Full text of DOI:10.1111/j.1365-2621.2000.tb16024.x

JFS: Food Engineering and Physical Properties
Mathematical Evaluation of Effective Moisture
Diffusivity in Fresh Japanese Noodles (Udon)
by Regular Regime Theory
T.INAZU AND K. IWASAKI
ABSTRACT: The effect of moisture content and temperature on the effective moisture diffusivity was investigated to
have the optimal drying condition of Japanese noodles (Udon) using regular regime theory. The drying of fresh Udon
of different moisture contents was carried out under constant conditions of relative humidity and airflow at 20, 30,
and 40 ꢀC. The existence of regular regime periods for fresh noodles was experimentally verified. Effective moisture
ꢂ7
ꢂ7
2
ꢂ1
diffusivity obtained ranged from 2.1 ꢁ 10 to 3.7 ꢁ 10 cm s . The effect of temperature on effective moisture
diffusivity was adequately modeled by the Arrhenius relationship, although the effect of moisture content was quite
small.
Key Words: Japanese noodle, moisture diffusivity, optimal drying
Introduction
shrinkage. The purpose of the present study is to establish the
THE PRODUCTION OF DRIED JAPANESE NOODLE (DRIED optimal drying conditions of fresh Udon in the finishing process.
Udon), the dough is molded into the slab and cut to shape af- The regular regime theory was used to evaluate the effective
N
I
ter mixing wheat flour with salt water (fresh Udon), and the stick- moisture diffusivity as a function of moisture content and tem-
shaped fresh Udon is dried to make a preserved food. The drying perature in the drying process, carried out under constant rela-
process of fresh Udon is difficult, because the shaped fresh tive humidity and air velocity conditions at 20, 30, and 40 ꢀC, us-
Udon is thick and delicate, with poor resistance to internal me- ing fresh Udon with different initial moisture content. The effec-
chanical stress caused by rapid drying. Therefore, in an industri- tive moisture diffusivities obtained were then compared with
al system, the drying process is divided into 3 steps such as pre-, those of pasta.
main, and final-drying. In the pre-drying process, the free water
that exists on the surface layer of fresh Udon is removed by dried
Results and Discussion
air at temperatures between 15 to 20 ꢀC to prevent the shape of
the noodle from becoming distorted by its own weight during Time changes of moisture content
drying. In the main-drying process, the relative humidity of air is
Typical time changes in the moisture content of fresh Udon at
adjusted to control the internal moisture diffusion under high 20, 30, and 40 ꢀC during the drying experiment are shown in Fig.
humidity conditions of 70 to 85% at 30 to 35 ꢀC. In the final-dry- 1. At 40 ꢀC, the variations of weight data at an arbitrary time were
ing process, the shaped noodles are dried to have an optimal almost within 0.2%. Similarly, the variations at 20 and 30 ꢀC had
moisture content (approximately14%)by circulating air with also the same values. In the initial stage of the drying experi-
gradually decreasing temperatures. The main-drying process,
which has the longest drying time among these processes, deter-
mines the product quality. However, optimal drying circumstanc-
es are not always obtained due to the complexity of operating
conditions (temperature, humidity, air velocity, and so forth).
The establishment of optimal operating conditions is needed to
produce dried Udon with high quality.
Murase and others(1993) monitored the weight of fresh Udon
as a function of drying time using an auto digital weight balance
and proposed the drying conditions in the main-drying process.
However, they did not consider the kinetics of drying. Miki and
others(1992) measured the time required for change in moisture
content of fresh Udon during its drying. The falling rate period
appeared after 2 h from the start of drying. However, they did not
analyze the drying process quantitatively. Mathematical analysis
of the system is necessary to determine drying conditions.
The regular regime theory developed by Schoeber and Thijs-
sen (1977) has been used recently to evaluate the drying behav-
ior of foodstuffs mathematically. Luyben and others (1980) and
Tong and Lund (1990) demonstrated that this theory was effec-
tive for the evaluation of the moisture diffusivity in food drying
systems with a strong concentration-dependence diffusivity and Fig. 1—Typical time changes in moisture content of fresh Udon.
4
40 JOURNAL OF FOOD SCIENCE—Vol. 65, No. 3, 2000
© 2000 Institute of Food Technologists

ment at each temperature, the differences in temperatures be- fied.
tween the internal and external noodle and the drop in humidity
In analogy with the surface area for moisture transfer, ꢃ was
s
of internal atmosphere were observed (data not shown). After also found to be dependent on moisture content (data not
about 10 to 20 min operation, the temperature and humidity be- shown). Temperature had very little effect on the ꢃs which was
came almost constant. This stage was ignored for the mathemati- found to be a linear function of moisture content. The following
cal analysis as described below, because the total drying period equation was established by the least-squares method:
needed longer time (20 to 22 h) than that in this initial stage (10
to 20 min).
In the drying process of fresh Udon, the moisture content
ꢃs ꢄ 1.45 ꢂ0.297M(R ꢄ ꢂ0.956***)
(1)
rapidly decreased over time after the initial drying stage, and
then slowed to a gradual decrease. This result was similar to that
of spaghetti reported by Dexter and others(1981). On increasing
0.218 ꢅ M ꢅ 0.577
The effect of temperature on effective moisture diffusivity
the drying temperature, the loss of the moisture content in- was adequately modeled by the Arrhenius relationship and the
creased and the values of 0.28, 0.32, and 0.35 g-water/g-solid value of B was 1.288 ꢁ 10ꢂ3 cm sꢂ1. An average activation energy
2
were obtained at 20, 30, and 40 ꢀC after 18 h.
of the effective moisture diffusivity over the moisture range of
.23 to 0.57 g-water/g-solid was 21.3 kJ molꢂ1
The effective moisture diffusivity was represented only as a
0
.
Shrinkage
Fig. 2 shows the surface area as a function of moisture content function of temperature (Eq. 9) because the effect of moisture
and temperature during the drying process of fresh Udon. The content on those is negligible (Fig. 4). Xiong and others (1991) re-
normalized area was defined as the ratio of the area at an aver- ported that the effective moisture diffusivity through porous
age moisture content at any time compared to the area at initial
moisture content. It was found that the sample area decreased
linearly with decreasing the moisture content, and the degree of
the shrinkage of fresh Udon was independent of the drying tem-
perature in the present experimental condition. This result was
similar to that of biscuits and muffins reported by Tong and
Lund (1990).
Data analysis
In the determination of effective moisture diffusivity as a
function of moisture content using regular regime theory, it is
necessary to confirm the existence of the regular regime period in
fresh Udon during the drying process. If the regular regime peri-
od does exist, all drying curves for the same material and geome-
try at 1 temperature merge into 1 curve (regular regime curve) re-
gardless of initial moisture content.
Fig. 3 shows each regular regime curve at 3 temperatures. At
40 °C, regular regime curves of initial moisture content of 0.58 g-
water/g-solid, 0.53 g-water/g-solid and 0.43 g-water/g-solid were
found to be expressed by 1 curve within experimental error.
Therefore, it is possible to conclude that the regular regime peri- Fig. 3—Regular regime curves for fresh Udon during drying at vari-
ous temperatures. Initial moisture content: ᭡ 0.58 g-water/g-solid;
0.53 g-water/g-solid; ᭪ 0.43 g-water/g-solid; ᭹ 0.58 g-water/g-
solid; ᭝ 0.54 g-water/g-solid; ꢁ 0.45 g-water/g-solid; ᭺ 0.57 g-wa-
ter/g-solid; ᭞ 0.54 g-water/g-solid; ᭿ 0.43 g-water/g-solid.
od does exist in fresh Udon in the present experimental condi-
ᮀ
tion. Similarly, regular regime periods at 20 and 30 °C also veri-
Fig. 2—Normalized area as a function of moisture content and tem- Fig. 4—Effective moisture diffusivity of fresh Udon as a function of
perature during drying the fresh Udon samples. Full line denotes the temperature for experimental data and those calculated by Eq. 9. See
best-fit line.
the text.
Vol. 65, No. 3, 2000—JOURNAL OF FOOD SCIENCE 441

Effective Moisture Diffusivity in Noodles . . .
Table 1—Comparison of effective moisture diffusivity for different noodles
Pasta
Fresh Udon
(1)
(2)
(3)
(4)
Moisture content
g-water/g-solid)
(
0.27
40
21
1.00-5.00
2.5ꢁ10
0.22
55
–
0.25
40
–
0.20
1.5ꢁ10
25.9
0.23
40
–
0.17
1.8ꢁ10
22.6
0.27-0.55
20
0.25-0.57
30
0.23-0.54
40
Temperature (°C)
Relative humidity (%)
75
75
75
-
1
Air velocity (m s )
–
1.70-1.80
1.70-1.80
1.70-1.80
2
-1
-7
-7
-7
-7
-7
-7
-7
Deff (cm s )
2.8ꢁ10
21.8
2.1ꢁ10
2.7ꢁ10
3.7ꢁ10
-
1
E (kJ mol )
21.8
21.3
21.3
21.3
Reference
Andrieu and
Stamatopoulos (1986)
Xiong and
others (1991)
Litchfield and
Okos (1992)
Waananen and
Okos (1996)
This work
food is fairly constant at moisture levels above 0.2 g-water/g-sol- under high pressure is considered to be more dense compared
id (on the basis of dry state) and decreases at lower moisture con- with that of fresh Udon made by rolling and cutting procedure
tents. The results obtained in the present study at moisture level (Oda, 1992), however the pasta is exposed to air in relatively
0
.23 to 0.57 g-water/g-solid is supported from the data reported high temperature compared with that of the fresh Udon during
by Xiong and others. the drying. As a result of above condition, the effective mois-
Various effective moisture diffusivities, activation energy, and ture diffusivity in pasta may become the same order as that of
drying conditions for different noodles are summarized and the fresh Udon.
compared in Table 1. Diffusivities reported in pasta at moisture
In the present study, the drying process of fresh Udon was
level 0.22 to 0.27 g-water/g-solid ranging from 40 to 55 ꢀC is al- found to be analyzed by the regular regime theory, and the
most constant (1.5 ꢂ 2.8 ꢁ 10ꢂ7 cm sꢂ1), while those obtained in effective moisture diffusivity was represented as a function
the present study at moisture level 0.23 to 0.57 g-water/g-solid of temperature. Further experiment under various conditions
2
ranging from 20 to 40 ꢀC is 2.1 ꢂ 3.7 ꢁ 10ꢂ7 cm s and increased of humidity and airflow and the development of mathemati-
slightly with temperature. The activation energy of the fresh cal model with porosity is necessary in order for these results
Udon obtained in the present study is similar to that of pasta. to be used to obtain the optimal drying condition in the noo-
The structure of pasta made by degassing and extruding process dle industry.
2 ꢂ1
Materials and Methods
humidity of about 75%) based on the method of saturated salt
solutions (Greenspan 1977). Relative humidity of 75% was
generally specified in the dried Udon factory as a specification
in the main-drying process.
Noodle Processing
Two hundred g of commercial soft wheat flour (moisture
content 13.5%, ash content 0.38%, protein content 9.2%) and 8
The outside of the desiccator was constructed from double
g sodium chloride (Wako Pure Chemical Inc., Osaka, Japan) acrylic plastic and was covered with a styrofoam layer similar
and distilled water were mixed in the Noodle-Bread produc- to that of the incubator. Heating cables were stretched around
the inside of the desiccator to control the surrounding temper-
tion machine (MK-500U, National Inc., Tokyo, Japan) for 5
min. After the dough was prepared, it was rested for 1 h to dis- ature to change as little as possible. The sample of fresh Udon
tribute the moisture uniformly. The dough sheet was prepared was suspended on the rod as the same manner as that used in
by passing through the production roll repeatedly and was cut the conventional factory. Two rods were prepared, and 15 lines
using a small noodle making machine (YM-568, Yamato Sei- of the fresh Udon per 1 rod were suspended, and each rod was
sakusho Inc., Kagawa, Japan) to obtain stick-shaped fresh set on the latticed test tube stand which was set on an elec-
Udon of about 3.5 mm width, 3.0 mm thickness, and 30 cm tronic weight balance.
length. In the following drying experiment, 15 lines of fresh
Udon were suspended in a rod. The fresh Udon is dried as an
infinite slab of about 60 mm width because of the closeness of
individual cuts on the rod. The initial moisture content was in
the range 0.53 to 0.58 g of water / g-solid as formulated, and
demonstrated to have initial moisture content of 0.43 to 0.45 g
of water / g-solid, prepared by controlling the relative humidity,
confirming the appropriateness of the regular regime theory.
Drying Experiment
Drying apparatus was made by remodeling the commercial
incubator and desiccator (Fig. 5). The outside of the incubator
was constructed from double acrylic plastic and was covered
with styrofoam to maintain constant temperature. The incu-
bator was equipped with a temperature controller. A 500 g of
sodium chloride was inserted into a plastic container with dis-
tilled water (5 layer) and used to generate humidity (relative Fig. 5—Schematic diagram of the experimental apparatus.
4
42 JOURNAL OF FOOD SCIENCE—Vol. 65, No. 3, 2000

ꢆ
Digital electronic weight balance (EG-2000, A & D Inc.,
Tokyo, Japan) was used to monitor the sample weight as a
function of drying time. The time-weight data was obtained
by the recorder (AD-8121, A & D Inc., Tokyo, Japan) through
an RS-232 interface.
fusion coefficient (D ) was calculated as follows:
r
ꢆ
M
D ꢄ 1/(M ꢂ M) ͐ D dM
(4)
r
i
M
r
i
where Mi is moisture content in equilibrium with the sur-
rounding gas phase (g-water/g-solid), Dr is the reduced diffu-
sivity (dimensionless). The average Sherwood number (Shd)
was calculated as follows:
Airflow was controlled by a damper, and the air was
flowed down in the same manner as that of the convention-
al factory. The airflow was held near constant at 1.7 to 1.8 m
sꢂ1 in the present study using an anemometer (CW-30,
CUSTOM Inc., Tokyo, Japan).
ꢆ
Shd ꢄ 2F/(M ꢂM )D
i
(5)
r
The portable fume (Iuchi Inc., Osaka, Japan) and the fan
(
Iuchi Inc., Osaka, Japan) installed in the desiccator were
The driving force for the drying process in the present
study with a constant surface concentration of fresh Udon was
expressed as the average moisture content of the sample mi-
nus the interfacial moisture content at any time. Drying curves
for samples were constructed by expressing the logarithm of
the flux parameter as a function of driving force.
used to generate the airflow.
The connected hose between the desiccator and the in-
cubator (diameter 50 mm) was heated at a constant temper-
ature by the heating tape.
The relative humidity was measured at the upper posi-
tion of the sample by thermo recorder (TR-72, T and A Inc.,
Nagano, Japan). Thermister SK-67sensor connected to the
recorder (R316, TECHNOL SEVEN Inc., Kanagawa, Japan)
was used to monitor the temperature.
The regular regime curve was differentiated to give dln(F)/
dln(M ꢂ M ) as a function of moisture content. The averaged
i
Sherwood number (Sh ) as a function of dln(F)/dln(M ꢂ M )
d
i
was presented by Schoeber and Thijssen (1977) in graphic
forms for infinite slabs, non-shrinkage infinite cylinders, and
non-shrinkage spheres. An empirical equation to relate the av-
erage Sherwood number and dln(F)/dln(MꢂMi) was devel-
oped by Tong and Lund (1990) as follows:
Drying method
The drying experiment was carried out at 3 tempera-
tures, 20, 30, and 40 ꢀC, according to the conventional pre-
and main-drying conditions. Moisture contents of samples
were determined by the air-oven method, drying at 135 ꢀC
X ꢄ dln(F)/dln(M ꢂMi)
(
AACC, 1995). Drying experiments at 20 and 30ꢀC were done
2
Shd = exp[1.74 ꢇ 0.43(lnX) ꢂ 0.076(lnX) ꢂ 0.0034(lnX) ]
3
in a refrigerator room (about 6 ꢀC), while that at 40 ꢀC, the
experiments were run at room temperature at 25 ꢀC. Time-
weight data were collected in triplicate for each tempera-
ture.
(6)
The Dr was calculated by combining Eq. 4 and Eq. 5 as fol-
lows:
Measurement of shrinkage
D ꢄ (d/dM)(2F/Sh )
r
(7)
d
The time changes of width, thickness, and length of the
fresh Udon were measured by a vernier caliper as a function
of sample weight. At the same time specific gravities of sam-
ples were measured by an electronic pycnometer (EW-
and the effective moisture diffusivity (Deff) (cm2 s-1) was then
obtained by
Deff ꢄ Dr/ꢃ2s
(8)
2
00SG, MIRARGE TRADING Inc., Osaka, Japan). The densi-
ties of samples were obtained from the values of specific
gravities by multiplying 0.999973.
3
where ꢃs is the density of sample (g-solid/cm -sample).
Tong and Lund (1990) presented that the relationship be-
tween the effective moisture content and temperature was de-
scribed by Arrhenius equation (Atkins 1992):
Data analysis
2
Water flux (j , g-water / cm ) relative to the moving inter-
w
face was calculated as follows (Luyben and others 1980):
D ꢄ Bexp(ꢂ E/RT)
eff
(9)
j ꢄ ꢂ(W /A(M))(dM/dt)
w
(2)
ds
where B is the frequency constant (cm sꢂ1), E is the activation
energy (J molꢂ1), R is the gas constant (8.314 J molꢂ1 Kꢂ1), and
T is the absolute temperature (K).
2
where Wds is the weight of dry sample (g), A is the area (cm2),
M is the average moisture content (g-water/g-solid), A(M) is
2
the area as a function of moisture content (cm ), t is the time
Statistical analysis
(
s). When jw was known, flux parameter (F, dimensionless)
was calculated from the following equation:
The relationship between the moisture content and nor-
malized area of the fresh Udon at 3 temperatures were ana-
lyzed by the least-squares method, using a microcomputer
with Delta graph® Pro 3 (Nippon Polaroid Inc., Tokyo, Japan).
2
F ꢄj ꢃ R /D ꢃ
w ds ds 0 s0
(3)
where ꢃds is the density of dry sample (g-solid/
3
cm ꢂsample), R is half the thickness of dry sample (cm),
Statistical analysis was conducted by Fisher’s z-transformation
method using Stat View® 4.02 (Abacus concepts Inc., Berkeley,
ds
and D0ꢃs02 is a dimensional constant with numerical value 1,
introduced for similarity reasons. The average reduced dif-
Calif., U.S.A). The relationship between the moisture content
and density data were analyzed in the same way.
Vol. 65, No. 3, 2000—JOURNAL OF FOOD SCIENCE 443

Effective Moisture Diffusivity in Noodles . . .
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