4495,
46
, pp.
219
231
.
42.
Kerker
,
M.
, 1969,
The Scattering of Light and Other Electromagnetic Radiation
,
Academic
,
New York
.
43.
van de Hulst
,
H. C.
, 1981,
Light Scattering by Small Particles
,
Dover
,
New York
.
44.
Bashkatova
,
T. A.
,
Bashkatov
,
A. N.
,
Kochubey
,
V. I.
, and
Tuchin
,
V. V.
, 2001, “
Light Scattering Properties for Spherical and Cylindrical Particles: A Simple Approximation Derived From Mie Calculations
,”
Proc. SPIE
0277-786X,
4241
, pp.
247
259
.
45.
Nichelatti
,
E.
, 2002, “
Complex Refractive Index of a Slab From Reflectance and Transmittance: Analytical Solution
,”
J. Opt. A, Pure Appl. Opt.
1464-4258,
4
, pp.
400
403
.
46.
Ho
,
W.
, and
Ma
,
C. M.
, 1998, “
Diffuse Reflectance and Transmittance of IR Absorbing Polymer Film
,”
Polym. Eng. Sci.
0032-3888,
38
(
10
), pp.
1666
1674
.
47.
Wassiljewa
,
A.
, 1904, “
Wärmeleitung in Gasgemischen
,”
Phys. Z.
0369-982X,
5
, pp.
737
742
.
48.
Mason
,
E. A.
, and
Saxena
,
S. C.
, 1958, “
Approximate Formula for the Thermal Conductivity of Gas Mixtures
,”
Phys. Fluids
0031-9171,
1
(
5
), pp.
361
369
.
49.
Basmadjian
,
D.
, 2004,
Mass Transfer: Principles and Applications
,
CRC LLC
,
Boca Raton, FL.
50.
Seifert
,
H.
,
Biedermann
,
A.
, and
Giesker
,
C.
, 2003, “
Can HFC245fa or Cyclopentane Blown Foams Match the Performance of HFC-Foams?
J. Cell. Plast.
0021-955X,
39
(
5
), pp.
417
426
.
51.
Zipfel
,
L.
,
Krücke
,
W.
,
Börner
,
K.
,
Barthélemy
,
P.
, and
Dournel
,
P.
, 1998, “
HFC 365mfc and HFC-245fa Progress in Application of New HFC Blowing Agents
,”
J. Cell. Plast.
0021-955X,
34
(
6
), pp.
511
525
.
52.
Willams
,
D. J.
,
Bogdan
,
M. C.
,
Parker
,
R. C.
, and
Knopech
,
G. M.
, 1997, “
Update on the Development of HFC-245fa as a Liquid HFC Blowing Agent
,”
J. Cell. Plast.
0021-955X,
33
(
3
), pp.
238
263
.
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