Full text of DOI:10.1111/j.1365-2621.2002.tb09459.x

JFS: Food Engineering and Physical Properties
Optimizing Processing Conditions for
Milk Coagulation Using the Hot Wire Method
and Response Surface Methodology
O.A. SBODIO, E.J. TERCERO, R. COUTAZ, AND E. MARTINEZ
ABSTRACT: To evaluate the relationship between the factors affecting coagulation, the hot wire method was used
for direct measurements of the renneting milk process as well as a central composite design with 3 factors:
rennet concentration (x1), renneting pH (x2), and temperature (x3). Second-order models for maximum voltage
(Y1), time at maximum voltage (Y2), and coagulation time (Y3) were employed to generate response surface
contours. Optimum conditions for cutting time were found with x1 = 0.0278 R.U./mL milk, x2 = 6.60, and x3 =
35 C, for which the responses were Y1 = 2854
171 V, Y2 = 14.08
3.04 min, and Y3 = 7.16
1.12 min. No
significant differences (p > 0.01) were found between the 3 responses obtained in the experiment and the ones
predicted by the models. The use of the objective and non-destructive monitoring of curd formation and the
response surface methodology can be recommended to optimize milk coagulation.
Keywords: cheese milk, rennet coagulation, technological properties, response surface
Introduction
coagulation. Most publications, however, emphasize the main
factor effects, information on interactions of milk coagulation
factors being limited (Ernstrom and others 1958; Jen and Ash-
worth 1970; Kowalchyk and Olson 1977; Dalgleish 1983; Okigbo
1985 (a); Okigbo 1985 (b); Noël and others 1991; Sbodio and oth-
ers 1997). In cheese-making, there are 3 relevant independent
variables – renneting pH, temperature, and chymosin concen-
tration - on which further investigation is needed to identify in-
teractions among them. Such interactions, if significant, will be
highly applicable in optimizing the variable levels to obtain opti-
mum curd firmness and product yields. Since there are several
dependent variables, including coagulation time (CT), firmness,
and time of maximum firmness, response surface methodology
turns out to be useful for studying and optimizing the coagula-
tion process.
HE COAGULATION OF MILK, WHICH IS THE FUNDAMENTAL PROCESS
T
in cheese-making, results in the formation of a gel, a conse-
quence of physicochemical changes taking place in the casein
micelles. Factories still cut curd according to time schedules used
in their manufacturing process and time corrections are made
mainly after subjective evaluation of curd firmness (Thomasow
and Voss 1977). Variation in curd firmness at cutting may result in
greater losses of milk components and reduced cheese yield,
suggesting that these drawbacks could be prevented by moni-
toring curd firmness (Bynum and Olson 1982; Marshall 1982;
Okigbo 1985a; Hori 1985), which would also allow setting opti-
mum conditions for milk-clotting enzyme preparations (Ustunol
and others 1991).
Taking into account economic and practical aspects, numer-
ous methods have been developed and studied for measuring
coagulation time (CT) and coagulum strength; among others,
viscometric and rheological(McMahon and Brown 1982; Noël and
others 1991; Sbodio and others 1997), ultrasonic (Gunasekaran
and Ay 1994) and optical methods (McMahon and others 1984;
Korolczuk and Maubois 1988; Banon and Hardy 1991). Hicks and
others (1990) have reported that diffuse reflectance profiles fol-
lowed coagulation parameters accurately when changes due to
pH, temperature, and enzyme concentration were monitored.
The same profiles were monitored using an optical fiber sensor
sensitive to infrared light at 950 nm (Ustunol and others 1991).
Recently, Laporte and others (1998) showed that near-infrared
reflectance is a reliable method for monitoring milk coagulation.
This again, makes it difficult to compare the results obtained
with the different instruments and methods. Hori (1985) pro-
posed an electrical method in which a platinum wire immersed in
milk was heated and the wire temperature monitored. As the
milk surrounding the wire coagulated, heat dissipation from the
wire decreased and the wire temperature increased.
The objective of this experiment was to evaluate the relation-
ship between the factors affecting coagulation and responses
that are relevant to the process, to establish optimum processing
conditions using a hot wire method.
Materials and Methods
Experimental design
Three responses were measured: maximum voltage (Y1), in
microvolts (ꢀV), the time at which the maximum voltage was ob-
tained (Y2), and the coagulation time (Y3), both of them in min.
Five levels of the variables - chosen as suggested by cheese in-
dustry experts - were coded as follows: -1.682, -1, 0, +1, and
+1.682. The variables, symbols, and levels are shown in Table 1.
Since a rotational design is made from a factorial one, in the
case of this experiment 23 (2 levels, 3 variables) additional data
are added, which are called axial data. The levels chosen to begin
the experiment are -1 and +1, which limit the real work region.
The central levels were chosen in agreement with the levels cur-
rently used in industrial practices to produce 3 types of cheese
Much has been published on factors affecting enzymatic milk
© 2002 Institute of Food Technologists
Vol. 67, Nr. 3, 2002—JOURNAL OF FOOD SCIENCE 1097

Optimizing conditions for milk coagulaton . . .
Table 1—Variables and their levels for central composite Table 2—Central composite design arrangement and re-
design
sponses
a
Coded-variable levels
-1
Variable levels
Responsesb
Y2
Variables Symbols -1.682
0
1
1.682 Run
x1
x2
x3
Y1
Y3
Rennet
x1
0.0048 0.0150 0.0300 0.0450 0.0552
1
2
3
4
5
6
7
8
-1
-1
-1.682
0
1
1
0
0
1
-1
0
0
0
1
-1
-1
1
0
0
-1
1
0
0
-1
-1
-1.682
0
0
1
-1
-1
0
0
1
1
0
0
-1
1
0
0
-1.682
-1
1
0
0
3065
3032
2737
2748
2964
3246
3046
2760
3433
3709
3809
2835
2741
3145
3459
3328
2060
3259
20.25
33.99
45.41
11.506.50
10.33
14.33
14.75
12.00
18.16
19.58
14.92
14.08
14.92
16.92
26.08
17.66
10.25
12.33
11.52
23.42
37.35
concentration
(R.U./mL )
pH
Temperature
(ꢁC)
x2
x3
6.43
29.9
6.50
32
6.60
35
6.70
38
6.77
40.04
3.84
7.76
7.17
6.89
4.38
9.93
4.02
7.13
8.19
8.33
20.10
11.39
3.54
7.11
Conversion from coded variable level to uncoded variable is given by the
following equations:
Rennet concentration = 0.015 x + 0.030; pH = 0.101 x + 6.60; T = 3 x +
35
9
1
2
3
10
11
12
13
14
15
16
17
18
1
1.682
0
(cuartirolo cheese, soft cheese, and hard cheese). This is the rea-
son the variables are represented graphically between -1 and +1
levels. Generally, milk clotting is performed by the cheese indus-
try under the following conditions: time: 7 to 10 min, pH: 6.5 to
6.6, temperature: 34 to 35 ꢁC, and enzymatic concentration: 0.02
to 0.03 R.U./mL milk.
0
1.682
0
0
1.682
a
b
Coded variables.
Y
= maximum voltage ( µV ). Y = time to reach maximum voltage (min ). Y =
1
2
3
coagulation time (min )
The central composite design (Myers and Montgomery 1995)
was arranged in such a way as to fit a 2nd order polynomial in R
(x1), pH (x2), and T (x3). Four replicates at the center of the design
(runs 4, 7, 8, and 12) were done to allow for estimation of “pure ment, 2 L of substrate was warmed to the corresponding temper-
error” or experimental error. Table 2 shows the variable levels ature and maintained at that temperature throughout the run.
and the corresponding experimental responses.
Antibacterial agents were not added.
The experiment was randomized to minimize the effects of
The composition analysis showed the following results: fat
unexplained variability in the observed responses due to extra- 25.03%; protein 25.12%; moisture 2.57%; total mesophilic aerobic
neous factors.
bacteria count < 9 ꢃ 103 CFU/g, total coliform count < 0.3 CFU/g,
fecal coliform count < 0.3 CFU/g, and yeast and mold count < 10
CFU/g. A fixed amount of CaCl2 (3.6 mM) (Cicarelli, Santa Fe, Ar-
gentina) was added to every 2 L assay sample and the milk sam-
ples were kept at their corresponding coagulation temperature in
a 30 L thermostatic bath (Haake F2-C, Germany), accuracy ꢄ 0.1
ꢁC. Once the desired temperature was reached, the different pH
levels were adjusted with 85% concentrated Lactic acid
(Mallinckrodt, Chemical Works, Argentina) and 40% NaOH
(Cicarelli, Santa Fe, Argentina). An Orion Research EA 940 pH-
meter, equipped with special electrodes adequate to protein-fat
solutions (accuracy ꢄ 0.01 pH units) and regulated with 2 buffer
solutions (Anedra, San Fernando, Buenos Aires, Argentina) at pH
4.00 and 7.00 respectively, was used for this purpose. When
checking the drift of pH after renneting, it had not exceeded 0.02
units. An auto-heating sensor of 99 % platinum hot wire (Aldrich
Chemical Company, Inc. Milwaukee. Wis., U.S.A.) (0.10 mm di-
ameter, 110 mm long) was used to measure coagulation time and
monitor curd processing. It was simple and did not disturb the
gel structure. Its commercial application for monitoring cheese
coagulation, and for determining cutting time have been studied
by Hori (1985). The platinum wire sensor, the Teflon holder, and
the software necessary to process the information were devel-
oped by the research team, according to Hori´s hot wire method
(Hori, 1985). This measurement method was chosen for its non-
destructive properties along with its objective measurement ca-
pacity and low cost. The platinum sensor, supported by a Teflon
holder, was immersed axially in the 2.0 L milk samples and heat-
ed with constant direct current of 500.00 mA. The voltage output
between the platinum wire terminals was monitored automati-
cally at 5 s regular intervals and measured with a 6.5 digit resolu-
tion digital multimeter (Model 2000, Test Instrumentation
Statistical analysis
The Statgraphics (Version 7.1 1994) software program was
used in order to fit the 2nd order model and generate the re-
sponse surface models. The model proposed for each response
was:
3
3
3
Y= bo + ꢂ bn xn + ꢂ b3nn xn2 + ꢂ bnm xn3 xm
n=1
n=1
n ꢀ m=1
where bo is the value of the fitted response in the central design
(0, 0, 0) and bn, bnn, and bnm the linear, quadratic, and cross-
product regression terms, respectively. The analysis of the re-
gression was done using the experimental design model (Stat-
graphics 1994). Tests to verify that the residues satisfied the
assumptions of normality, independence and randomness, were
carried out (Montgomery 1991).
Due to the significant lack of fit of the original model at 1%,
the experimental data, togetherwith the appropriate procedure,
were used to convert Y3 to Log Y3.
Coagulation assay
Milk substrate was prepared by dissolving 120 g low heat
whole dry milk in 1 L of distilled and deionized water (GT-Lab,
Rosario, Argentina) at 40 ꢁC. It was then covered with parafilm to
avoid bacterial contamination, stirred for 15 min and warmed at
65 ꢁC for 30 min. Substrate solutions were kept refrigerated for 2
h to allow time for complete hydration. Low heat whole milk pow-
der (WPNI > 6.0 provided by SanCor (SanCor Cooperativas, San-
ta Fe, Argentina) was preserved under vacuum, in the darkness,
at a temperature <10 ꢁC. Thirty minutes prior to each experi-
1098 JOURNAL OF FOOD SCIENCE—Vol. 67, Nr. 3, 2002

Optimizing conditions for milk coagulaton . . .
Table 3—ANOVA for the fitted models
Y1
Y2
ss
Y3
ss
Source
df
ss
F
df
F
df
F
x1
x2
x3
x1 x2
1
1
1
1
1
1
1
1
1
191118.4
88268.9
181447.8
9591.1
258840.1
15576.1
133084.0
1224110.0
153305.0
410321.4
57114.7
10.04*
4.64
9.53*
0.50
13.60*
0.82
6.99
64.30**
8.05
4.31
1
1
1
1
1
1
1
1
1
722.15077
55.87885
39.90463
38.28020
0.42023
290.47**
22.48*
16.05*
15.40*
0.17
0.20
142.23*
7.41
1
1
1
1
1
1
1
1
1
0.8547412
0.28145442
0.0076533
0.0001120
0.0002236
0.0000751
0.0954062
0.0003847
0.0072827
0.0357343
0.0003865
1.27876195
0.971771
2211.53**
728.23**
19.80*
0.29
0.58
0.19
246.85**
1.00
18.84*
18.08*
x1 x3
x22x3
0.49992
x12
353.60664
18.41900
0.88087
28.06543
2.48614
1368.75878
0.89203
16.704 %
3.039171
x22
x3
0.35
11.29*
Lack-of-Fit
Pure Error
Total
5
3
17
8
3
17
9
3
17
28831190
0.837875
5.556 %
170.92261
R2
CV (%)
Estimate dev.
5.127 %
0.047498
16
16
16
* Significant at the 5 % level
** Significant at the 1 % level
Y
: Maximum voltage Y : maximum voltage time Y : Log of
1
2
3
Group, Keithley Instruments, Inc. Cleveland, Ohio, U.S.A.) con- showed a significant lack of fit at 5% level, a high R2, and a rela-
nected directly to an IBM Desk-top computer specially designed tively high CV (16.7%). This may be attributed to difficulties in
for this kind of experiment. The electric current was supplied by obtaining a representative time by the software. The CV indicat-
a 6177C 0 to 50 V, 0 to 500 mA power supply device (Hewlett Pack- ed that the reproducibility of time measurements was less than
ard, (Santa Clara, Calif., U.S.A.) with 0.03% resolution. Once the 90%.
sensor was set, it was left sitting for 30 min before each assay in
Model Y3 exhibited non-significant lack of fit at 1% level and
order to allow the milk to reach the selected temperature. One satisfied the assumptions of normality, independence, and ran-
gram of enzyme (code 1010914, Chymogen 2080, Chr. Hansen, domness, being for this reason accepted.
Horsholm. Denmark,) was diluted, according to the instructions,
Maximum voltage
with 0.01 M sodium citrate (Cicarelli, Santa Fe, Argentina) buffer
at pH 6.0 and maintained below 5 ꢁC for the duration of each ex-
periment. One rennet units (R.U.) was defined as the enzyme ac-
tivity that coagulates 10 mL of reconstituted low-skim milk pow-
der (12% in 10 mM aqueous CaCl2, pH 6.5) at 30 ꢁC in 100 s
(Berridge, 1952). Two liters of milk was then coagulated with the
corresponding rennet amount, according to the design (0.0048,
0.015, 0,030, 0.045, and 0.055 R.U./ mL milk). Enzyme solutions
were adjusted for adding 1.5 ml/L milk.
In order to verify the goodness of fit, a regression analysis was
done through ANOVA. For each model, every term found signifi-
cant by the ANOVA was included. The model obtained according
to the maximum voltage (Y1) was:
Y1 = 2835 – 118.3 x1 – 80.4 x2 + 115.3 x3 + 34.6 x1.x2 – 179.8 x1.x3 +
44.1 x2.x3 – 102.6 x12 + 311 x22 + 110 x3 .
2
After verifying that the wire reached a stationary heat dissipa-
tion level, the enzyme was added and the starting time of the as-
say recorded. The voltage output through the wire was recorded at
the beginning, before enzyme addition, and throughout the ex-
periment, varying from 0 to 5000 ꢀV during the complete assay.
The tangent to the inflexion point on the voltage output against
time plot provided the coagulation time Y3 (Figure 1). The maxi-
mum voltage y1 represents the highest value of the coagulation
curve with almost null slope and y2 is the time necessary to reach
the maximum voltage calculated through a mathematic algorithm.
Results and Discussion
HE RESULTS OF ANOVA FOR THE FITTED MODEL ARE SHOWN IN TA-
T
ble 3. According to the F-test, Y1, Y2, and Y3 were significant at
1% confidence level. The models exhibited non-significant lack
of fit at 1% confidence level. The coefficient of variation (CV) -
the ratio of the standard error of the estimate to the mean value
response expressed as a percentage - is a measure of the repro-
ducibility of the models. The 3 models may represent the data
and could be used to generate surface contour plots for optimiza-
tion. Models Y1 and Y3 are reasonably reproducible because their
CVs are not greater than 10%: 83.78% of the variability was ac-
counted for by model Y1 and 97.17% by model Y3. Model Y2
Figure 1 — Illustrative relationship between mV of the hot
wire and time during rennet treatment of milk.
Vol. 67, Nr. 3, 2002—JOURNAL OF FOOD SCIENCE 1099

Optimizing conditions for milk coagulaton . . .
The model was significant at 1% level (F test). The determina- The response decreased when the variable levels were modified
tion coefficient (R2 = 0.8378) was satisfactory, having a low experi- from –1 to +1. The positive slope 115.3 and the other effects on
mental error according to ANOVA (Table 3). The enzyme concen- the interaction and quadratic terms indicated a maximum volt-
tration, pH and temperature had a significant effect (p < 0.05) at age increase with increasing temperature. Noël and others
the maximum voltage. The enzyme concentration-temperature (1991), on combined enzymatic and lactic milk coagulation using
interaction term (x1.x3) and the quadratic terms (x2 and x3) of the a multifactorial experimental design, showed that renneting pH
2nd order model also had a significant effect (p < 0.01). The neg- has an important effect on the curd stress or firmness.
ative slopes 118.3 and 80.4 that directly affect the enzymatic con-
For the contour plots, pH and enzyme concentration were se-
centration and pH, respectively, show that when both variable lected for the vertical and horizontal axes, respectively.
levels increased, the response maximum voltage (Y1) decreased.
As explained before, the range –1, +1 was selected as working
area to follow the cheese-maker practices, which sets the level
variables close to the central values of the existing design. The
gradient method (Statgraphics 1994) and the calculations of the
intersection result in a maximum voltage of 3211 ꢀV, under the
following conditions: x1 = 0.021 R.U./mL milk, x2 = 6.51, and x3 =
37.7 ꢁC, and a minimum of 2786 ꢀV for: x1 = 0.0345 R.U./mL milk,
x2 = 6.61, and x3 = 34.6 ꢁC. Figure 2 (a) represents the maximum
voltage contours at 35 ꢁC in a pH compared against enzymatic
concentration graph. The marked area shows the zone where the
cheese-maker achieves the maximum and minimum voltage of
the curd.
(a)
The dT – current temperature of the wire as related to the ini-
tial temperature - measurements with the present method char-
acterize the kinematic viscosity behavior of the coagulating
milks, the relative kinematic viscosity increasing 9 times com-
pared to the initial value when the curd of whole milk sample
reached the empirical required firmness (Hori 1985). Unlike
Hori, in this experiment voltage output was measured instead of
calculating dT. Assuming that maximum voltage corresponds to
maximum firmness, and considering that a constant amount of
CaCl2 (0.02%) was added in this experiment, the maximum volt-
age value was obtained with a relatively low rennet concentra-
tion (0.021 R.U./ mL milk) along with a pH slightly lower than the
original one (pH: 6.51). Obviously, more research is required in
order to relate these findings to the reference method.
In the cheese-making process it is important to know the max-
imum firmness developed, because yield and quality are con-
(b)
(c)
Figure 2 — (a) Contour plot for maximum curd voltage (Y1),
T = 35°C. The marked area represents 2786
Y
3211
µV. (b) Time at maximum voltage (Y2), T = 35 °C. The 1marked
area represents 10.51
Y
21.79 min. (c) Coagulation time
(Y3), T = 35 °C . The ma2rked area represents 3.69 Y3
13.81 min.
1100 JOURNAL OF FOOD SCIENCE—Vol. 67, Nr. 3, 2002

Optimizing conditions for milk coagulaton . . .
nected to the cutting time for some cheese varieties (Bynum and concentration and pH, respectively, show that as the enzymatic
Olson 1982; Hori 1985). Cutting too early results in fat losses concentration increases, CT decreases, and as the pH moves
(Ridell-Lawrence and Hicks 1988), while cutting too late, after from 6.4 to 6.8, CT increases. Through the gradient analysis and
maximum firmness is reached, results in whey retention (Van the calculation of the intersections of the variables x1, x2, x3, used
Slyke and Price 1952; Wilson and Reinbold 1965).
at the same level as the cheese-maker, the maximum CT (13.89
The maximum firmness is more important than CT due to its min) was obtained with the following variable levels: x1 = 0.0185
influence on yield and cheese quality. Bynum and Olson (1982), R.U./mL milk, x2 = 6.64, and x3 = 34.8 ꢁC and the minimum CT
Garnot and others (1982), Hori (1985), Okigbo and others (1985b) (3.69 min) for x1= 0.045 R.U./mL milk, x2 = 6.52, and x3 = 35.3 ꢁC.
and others agree with the fact that obtaining a suitable firmness
When the surface contours are represented by pH against en-
without changing the milk pH can be achieved by adding a high zymatic concentration between the range +1 and –1, at a con-
concentration of rennet as well as CaCl2.
stant temperature of 35 ꢁC, the marked area in Figure 2 (c) repre-
sents the area where the maximum and the minimum
coagulation time would be obtained. A significant variation of CT
(3.69 to 13.89 min) can be observed for a pH range between 6.52
and 6.64, when the enzymatic concentration varies between
0.018 and 0.045 R.U./mL milk.
Time of maximum voltage
The obtained model corresponding to the time necessary to
reach the maximum voltage was significant (p < 0.01) according
to the F test. The ANOVA shows an effect for every variable. The
resulting model corresponds to:
It has been shown that the Nametre (Edison, N.J., U.S.A.) vis-
cometer and the hot wire method were more sensitive in measur-
ing the coagulation time as compared to the Formagraph
(Hellerup, Denmark) and rigidity modulus monitor (Sharma and
others 1992). Okigbo and others (1985b), using a Formagraph,
(Hellerup, Denmark) showed that high chymosin content pro-
duced a greater decrease in CT at high rather than at low milk
pH. Storry and Ford (1982), using an Instron Universal Testing
Instrument, (Canton, Mass., U.S.A.) showed that rennet CT de-
creased with a lower pH, higher temperature, and higher rennet
concentration. Recently, Noël and others (1991), in a multifacto-
rial study of combined enzymatic and lactic milk coagulation
measured by viscoelasticity concluded, in accordance with our
studies, that over a limited temperature variation (32 to 34 ꢁC),
temperature effect had little significance, while pH had an im-
portant effect on all the parameters. Hori (1985), using the same
method, proved that the enzymatic concentration effect on CT
decreased as the acidity increased. He also showed that, for non-
fat milk samples, CT decreased with increased enzymatic con-
Y2 = 13.07 – 7.27 x1 + 2.02 x2 – 1.71 ꢃ 3 – 2.19 x1.x2 – 0.23 x1.x3 – 0.25
2
x2.x3 + 5.29 x12 + 1.21 x2 2 + 0.26 x3
The determination coefficient R2 = 0.89203 was satisfactory,
with a low experimental error. The highest coefficients are those
corresponding to x1, x2, x3, x1.x2, x12, and x22, which coincides with
ANOVA. The quadratic term (x1) and the enzyme concentration-
pH interaction (x1.x2) also had a significant effect (p < 0.05). From
this information, it can be concluded that the enzymatic concen-
tration shows the highest influence. The negative slope 7.27
shows that as the concentration decreases, the time where the
maximum voltage is obtained increases. Under these conditions,
the variables pH and T had a lower influence. It was observed
that the positive slope of 2.02 shows an increment of time when
the pH rises. Furthermore, as temperature increases, the time it
takes voltage to reach the maximum value decreases.
As was done for model Y1, we calculated in the range –1 to +1
that the maximum time (21.79 min) at which the maximum volt-
age was obtained met the following conditions: x1 = 0.019 R.U./
mL milk, x2 = 6.62, and x3 = 34.5 ꢁC and the minimum time (10.51
min), with x1 = 0.040 R.U./mL milk, x2 = 6.58, and x3 = 35.5 ꢁC.
Figure 2 (b) shows the surface contours where the pH against
enzymatic concentration is represented while the temperature is
kept constant at the central value (35 ꢁC). The gradient method
and the calculation of the intersections of the variables resulted
in the marked area, which includes the minimum and the maxi-
mum time of maximum voltage. Another important fact to con-
sider to set the cutting time is the exact time the maximum volt-
age is reached, as the cheese-maker will have precise elements to
achieve the maximum yield without altering the final quality of
cheese.
Coagulation time
All the factors and the interactions were processed with the
purpose of analyzing the response Y3. Through this analysis, a
model with a non-significant lack of fit at 1% was obtained, ac-
cording to the F test. However, log Y3 - obtained by a mathemati-
cal transformation of the variable - was used instead due to its
better fit.
Log Y3 = 0.8381 – 0.2502 x1 + 0.1435 x2 – 0.0237 ꢃ 3 – 0.0037 x1x2
2
+ 0.0053 x1x3 + 0.0031x2x3 + 0.0868 x12 + 0.0055 x22 + 0.0239 x3 .
The highest coefficients correspond to x1, x2, and x12. As can be
observed, there is little influence on the temperature. The slopes
–0.2502 and 0.1435, which have a direct influence on enzymatic
Figure 3 — Overlap area of superimposing Figure 2(a), 2(b),
and 2(c). Shaded area represents the area that satisfies
the 3 conditions, range of CT, maximum voltage and the
time at maximum voltage
Vol. 67, Nr. 3, 2002—JOURNAL OF FOOD SCIENCE 1101

Optimizing conditions for milk coagulaton . . .
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Gunasekaran S, Chyung AY. 1994. Evaluation of milk coagulation with ultrason-
ics. Food Tech 48(12):74-78.
Hicks CL, Milton K, Payne FA. 1990. Effect of enzyme concentration, temperature
and pH on the diffuse reflectance of coagulating. J Dairy Sci 73:(suppl.1):D22.
Hori, T. 1985. Objective Measurements of the Process of Curd Formation during
Rennet Treatment of Milks by the Hot Wire Method. J Food Sci 50:911-917.
Jen JJ, Ashworth US. 1970. Factors influencing the curd tension of rennet coag-
ulated milk. Salt balance. J Dairy Sci 53:1201-1208.
centration, acidity, and temperature, concluding that the milk
pH, which must be under strict control, should be the main factor
in cheese manufacture.
Since the results of the gradient method over the variable x3
were acceptable for the 3 responses, the conclusion can be
reached that optimum conditions should be met with a tempera-
ture close to 35 ꢁC.
In search of the appropriate variable level for cheese industry
to improve its production efficiency, the models used also seem
to be useful for pH, enzymatic concentration, and temperature
optimization when the concern focuses on the maximum voltage
that can be obtained and at which specific time.
The area that satisfies the 3 conditions (range of CT, maxi-
mum voltage, and the time at which this 1 is reached) is obtained
by superimposing the contour plots belonging to Figure 2 (a), 2
(b), and 2 (c) for the different responses y1, y2, and y3. From the
resulting area (Figure 3), we can get the optimum conditions to
Kovolczuk J, Maubois JL. 1988. Effect of pH, calcium concentration and temper-
ature on the evolution of refractometric signal produced during rennet coag-
ulation of milk. J. Dairy Res 55:81-88.
Kowalchyk AW, Olson NF. 1977. Effects of pH and temperature on the secondary
phase of milk clotting by rennet. J Dairy Sci 60:1256-1259.
Laporte MF, Martel R, Paquin P. 1998. The Near-infrared Optic Probe for Moni-
toring Rennet Coagulation in Cow´s Milk. Int Dairy Journal 8:659-666.
obtain Y1 = 2854 ꢄ 171 ꢀV; Y2 = 14.18 ꢄ 3.04 min, and Y3 = 7.26 ꢄ Marshall RJ. 1982. An improved method for measurement of the syneresis of
curd formed by rennet action on milk. J Dairy Res 49:329-336.
1.12 min. An enzymatic concentration of 0.028 R.U./mL milk, a
McMahon DJ, Brown RJ. 1982. Evaluation of Formagraph for composing rennet
solutions. J Dairy Sci 65:1639-1642.
pH of 6.60 and a temperature of 35 ꢁC could thus be taken as an
average optimum working conditions. A verification experiment
at the optimum conditions, consisting of 8 runs, was performed,
the results being: Y1 = 3101 ꢄ 136 ꢀV; Y2 = 15.39 ꢄ 0.57 min, and Y3
= 8.11 ꢄ 0.65 min. By using the T-student test, the difference for
the 3 responses showed to be non-significant at the 1% level.
McMahon DJ, Brown RJ, Richardson GH, Ernstrom CA. 1984. Effects of calcium
phosphate and bulk culture media on milk coagulation properties. J Dairy Sci
67:930-939.
Montgomery DC. 1991. Diseño y Análisis de experimentos. Editorial Iberoamer-
icana. Mexico.
Myers RH and Montgomery DC. 1995. Response Surface Methodology Process
and Product Optimization Using Designs Experiments. Wiley series inc. Prob-
ability and Statistics
Noël Y, Durier C, Lehembre N, Kohilinsky A. 1991. Étude multifactorielle de la
coagulation mixte du lait analysée par viscoélasticimétrie. Lait 71:15-39.
Okigbo LM, Richardson GH, Brown RJ, Ernstrom CA. 1985 (a). Effects of pH, cal-
cium chloride and chymosin concentration on coagulation properties of ab-
normal and normal milk. J Dairy Sci 68:2527-2533.
Okigbo LM, Richardson GH, Ernstrom CA. 1985 (b). Interactions of Calcium, pH,
Temperature, and Chymosin During milk coagulation. J Dairy Sci 68:3135-
3142.
Conclusion
HE OBJECTIVE AND NON-DESTRUCTIVE MEASUREMENT OF ENZYMAT-
T
ic coagulation through the hot wire method proved to be sim-
ple and practical. The response surface represents a useful tech-
nique in the difficult process of variable study.
Ridell-Lawrence LS, Hicks CL. 1988. Effect of curd healing time on stirred curd
cheese yield . J Dairy Sci 71:2611-2617.
The mathematical models, which relate the responses
achieved regarding enzymatic concentration, pH, and tempera-
ture, allow the cheese-maker to make improvements over his
field of work.
Optimum conditions found for pH and enzymatic concentra-
tion, keeping the temperature constant at 35 ꢁC, were 6.60 and
0.028 R.U./mL milk, respectively. Under these conditions, the
addition of coagulant enzymes provided by genetic engineering
can make whole milk clot in 7.26 min, getting the maximum volt-
age of 2854 ꢀV in 14.2 min. In this way, by knowing the treatment
to be applied to each type of cheese, the cheese-maker could de-
termine the cutting time with more certainty.
Sbodio OA, Tercero EJ, Coutaz VR, Luna JA, Martinez E. 1997. Simultaneous inter-
action of pH, CaCl2 addition, temperature, and enzyme concentration on milk
coagulation properties. Food Science and Tech Intl 3:291-298.
Sharma SK, Hill AR, Mittal GS. 1992. Evaluation of methods to measure coagula-
tion time of ultrafiltered milk. Milchwissenschaft 47(11):701-704.
Statgraphics plus version 7.1. 1994. Users guide reference. Statistical graphics.
(Statistical Graphics Corp., Manguistics Inc., Mexico, DF. P 63-73.
Storry EJ, Ford GD. 1982. Some factors affecting the post clotting development of
coagulum strength in renneted milk. J Dairy Res 49:469-477.
Thomasow J, Voss E. 1977. Methods for the determination of firmness of milk
coagulum. IDF Annual Bulletin, Document 99:1-5. Brussles: IDF.
Ustunol Z, Hicks CL, Payne FA. 1991. Diffuse reflectance profiles of eight milk
clotting enzyme preparations. J Food Sci 56:411-415.
Van Slyke LL, Price WV. 1952. Cheese. New York: Orange Judd Publishing Compa-
ny. P.58.
Wilson HL, Reinbold GW. 1965. Long-hold Cheddar cheese. In American Cheese
Varieties. New York: Pfizer and Co. p. 22.
References
MS20010201 Submitted 4/25/01, Accepted 11/10/01, Received 11/10/01
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The authors are at Instituto de Tecnología de Alimentos Facultad de Ingeniería
Química - Universidad Nacional del Litoral C.C. 266 - 3000 Santa Fe, Ar-
gentina. Direct inquiries to author Sbodio (E-mail: sbodio@fiqus.unl.edu.ar
Banon S, Hardy J. 1991. Study of acid milk coagulation by an optical method
using light reflection. J Dairy Res. 58:75-84.
Bynum DG, Olson NF. 1982. Influence of curd firmness at cutting on cheddar
1102 JOURNAL OF FOOD SCIENCE—Vol. 67, Nr. 3, 2002