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Density Modeling of Polyurethane Box Foam
Lu Shen,
1
Yusheng Zhao,
1
Ali Tekeei,
1
Fu-Hung Hsieh,
2
Galen J. Suppes
1
1
Department of Chemical Engineering, University of Missouri-Columbia, Columbia, Missouri 65211
2
Department of Biological Engineering, University of Missouri-Columbia, Columbia, Missouri 65211
A model based on about a dozen fundamental differen-
tial equations is used to evaluate and simulate the ure-
thane reactions and physical processes of urethane
box foaming. This work focuses on quantitative model-
ing of foam density for foams using water and physical
blowing agents. The final densities of foams range
from 30 to 90% of the density as projected with full uti-
lization of the blowing agent. The primary sources of
inefficient use of blowing agent are loss of the physical
blowing during open-air mixing and degassing—basi-
cally, physical blowing agents with boiling points
between 25 and 80C will evaporate and experience
cell rupture in box foams. This loss of blowing agent
would not apply to in-line mixers used for commercial
production and should be taken into account with
scaling up box or cup foams commercial processes.
POLYM. ENG. SCI., 54:1503–1511, 2014. V
C2013 Society of
Plastics Engineers
INTRODUCTION
Polyurethanes (PU) play a significant role in global
industry with over three-quarters of the consumption in
the form of foams [1]. They are extensively used in the
field such as rigid insulations in the walls of refrigerators
and buildings, high-resilience and flexible foam cushions,
and elastomeric wheels and tires.
Foams can expand from during polymerization if gases
or vapors are produced in concert with the polymeriza-
tion. A common mechanism for gas generation is the
chemical reaction between water and isocyanate forming
carbon dioxide. In addition, exothermic polymerization
reactions can provide heat to evaporate volatile blowing
agents such as methyl formate (MF) and pentane. For
rigid foams, the physical properties of most interest are
density, compressive strength, and thermal conductivity.
Both cell size and cell number contribute to change of
density and compressive strength [2]. For PU foam, to a
first approximation, there exists a linear relationship
between density and compressive strength [3]. Density
impacts the thermal conductivity due to the lower thermal
conductivity of the gas phase relative to the resin phase
[4]. Therefore, accurately predicting density during poly-
urethane foaming is both important in its own right and
as a critical step to ultimately predict other physical prop-
erties of foams [5–7].
Baser and Khakhar [8, 9] carried out a detailed experi-
mental study of chemical and physical blowing agents
with measurement of both temperature and density
changes during the foaming process. The theoretical
model was based on the hypothesis that the foam was
under a single pseudohomogeneous phase, and the varia-
tion of density with time was obtained by applying
energy and mass balances along with the kinetic and ther-
modynamic relations. Later, Tesser et al. [10] developed
a mathematical model to simulate the temperature and
density of the foams with the evaluation of kinetics of the
reaction between polyol and isocyanate during the foam-
ing process with an emphasis on Flory–Huggins modeling
of blowing agent activity.
Gibson and Ashby [11] came up with an elastic modu-
lus based on the relative density for closed-cell (cc) foam
taking into account of three components: the strut flexion,
the stretching of the cell walls, and the gas pressure
inside the cc. Saint Michel et al. [12] characterized the
influence of the density and compared the experimental
results with Gibson and Ashby [11] and Christensen et al.
[13] in the linear domain and then extended to the nonlin-
ear domain.
Avalle et al. [14] tested several types of foams and
performed a study based on the Gibson model and the
Rusch (of the phenomenological type) model [15–17]
together with two other models namely a modified Gib-
son model and a new phenomenological model to charac-
terize the mechanical properties. Additionally, available
experimental data were used to obtain the relationship
between material density and model parameters.
These previous works illustrate the importance of
quantifying foam density in foam formulation. The work
of this article differs in two ways from this other work:
(a) the current work is based on over a dozen fundamen-
tal ordinary differential models for the reactions and
Correspondence to: Lu Shen; e-mail: lsc38@mail.missouri.edu
Contract grant sponsor: United Soybean Board.
DOI 10.1002/pen.23694
Published online in Wiley Online Library (wileyonlinelibrary.com).
V
C2013 Society of Plastics Engineers
POLYMER ENGINEERING AND SCIENCE—2014
physical processes and (b) this work evaluates sources of
blowing agent loss in addition to solubility of blowing
agents in the resin phase.
This work builds on the work of Zhao et al. [18] on
modeling the foaming process using a series of ordinary
differential equations with Arrhenius constants and
enthalpy parameters. Although the emphasis of Zhao’s
work was the prediction of polyol mixture performance in
formulations, the emphasis of this work is the modeling
and simulation of foam height (density).
EXPERIMENTAL DESIGN
Blowing Agents
As a chemical blowing agent, water reacts with isocya-
nate (RNCO) and produces carbamic acid (RNHCOOH)
which further decomposes into carbon dioxide and thus
generates gas bubbles in the resin according to reaction
Schemes 1 and 2 forming an amine (RNH
2
).
RNCO 1H2O!RNHCOOH (1)
RNHCOOH !RNH21CO21HEAT (2)
MF serves as a physical blowing agent that does not
rely on any chemical reactions. Table 1 summarizes phys-
ical properties of MF. The MF is initially soluble in the
mixture of isocyanate and polyol at ambient temperature.
Equation 3 is used to estimate the vapor pressure of
MF as a function of time [19].
ln Psat
i
PC
512xðÞ
21Ai
ðÞx1Bi
ðÞx1:51Ci
ðÞx31Di
ðÞx6
(3)
x51—T/T
c
where T
c
is critical temperature in Kelvins,
Psat
iis vapor pressure, in bars, P
c
is critical pressure, in
bars, Eqs.3 and 4 are valid at the temperature range of
220–487.2 K.
The vapor pressure is used in the modified Raoult’s
Law (Eq.4) equation which is used in combination with
heat and energy balances to estimate the amount of MF
that evaporates from the resin phase and proceeds to form
bubbles/cells. It should be noted that because the resin
phase is comprised of macromolecules, mass fraction was
used instead of mole fraction.
xicPsat
i5yiP(4)
It is assumed that the carbon dioxide and vapor-phased
MF are ideal with fugacity equaling to 1. Deviation from
ideality is accommodated by modifying the activity coef-
ficient. Mass balance equations are solved under the con-
straint of Raoult’s law to determine the extent to which
MF evaporates. During analysis of the data, performance
at an activity coefficient of 1.0 is compared to 15 to eval-
uate the extent that actual foam density varies from the
ideal model.
Materials
The isocyanate and petroleum-based polyols used in
this study were RUBINATE M isocyanate, Poly G76–
635, Voranol 360, and Jeffol R315x from Huntsman
Company and Dow Chemical Co. and their specifications
are shown in Tables 2. N,N-dimethylcyclohexylamine and
N,N,N0,N000 ,N00-pentamethyldiethylenetriamine were
used as gelling catalyst and blowing catalyst, respectively.
Momentive L6900 was used as the surfactant for rigid
foams, Tris (1-chloro-2-propyl) Phosphate (TCPP) was
used as fire retardant, and distilled water was use as
chemical blowing agent.
Experimental Procedure
Gelling and Foaming Experiment. Experiments were
performed to create polyurethane gels as well as rigid
polyurethane foams. The gel reactions were used as a
control to assist in interpreting the data for the foam reac-
tions. Table 3 provides the control formulation used in
these studies. The amount of water and MF in this formu-
lation was used as parameters to better understand the
foaming process.
The following steps were used in both the gelling and
foam experiments.
1. Polyols, water, blowing catalyst, gelling catalysts, and sur-
factant (B-side components) were added into a plastic cup
successively.
2. These B-side components were mixed for 10–15 s.
3. The mixture was allowed to degas for 2 min.
TABLE 1. Specifications of methyl formate (MF).
MW 60
Physical state Liquid
Boiling point (C) 31.5
P
c
(bar) 60.075
T
c
(K) 487.2
A
i
26.99601
B
i
0.89328
C
i
22.52294
D
i
23.16636
TABLE 2. Specifications of RUBINATE M isocyanate and three dif-
ferent polyols.
Product: RUBINATE M
Fn 2.70
Sp. gravity @25C 1.23
% NCO 31.2
Eq. wt. 135
Viscosity cps @25C 190
Product OH number
Poly G76–635 635
Voranol 360 360
Jeffol R315x 315
1504 POLYMER ENGINEERING AND SCIENCE—2014 DOI 10.1002/pen
4. Thereafter, preweighed isocyanate (A-side material) was
added and mixed at the same speed for 7–10 s.
5. The reacting mixture was then quickly poured into a box
with aluminum foil lining, and the foam was allowed to
rise and sit at ambient conditions (25C) during curing.
All the B-side chemicals were added in the foam reac-
tion, whereas water and blowing catalyst were not added
in the gel reaction.
A high-speed mixer blade attached to a floor-model
drill press was used to mix the chemicals. LabVIEW soft-
ware was used to monitor the temperature of the gel or
foam reactions for the first 15 min with a type-k thermo-
couple attached through a National Instruments SCB-68
box to a National Instruments PCI 6024E data acquisition
card.
Mass Loss Test. Experiments were also performed to
evaluate the amount of mass loss during box foaming. A
cardboard box containing the reacting foam mixture was
placed on a digital balance accurate to 0.01 g. The fol-
lowing sequence describes the manner in which mass was
balanced and measured:
1. Polyols, water, blowing catalyst, gelling catalysts, and sur-
factant (B-side components) were added and stirred in a
plastic cup. The B-side component was weighed and set
aside in a second plastic cup. About 2 min were allowed
for degassing.
2. The B-side components were mixed and stirred with A-
side for 15 s.
3. The mixtures were quickly poured into the cardboard box
(designated at t50 s) located on the balance. The foam
was allowed to rise and sit at ambient conditions during
curing.
4. Residual masses in the mixing cup and stirrer were meas-
ured (by mass differences) and recorded for subsequent
mass balance calculations.
RESULTS AND DISCUSSION
Foaming Height Studies
Figure 1 demonstrates the effect of water content on
the height of PU foams. Increasing water content leads to
increasing height of the box foam and decreasing density.
A doubling of the water content resulted in an approxi-
mate doubling of the height.
As a physical blowing agent, MF does not react with
isocyanate; it provides an additional degree of freedom to
control foam volume. Because of a lower boiling point
and volatility, MF volatilizes and dissolves in polymer
phase and consequently bubbles inside the foams come
into being. Figure 2 illustrates how more MF produces
more vapor which contributes to the volume increase.
Based on inspection, water appears to be more effective
in forming cells; the subsequent discussion pursues a
quantification and insight into the differences.
Increased amounts of both water and MF provide
lower foam densities. These trends are qualitatively con-
sistent with the mechanisms of Eqs.2 and 4. Figure 3
compares performances to what the ordinary deferential
TABLE 3. Foaming formulation of rigid polyurethane foam.
Weight/g Equivalents
B-side materials
Poly G76–635 13.84 0.1569
Voranol 360 15.68 0.1008
Jeffol R315x 4 0.0225
Dimethylcyclohexylamine
(gelling catalyst)
0.12
Pentamethyldiethylenetriamine
(blowing catalyst)
0.32 (foam reaction only)
Momentive L6900 0.6
TCPP 2
Distilled water (blowing agent) 1.04 (foam reaction only) 0.08
A-side material
RUBINATE M 61.548 0.4559
FIG. 1. Foaming height with different water content. Symbols “w”, “䊊”, and “D” represent two repeated
samples containing 2.4 g MF with 1.0, 0.75, and 0.5 g water, respectively.
DOI 10.1002/pen POLYMER ENGINEERING AND SCIENCE—2014 1505
equation model predicts for extreme cases of the activity
coefficient equal to 1 and 15. Even in the extreme case of
high activity coefficients, the actual foam height is much
less than what is projected by the model. Temperatures in
the foam exceed 100C during curing, and as such, little
MF remains in the liquid even if high activity coefficients
impacted performance. The model trends show that the
activity coefficient predominantly has an impact during
foam rise when the temperature ranged from MF’s boiling
point to about 40C greater than MF’s boiling point.
Actual foam height only attained about 63% of what
was projected with full use of the blowing agents and
ideal gas law calculation of the gas volume. Possible fac-
tors leading to the inconsistency are low-efficiency water-
isocyanate reaction, the rupture of carbon dioxide and MF
gas cells, and higher internal pressure. Further studies
were conducted that evaluated the mass of the foam dur-
ing the foaming process.
Mass Loss Studies
The box used to contain the rigid foam during the
foaming process was placed on a digital balance accurate
to 0.01 g to monitor weight loss during the foaming reac-
tion. Possible sources for weight loss are (1) air’s buoyant
force applied by the increasing volume of the foam, (2)
rupture of foam cells (bubbles) with collapse of the cell
or replacement of the vapors by new vapors, and (3)
evaporation/escape of MF, water, or carbon dioxide along
the upper surface of the foam.
Figure 4 illustrates the mass loss for a sample that
used only MF blowing agent and distinguishes between
FIG. 2. Foaming height with different MF content. Symbols “w”, “䊊”, and “D” represent two repeated
samples contain 1.04 g water and 2.4, 1.5, and 0.5 g MF, respectively.
FIG. 3. Experimental height versus modeling height. Symbols “䉫” and “w” represent two repeated samples
with 0.75 g water and 2.4 g MF. The smooth and dash lines represent MATLAB Simulation with 100%
water and MF when cequals to 15 and 1, respectively.
1506 POLYMER ENGINEERING AND SCIENCE—2014 DOI 10.1002/pen
buoyant force and true weight loss. The volume caused
by buoyancy was calculated using Eq.5.
Vb5DVqa5Vo2Vexp
qa(5)
V
b
is volume of the buoyancy, q
a
is density of the air,
V
o
is initial volume before the growth of the foam, which
corresponds to the total volume of isocyanate, polyols,
water, and MF, V
exp
is experimental volume of the foam.
For the foam of Fig. 4, V
o
592.5 cm
3
and V
exp
5572.7
cm
3
resulting in an equivalency of 0.57 g of buoyancy. It
is presented from Fig. 4 that the total amount of loss is
2.13 g, which indicates 1.38 g of mass loss attributed to
the inefficiency of blowing agent (much of which is
attributed to the box-foaming technique rather than the
blowing agent).
Table 4 summarizes the buoyancy forces and mass
loss of several foams. Dmand Dhare total mass loss
from experiment and height decrease associated with the
release of the blowing agents. The foam in Fig. 4 stopped
expanding at 75 s because an increase of viscosity facili-
tated the rigidity of the foam that did not allow further
expansion. During the first 75 s, the mass loss was
resulted from the buoyancy applied by the increasing vol-
ume of displaced air and the rupture of blowing agent
characterized as Dm
2
and Dm
3
in Fig. 4. Afterwards, no
expansion occurred in the system, and all the mass loss
was attributed to the escape of gases in the cells.
Figures 5 and 6 compare actual to model heights
where the model heights are for no loss of blowing agent
versus losses as summarized by Table 4. The results sub-
stantiate that a primary mechanism for the inefficiency of
blowing agent is the loss of blowing agent through the
upper surface of the foam through cell rupture (convec-
tion) or through the surface evaporation. Loss from the
top surface could be through diffusion straight from the
resin to the air or it could be from cells/bubbles that rup-
ture through the top surface.
Modeling Loss of Blowing Agent Efficacy
Possible sources of inefficacy of blowing agents
include: (1) higher than atmospheric pressure in cells, (2)
solubility of blowing agent in the polymer phase, and (3)
release of blowing agent through the upper surface. The
impact of these is summarized by Eq.5in terms of gas
volume.
FIG. 4. Mass change during box foaming process. Symbols “w” and “䉫” are corresponding to the mass
value prior to and during the foaming process. 1,2,3, and 4represent the stage of degassing, stirring, foam
rising, and after complete rise. Dm
1
is mass loss prior to expansion of foam cells, Dm
2
is buoyancy weight
adjustment, Dm
3
is mass loss during foam growth, and Dm
4
is mass loss after the maximum foam height is
attained.
TABLE 4. Results of mass loss of different samples.
Foam type
Dm
(g equivalent)
Dh
(cm)
Dmfrom
buoyancy
Dmfrom
blowing
agent
Efficiency
of blowing
agent (%)
Efficiency
calculated by
height (%)
Foam only with MF 1 2.13 8.83 0.57 1.38 42.4 40.0
Foam only with MF 2 2.12 8.48 0.52 1.42 41.0 33.2
Foam only with water 1 2.22 12.47 1.72 0.50 80.2 80.1
Foam only with water 2 2.26 11.61 1.78 0.48 81.1 82.7
Gel 1 0.38 2.02 0.10 0.28 – –
Gel 2 0.29 1.54 0.11 0.18 – –
DOI 10.1002/pen POLYMER ENGINEERING AND SCIENCE—2014 1507
V5Vi2Vp2VS2Rb(6)
V
i
is ideal volume of the foam without the gas rupture,
V
p
is volume loss due to the pressure, V
S
is volume loss
due to the solubility of the MF, R
b
is release of the blow-
ing agent.
This approach does not distinguish between the sus-
ceptibility of MF versus carbon dioxide to these mecha-
nisms. Under the assumption that the pressure buildup
has a minor contribution, V
p
is cancelled out in Eq.6.
Closed cell content is a property commonly measured
in rigid foam. A reasonable hypothesis is: if the final
foam has a high cc content, the foam would have main-
tained a high cc content during the entire foaming pro-
cess; and cc’s correlate this low release of blowing agent.
The Eq.7is an example correlation that can be tested
with data where cc is close cell content (%).
Rb5k212ccðÞ (7)
Two assumptions to simplify this model are assuming
ideal gas behavior and assuming that only MF partitions
in the resin phase. Substituting Eq.6to8, where n
1
and
n
2
are moles of MF and carbon dioxide, and S
1
is the
fraction of MF that is in the resin (soluble).
V5n11n2
ðÞRT
P
2n1RT
PS12k212ccðÞ (8)
By setting V
o
equals to the first two terms of the three
on the right-hand side of Eq.8and expressing volume in
term of density, Eq.8can be represented as a linear equa-
tion where the extent to which avaries from k
2
provides
a point of discussion. Equation 9 displays a relationship
between density and close cell content used to interpret
the data.
FIG. 5. Samples with 4.0 g MF. Symbols “䉫” and “D” represent two repeated samples with 4.0-g MF
blowing agent. Smooth and dashed lines symbolize MATLAB Simulation with 30 and 100% efficiency of
MF.
FIG. 6. Samples with 1.0 g water. Symbols “䉫” and “D” represent two repeated samples with 1.0 g water.
Smooth and dashed lines symbolize MATLAB Simulation with 80 and 100% efficiency of water.
1508 POLYMER ENGINEERING AND SCIENCE—2014 DOI 10.1002/pen
1
qo21
q
5k2cc1a(9)
Figure 7 summarizes this trend for density versus close
cell content data collected as summarized by Table 5. The
figure illustrates that while k
2
is close to a, the best fit is
not with them equal. Furthermore, the data illustrate that
the primary cause for them not being equal is the concen-
tration of data at a nonzero limit as cc approaches 1.
For foam cells to expand, they must have a pressure
greater than the surroundings. For foams with nearly
100% cc content, the strength of the resin to preserve cell
integrity is at its greatest relative to foam with an open
cell nature, weak cell walls, and respective low cc con-
tent. The conclusion is that the internal pressure is signifi-
cant, is a function of cc, and is likely near a value of
2.02 atm at 100% cc content.
The lower dashed line of Fig. 7 represents a linear rela-
tion for internal cell pressure. Within the standard deviation
of the data, the linear model (solid line) as represented by a
combination of the two dashed lines is substantiated.
Future work on this area would include several topics
of interest, including: (a) development of fundamentally
based (not simple linear equations) for the relations of
cell pressure and release to cc., (b) acquiring more accu-
rate data, and (c) developing fundamentally based models
that can predict cc based on the properties of the reagents
used to make the foam and the foaming formulation.
Figure 8 displays the comparison between modeling and
experimental density, which presents slight deviation
FIG. 7. Linear correlation for Eq.9. Symbols “䉫” represent experi-
mental data between 1/q
o
21/qand close cell content. Smooth line rep-
resents the modeling line characterizing 1/q
o
21/q520.0846*
cc 10.0967. “--” line is displayed as trend of internal bubble pressure in
which pressure reaches highest at 2 atm when close cell content c is
close to 100%. “-.-” line stands for k
2
52a.
TABLE 5. Experimental and modeling density from samples displayed in Fig. 7 with comparison of efficiency, close cell content and quantities of
blowing agent.
Close cell content (%) Efficiency (%) Density exp (g/ml) Density model (g/ml) Quantities of MF (g) Quantities of Water (g)
87.55 54.29 33.00 21.43 2.40 1.04
90.30 53.64 33.90 21.76 2.41 1.02
91.66 69.16 33.36 26.55 2.42 1.06
94.06 69.12 28.50 24.75 2.45 1.01
94.63 58.05 42.22 26.76 2.39 0.76
91.96 57.27 52.50 34.24 2.40 0.50
95.46 50.80 57.20 33.12 2.48 0.50
94.40 66.21 44.85 35.17 2.47 0.51
94.31 71.16 33.31 26.83 1.51 1.01
98.20 58.72 42.09 28.81 1.53 1.05
99.66 67.48 39.80 27.31 1.50 1.04
93.99 62.89 44.79 29.96 0.52 1.01
89.10 56.32 43.63 27.01 0.50 1.07
98.80 63.79 40.03 27.12 0.50 1.04
94.84 62.00 48.60 30.14 0.00 1.05
97.76 71.20 39.59 30.58 0.00 1.04
83.22 54.48 27.05 18.32 2.35 1.53
73.16 50.21 24.59 16.26 2.29 1.97
93.39 59.68 32.32 21.83 2.20 1.03
71.80 50.67 31.5 17.19 2.40 1.50
56.83 44.32 25.72 12.63 2.30 2.00
94.96 55.33 34.76 18.60 2.32 1.02
90.27 60.88 41.32 26.67 2.33 1.03
74.62 50.00 36.87 28.42 2.25 1.00
78.70 50.00 32.76 27.01 2.20 0.98
91.36 55.33 36.32 21.14 2.42 1.05
97.63 63.79 36.10 23.59 2.40 1.06
97.67 67.26 32.91 24.58 2.42 1.05
98.53 64.16 33.37 22.39 2.41 1.05
98.53 64.37 30.99 21.10 2.41 1.06
96.78 68.61 33.36 24.92 2.41 1.05
DOI 10.1002/pen POLYMER ENGINEERING AND SCIENCE—2014 1509
caused by higher internal bubble pressure and potential
experimental error. It is predictable to estimate the density
with the aid of MATLAB Simulation when we have the
foaming formulation.
CONCLUSIONS
The measuring of mass and height in combination with
computer-based simulation of the foaming process pro-
vided a closure of the mass balance of blowing agents
used to make rigid box foams. The results indicated that
evaporation losses during the mixing and degassing steps
leads to a loss of efficacy of the blowing agent. This con-
clusion would broadly apply to blowing agents that rely
on low boiling points which form gas cells in urethane
foams at temperatures between 30 and 80C.
The primary sources of inefficient use of blowing
agent are loss of the physical blowing during open-air
mixing and degassing. This loss of blowing agent would
not apply to in-line mixers used for commercial produc-
tion and should be taken into account with scaling up box
or cup foams commercial processes.
Although previous modeling work that was able to cor-
relate inefficiency with Flory–Huggins parameters
appeared to exaggerate the impact of activity coefficients,
the activity coefficients considered in this were reason-
ably close to 1.0. A correlation relates to lack of efficacy
of blowing agents to both closed cell (cc) content and the
buildup of pressure in the cells. The implication is that if
cc content is able to be simulated from a foam recipe,
increasingly accurate estimates/simulations of density can
also be attained. This was a major finding of this study as
it identifies that the modeling of cell formation and rup-
ture is critical to accurately model foam density.
ABBREVIATIONS
PU polyurethanes
cc closed-cell
MF methyl formate
ODE ordinary deferential equation
MW molecular weight
Fn functionality
Eq. Wt equivalent weight
csolubility
R ideal gas constant (L atm/K mol)
T temperature (K)
P pressure (atm)
t time (s)
V volume (ml)
qdensity (g/ml)
m mass weight (g)
h height (cm)
T
c
critical temperature (K)
P
c
critical pressure (bar)
P
sat
vapor pressure (bars)
V
b
volume of the buoyancy
q
a
density of the air
V
o
initial volume before the growth of the foam
V
exp
experimental volume of the foam
V
i
ideal volume of the foam without the gas rupture
V
p
volume loss due to the pressure
V
S
volume loss due to the solubility of the MF
R
b
release of the blowing agent
ACKNOWLEDGMENT
The authors thank the United Soybean Board for finan-
cial support of the experimental studies used to validate the
modeling work. Thanks to FSI Company providing foam
formulas and technology support.
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DOI 10.1002/pen POLYMER ENGINEERING AND SCIENCE—2014 1511
