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EXPANSION OF THE WHOLE WHEAT FLOUR EXTRUSION

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A new model framework is proposed to describe the expansion of extrudates with extruder operating conditions based on dimensional analysis principle. The Buckingham pi dimensional analysis method is applied to form the basic structure of the model from extrusion process operational parameters. Using the Central Composite Design (CCD) method, whole wheat flour was processed in a twin-screw extruder with 16 trials. The proposed model can well correlate the expansion of the 16 trials using 3 regression parameters. The average deviation of the correlation is 5.9%.
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EXPANSION OF THE WHOLE WHEAT FLOUR EXTRUSION

Hongyuan Cheng and Alan Friis
Food Production Engineering, National Food Institute
Technical University of Denmark
Søltofts Plads, Building 227, DK-2800, Lyngby, Denmark
E-mail: hyc@bio.dtu.dk



KEYWORDS
which affects the extent of biopolymer modification and
Expansion, Extrusion, whole wheat flour, modelling.
finally the expansion and texture of extruded products.

Although starch is known to be the key biopolymer in
ABSTRACT
extrusion cooking, other ingredients of cereal-based food

systems such as proteins, fat or fiber also influence the
A new model framework is proposed to describe the
system and product characteristics, e.g. by competing with
expansion of extrudates with extruder operating conditions
starch for water (Moraru and Kokini, 2003). Due to these
based on dimensional analysis principle. The Buckingham pi
compositional and structural complexities of the raw material
dimensional analysis method is applied to form the basic
as well as the large number of operational parameters
structure of the model from extrusion process operational
involved in the extrusion process, obtaining the desired
parameters. Using the Central Composite Design (CCD)
extrudate properties, e.g. optimal expansion and texture, is a
method, whole wheat flour was processed in a twin-screw
challenging task and often depends on trial and error
extruder with 16 trials. The proposed model can well
experience. The empirical experience is often valid only for
correlate the expansion of the 16 trials using 3 regression
the specific extrusion equipment that has been used to
parameters. The average deviation of the correlation is 5.9%.
generate the good operation conditions.



In practical food industrial applications, one often
INTRODUCTION
needs to run some trials in a pilot extrusion process in a new

food product development stage. Through the trials, a set of
Diets with high amounts of whole grains may help
specific operating parameters can be established for the new
achieve significant weight loss, and also reduce the risk of
recipe material extrusion. The procedure sometimes is out of
chronic diseases such as diabetes and cardiovascular disease.
control in the time or raw materials cost frame. In this work,
Epidemiological studies have shown that increased intakes of
we present an engineering procedure to find out the suitable
whole grain products are associated with reduced risks of
process parameters to reach correct expansion for whole
diabetes mellitus, hypertension, and cardiovascular disease
wheat flour extrusion in a pilot plant, which includes
(Jones, 2000, Slavin, 2004, Katcher et al. 2008). However,
experimental design and process parameter correlation.
most cereal products available in Europe and the United

States are produced from highly refined grains, which lead to

the loss of many potentially beneficial micronutrients,
EXTRUSION EXPERIMENTS DESIGN
antioxidants,
minerals,
phytochemicals,
and
fiber.

Subsequently, the consumption of whole grain is far less than
The extrusion experiments design was setup by a
the three servings on a daily basis as suggested by the food
traditional way. With considering the extruder limitation, a
pyramid of the United States Department of Agriculture
Central Composite Design (CCD) (Esbensen, 2000) was used
(Slavin, 2004). Whole grain breakfast cereals might
in the study, which was based on five levels of three
contribute to satisfy the recommended daily intake, since
variables (Table 1). The independent extrusion variables
they fit to the increasingly fast-paced nature of consumer
considered were barrel temperature in different zones, feed
lifestyles. Breakfast cereals are convenient to prepare and
water content and screw speed. All other parameters were
easily consumed. In addition, they appeal to consumers of all
kept constant. Operating ranges and five standardized levels
income levels (Jones, 2000)
were established by preliminary study of each variable.

According to the CCD, the experimental plan comprised 15
Extrusion cooking has become a well-established
trials (8 factorial points, 6 axial points and 1 central point).
industrial technology by offering continuous and flexible

processes which allow producing breakfast cereals with
Table 1 Coded levels for the central composite design
diverse textures and shapes and ultimately reducing the costs
Variables
Levels
of the final products. The extrusion cooking process can be
-?
-1
0
1
+?
analyzed in terms of operational parameters, system and
T5, °C
101
111
125
139
149
product characteristics. By changing the operational
Xw, %
9.2
10.5
12.5
14.5
15.8
parameters it is possible to influence the time-temperature-
Ns, rpm
208
245
300
355
393
shear history of the grain flour in the extruder. System
parameters such as specific mechanical energy (SME) are
generally used to describe the time-temperature-shear history,

In Table 1, T5 is the temperature of zone 5 (closest zone to
solid theoretic background and is the direction to develop a
die), °C, X
model to describe the extrusion process operation. However,
w is the water content, weight percent, %, Ns is the
screw speed, rpm, ? equals to 1.682.
the mechanism-based model often needs accurate food fluids

physical property correlations to support its prediction and
In the investigation, the extrudate expansion was set
estimation for the extrusion process behaviors. Because the
as the objective of the extrusion process operation. Through
food fluids belong to non-Newtonian fluid and have very
the experiments, it was expected to develop a quantitative
complicated behaviors, the development of a precise physical
correlation for extrudate expansion and extrusion operating
property calculation model for such food fluid is very
conditions. With the help of the correlation model, the
difficult.
number of runs could be reduced for a similar recipe food

extrusion using the whole wheat flour.
In this work, a dimensional analysis based model is

proposed to correlate the extrudate expansion and extruder

operating conditions. Dimensional analysis method is a
EXTRUSION EXPERIMENTS
classical way in industrial applications to setup a model. In

the applications of fluid mechanics and fluid heat transfer,
Whole wheat grain was milled to obtain the whole wheat
the dimensional analysis method has obtained tremendous
flour. The whole wheat flour was processed in a Werner &
successful achievements. However, this method is seldom
Pfleiderer Continua 37 co-rotating twin-screw extruder. The
used to setup the correlation between extrudate expansion
CCD table, i.e. Table 1, was used to set up 15 experimental
and extrusion operating parameters.
runs. First, 15 trials were carried out to search the optimal

extrusion conditions for maximum expansion. After the 15
Extrudate expansion is a reflection of extrusion
trials, one more run was carried out to obtain the maximum
equipment design and process operation conditions. The
expansion. The last trial conditions were estimated from the
equipment design may include different pre-mixing methods,
response surface methodology. The trial capacity was in 22-
various screw structures, die design, etc. Because the process
27kg/hr levels. In the experimental work, the wheat flour,
operation conditions are the adjustable process control
water and additives are directly fed into extruder without pre-
parameters for an existing production line, we will only study
mixing. The extrudates were dried at 110°C for about 10
the correlation between process operation conditions and
minutes in a continuous processing oven. The extrudate bulk
extrudate expansion in this work. In an extrusion process,
density was measured during the extrusion operations using
many process parameters have influence on the extrudate
weight method for 1 liter extrudates.
expansion, e.g. different zone temperatures, die temperature

and pressure, process capacity, screw speed, torque, water

content, fluid viscosity, specific mechanical energy, etc.
MODEL CONSTRUCTION
Many researchers have used different methods to correlate

the process parameters with extrudate expansion (bulk
In decades, many investigations have been carried
density) and achieved their successes. In this work, the
out for the relationship between extrudate expansion and
dimensional analysis method will be applied to analysis and
operating conditions (Alvarez-Martinez, et al. 1988, Cai and
correlate these parameters.
Diosady, 1993, Moraru and Kokini, 2003). As the food

market is very volatile, food producers have to change their
Historically, the dimensional analysis methods
recipe all the time. Sometimes the maximum expansion is the
include the Rayleigh method and the Buckingham pi method
target. In other cases, mild extrusion conditions are expected
(Buckingham, 1914, Rayleigh, 1915, Perry and Green,
in order to improve the nutritional quality of products (Singh
1999). In this work, the Buckingham pi method is applied to
et al. 2007). A quantitative correlation for the extrudate
construct a model. For an extrusion process, we can find out
expansion and operating condition will significant benefit the
a set of key variables and their dimensions in the engineering
food extrusion applications.
system as below:

T0, Td=temperature, T
In these correlations and models, some are based on
FT, Fw=flowrate, mass/time, M/t
empirical regression from operating conditions (Ding, et al.
Ns=screw speed, 1/time, 1/t
2006). Others use the models from a sort of theories or
? =torque, force?length F?L
mechanisms (Fan and Mitchell, 1994). In the empirical
Pd =die pressure, force/length2 F/L2
regressions, a model is often constructed with linear and
? =density, mass/volume, M/L3
B
quadratic terms according the statistical significant for a
Here, the units T, M, t, F and L respectively represent
specific extrusion process. This kind of model construction
temperature, mass, time, force and length. Among the
normally results in many regression coefficients to be
variables, ? is the bulk density of extrudates, g/liter, F
B
w is
determined from experimental data. No doubt, the empirical
the water flowrate added into the extruder, kg/hr, F
equation has played an important role in extrusion product
T is the
total flowrate of all feed materials (wheat flour, water and
development. However, sometimes the empirical models
additives), kg/hr, T
contain many operating parameters and product properties.
d is the die temperature, °C, T0 is the room
temperature (25°C), which is also the raw material initial
The uncertainty of the measurement of the product properties
could be very diverse. Thus, the uncertainty can transfer into
temperature, Pd is the die pressure, bar, ? is the torque, Nm,
the empirical correlation model. The mechanism model has a
Ns is the screw speed, rpm.

From the key extrusion process parameters, a
in Figure 2. As shown in Figure 2, the bulk density
variable and units matrix is formed as shown in Table 2.
estimation errors are evenly distributed.


Table 2 Selected variables and units matrix
Table 3 Coefficients of equation (1)
Unit
T
?
Coefficient
K
?
?
0
Td
FT
Fw
Ns
Pd
?
B
T
1
1
0
0
0
0
0
0
Value
13508
0.7774
-0.2882
M
0
0
1
1
0
0
0
1

t
0
0
-1
-1
-1
0
0
0
F
0
0
0
0
0
1
1
0
L
0
0
0
0
0
-2
1
-3

In the formation of Table 2, we assume that the fluid density
just before flash-out from die linearly proportions to the bulk
density.

Through calculation, it can be found out that the
rank of the matrix shown in Table 2 is 5. The physical
variables in Table 2 are 8. From the Buckingham pi theorem,
three dimensionless groups can be established from the

Figure 1: Correlation results of bulk density at different runs
matrix, which are given as follows:

?
F
T
d
P
T
F
, w , d
? ?? ? N
B
s
F
T
T
0
In the studied extrusions process, the term Fw/FT represents
the water content of processing materials. The term Td/T0 is
the temperature changes of processing materials from its
initial condition to the vicinity of flash-out from extruder.
P ? F
The term
d
T
represents the energy added into the
? ?? ? N
B
s
processing materials. In fact, the term ??Ns/FT reflects the
widely used specific mechanical energy (SME). From the
three dimensionless groups, different model expressions can
be constructed. In this work, a model is obtained as
?
?

?
T ? ? P ? F ?
? =
d
d
T
Figure 2: Relative deviations of equation (1) in correlation
B
K (X W )
(
1)
?
?
?
? ??
?
?
? T ?
? ? N
with bulk density and extusion operating conditions
0
?
s ?



where ? is the bulk density of extrudates, g/liter, X
B
w is the
In Figure 2, the relative deviation (Rd) is calculated as
water content of feed material and equals to Fw/FT, weight
exp
cal
?
? ?
fraction. K, ? and ? are the model coefficients, which need to
B
B
R =
%

(3)
d
exp
be determined from experimental data.
?B

From the equation (1), it can be seen that the

DISCUSSIONS AND CONCLUSIONS
equation lacks of physical properties of food fluids. Thus it is
only suitable to the specific whole wheat flour extrusion.

However, the equation is simple and contains only
In engineering applications, a simple and reliable
correlation coefficients. The simple format model meets the
model often can help engineers to reach an optimal solution
engineering applications.
through observing the interactions of different operational

parameters. In this work, the model construction is based on
Using the data from the 16 runs for whole wheat
the engineering principle. A dimensional analysis method is
flour extrusion, the model coefficients are determined as
used to build a model with the key process parameters. From
shown in Table 3. The average absolute deviation (AAD) of
the model one can quantitatively estimate the extrudate bulk
the model correlation with experimental bulk density data is
density changes with different control parameters and the
5.9%, where AAD is calculated as.
interactions of these parameters.
The model estimation results show that the proposed
1
exp
cal
?
?
?
? ?
AAD =
?? B
B
?%

(2)
can successfully represent the extrudate bulk density in
exp
n
?
?
different extruder operating conditions. The average absolute
n ?
?
B
?
In equation (2), n is the number of experimental
deviation in the estimation of extrudate bulk density is 5.9%.
runs. The model correlation results for the extrudate bulk

density are shown in Figure 1. The estimation error

distribution of the model for extrudate bulk density is shown




ACKNOWLEDGMENTS
We acknowledge Hanne T. Pedersen, Jørgen Busk
from Danish Technological Institute and Danish
Technological Institute for providing its pilot plant, raw
materials and technical support in this research work.

REFERENCES
Alvarez-Martinez, L.; K. P. Kndury and J. M. Harper 1988. “A
general model for expansion of extruded products.” Journal
of Food Science
, 53, 609-615
Cai, W. and L. L. Diosady. 1993. “Modeling of expansion and
water solubility index of wheat starch during extrusion
cooking” Acta Alimentaria, 22, 181-92.
Buckingham, E. 1914. “On physically similar systems; illustrations
of the use of dimensional equations". Phys. Rev. 4: 345-376.
Ding, Q.-B.; P. Ainsworth; A. Plunkett; G. Tucker and H. Marson.
2006. “The effect of extrusion conditions on the functional
and physical properties of wheat-based expanded snacks”.
Journal of Food Engineering, 73, 142-148.
Esbensen, K.H. 2000, “Multivariate Data Analysis-in Practice” 4th
Ed. CAMO ASA, Oslo, Norway
Fan, J.; J.R. Mitchell; J. M. V. Blanshard. 1994. “A computer
simulation of the dynamics of bubble growth and shrinkage
during extrudate expansion”. Journal of Food Engineering,
23, 337-356.
Jones, J. M., 2000. “Cereal nutrition”. In: Fast, R. B.; Caldwell, E.
F.: Breakfast Cereals and how they are made. St. Paul:
American Association of Cereal Chemists. p.411-442.
Katcher, H. I.; R.S. Legro; A.R. Kunselman; P.J. Gillies; L.M.
Demers; D.M. Bagshaw and P.M. Kris-Etherton. 2008. “The
effects of a whole grain-enriched hypocaloric diet on
cardiovascular disease risk factors in men and women with
metabolic syndrome”. American Journal of Clinical
Nutrition
, 87, 79-90.
Moraru, C. I. and J.L. Kokini. 2003 “Nucleation and expansion
during extrusion and microwave heating of cereal foods”.
Comprehensive Reviews in Food Science and Food Safety, 2,
120-138.
Perry, R.H and D. W. Green. 1999. Perry’s Chemical Engineers
Handbook, 7th Ed. McGraw-Hill, New York, p.3-89 to 3-90
Rayleigh, 1915. “The principle of similitude”. Nature, 95, 66-68.
Singh, S.; S. Gamlath and L. Wakeling. 2007. “Nutritional Aspects
of Food Extrusion: a Review” International Journal of Food
Science and Technology
, 42, 916-929.
Slavin, J. 2004. “Whole grains and human health”. Nutrition
Research Review, 17, 99-110.


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