Moscow, Moscow, Russian Federation
Moscow, Moscow, Russian Federation
Moscow, Moscow, Russian Federation
Sweetened condensed milk is a popular food in various climatic zones, including those regions where average winter temperature falls below –30°C. Such low temperatures can trigger crystallization because they disrupt the native structure of biopolymers. These processes spoil the quality of sweetened condensed milk. However, no scientific publications feature the cryoscopic temperature of sweet condensed milk or systematize the data on its low-temperature storage. Sugar, sugar-milk, and milk solutions of various concentrations were frozen to determine their cryoscopic temperature by the thermographic method using a Testo 176T4 meter (Germany) with K-type probes (NiCr-Ni) at –78.5°C. The phase transitions were studied using a Mettler Toledo DCS 822e DSC analyzer. The nucleation temperature, the cryoscopic temperature, and the subcooling degree depended on the concentration and the type of the solute. For sugar solutions, the cryoscopic temperature varied from –0.4 ± 0.1 to –6.4 ± 0.1°C; for sugar-milk solutions, it ranged from –2.1 ± 0.1 to –10.9 ± 0.1°C; for whole milk solutions, it was from –0.4 ± 0.1 to –4.6 ± 0.1°C. The thermographic method failed to obtain the phase transition and the cryoscopic temperature in analogue models of sweetened condensed milk. The loss of fluidity was about –30°C when the storage time exceeded 2 h. This effect was comparable to 54 min of storage at –35°C. The differential scanning calorimetry meth od showed that the phase transition occurred at –80°C. This research opens new prospects for differential scanning calorimetry studies of phase transitions in condensed sweetened dairy products.
Sweetened condensed milk, cryoscopic temperature, freezing, loss of fluidity, storage
Introduction
Sweetened condensed milk is a strategic high-energy
food product because it is rich in milk and sucrose [1–6].
It is especially popular in the Business-to-Consumer
segment and highly applicable in the daily diet. Its
use patterns in the industrial sector are also extremely
diversified, the main consumers being the confectionery
industry and the ice-cream production [7–13]. Sweetened
condensed milk has a high nutritional value and a long
shelf life, which explains why this product has become
an integral part of the state food reserve, humanitarian
aid, dry rations, etc. [4, 7, 11]. Regions with no dairy
farming of their own are stable consumers of sweetened
condensed milk. The indigenous peoples of the Russian
Arctic are known to depend on sweetened condensed
milk because they have to eat a lot of high-carbohydrate
foods [6]. The air temperature in the region can fall much
below –40°C. As a result, consumers cannot but violate
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the recommended storage conditions of 0–10°C. However,
industry experts put stress on the universality of the
use of sweetened dairy products, regardless of climatic
conditions and geographical location, which explains
the relevance of research on their low-temperature
storage.
Our review of scientific and technical publications
revealed no systematic data on the freezing point of
sweetened condensed milk and its subsequent storage at
freezing temperatures [14–19]. The only publication that
mentioned low-temperature storage of condensed milk
was that by Pavlova, where the cryoscopic temperature
of fresh sweetened condensed milk ranged from –26
to –29°C [14]. When the product reaches the cryoscopic
temperature, moisture begins to crystallize. The resulting
crystals of various shapes can trigger the abiogenic
degradation of macrocomponents, which implies a
decrease in storage stability [20–23]. Low storage
temperature also reduces the rate of biochemical reactions.
In theory, the freezing process for simple solutions
means that the stability of one phase ends at a certain
point that corresponds to a particular set of system
variables. In practice, point phase transitions are
abstractions that imply infinite ideal and defect-free
systems [24]. In real systems, they are a priori blurred.
The diffusion dilemma consists in determining the range
of characteristic values. In some cases, this diffusion can
be so weak that the point phase transition stops being
an abstraction. In other cases, the phase transition can
be so blurred that its limits are impossible to determine.
Therefore, no boundary exists between phase transitions
of the first and second levels. For instance, point phase
transition can be determined for the system of water –
extra pure sucrose but not for the system of water – food
grade sucrose – milk powder, for which the probability
of a point phase transition vanishes as the concentration
of the components increases.
The present research objective was to analyze the
change in the aggregate state of analogue models of
sweetened condensed milk in the temperature range
from +20 to –50°C and to determine its cryoscopic
temperature.
Study objects and methods
The research was conducted at the Laboratory of
Canned Dairy Products of the All-Russian Dairy Research
Institute.
The study featured sugar, sugar-milk, and milk
solutions of various concentrations, whole milk powder,
Table 1. Formulation of sugar-milk solutions
Таблица 1. Рецептурный состав сахарно-молочных растворов
Component Variants of solution models
Sucrose solution
А1 А2 А3 А4
Sugar, g 15.0 30.0 45.0 68.0
Distilled water, g 85.0 70.0 55.0 32.0
Sugar-milk solution
В1 В2 В3 В4
Whole milk powder, g 28,5
Distilled water, g 85.0 70.0 55.0 32.0
Sugar, g 15.0 30.0 45.0 68.0
Solids, % 33.9 45.5 57.2 75.1
Whole milk solution
С1 С2 С3 С4
Whole milk powder, g 12.5 25.0 37.5 50.0
Distilled water, g 87.5 75.0 62.5 50.0
Figure 1. Experimental stand for determining the
cryoscopic temperature
Рисунок 1. Экспериментальный стенд для определения
криоскопической температуры
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Рябова А. Е. [и др.] Техника и технология пищевых производств. 2022. Т. 52. № 3. С. 526–535
and commercial samples of sweetened condensed milk
(State Standard 31688).
The sugar solutions had a concentration of 15, 30, 45,
and 68%, while the milk solutions had a concentration
of 12.5, 25, 37.5, and 50%. They were prepared by
dissolving a certain mass of sucrose and whole milk
powder in a given amount of water at 25 and 40°C,
respectively. The calculations ignored the moisture
content in the powder.
To assess the effect of the milk solid concentration
on freezing and defrosting, the sugar-milk solutions
were obtained by restoring the whole milk powder at
40°C for 20 min, followed by adding sugar according to
State Standard 33222-2015 (Table 1). The whole milk
powder was produced according to State Standard 33629-
2015: 96.46% solids, 26% fat, 26% protein, solubility
index = 0.1 mL of crude residue. The low saturation of
the solution was maintained by the controlled mixing
rate of 27 min–1 during the dissolution process.
All the solution samples weighed 35 g. They were
poured into plastic flasks and sealed hermetically with
lids with integrated temperature probes (Fig. 1).
The solutions were frozen in a low-temperature
laboratory freezer Vestfrort VT 327 (Denmark)
at –50 ± 1°C. Solid carbon dioxide in thermally insulated
containers made it possible to obtain temperatures as low
as –78.5 ± 0.5°C. The temperature was recorded every
second using a combined Testo 176T4 meter (Germany).
The device had four waterproof food probes made of
K-type stainless steel (NiCr-Ni) with boundary values
from –60 to –400°C. The samples were stored at the
specified temperature. After they were taken out of the
freezer, they thawed at 22 ± 1°C. Instrument readings
and data export to Microsoft Excel for analysis and
visualization were processed using the Testo-ComSoft
Basic software.
The cryoscopic temperature was determined
thermographically based the temperature curve
plateau [25].
The fluidity of sweetened condensed milk analogue
models was determined by freezing, followed by
retrievability and visual assessment of the probes
at –25 ... –50°C under refrigerator conditions.
The thawing kinetics of the analogue models was
studied using a DSC822e Mettler Toledo differential
scanning calorimeter under conditions of dynamic heating
at a constant rate (https://www.mt.com). The results
were processed using the STARe software.
Results and discussion
We divided the freezing process into three successive
stages to ensure the terminological uniformity (Fig. 2):
– pre-freezing stage: the period of time between the start
of freezing and the cryoscopic temperature (freezing
point). At this stage, the system is supercooled to the
nucleation temperature to trigger the nucleation of
ice crystals. The release of latent crystallization heat
corresponds to the start of the thermostatic plateau;
– freezing stage: the temperature at the considered area of
the product is almost constant because the heat removal
makes a large amount of water turn into ice, i.e., phase
transformation;
– decline to storage temperature: most of the water has
frozen, and the temperature decreases to the required
end temperature [26].
At the first stage, we determined how the time of
rational low-temperature storage of solutions affected
their aggregation state. The main criterion for determining
the exposure time in the dynamic temperature – time –
concentration system was to register all the stages of
the freezing process. Figure 3 shows the data for sugar
Figure 2. Freezing process
Рисунок 2. Схематическое представление процесса замораживания
Temperature, ℃
Time, min
Pre-freezing
stage
Decline t Freezing stage o storage temperature
Nucleation
temperature
Subcooling
degree
Cryoscopic
temperature
Thermostatic
plateau
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solutions. Milk and sugar-milk solutions underwent
the same procedure.
The onset of moisture crystallization process
correlated with the temperature of the system: for 5%
sucrose, the crystallization temperature was 0°C; for 45%
sucrose, it was –9.9°C. Also, it was inversely dependent
on the concentration of solids. The crystallization
time decreased in proportion to the concentration of
sucrose: for 5% sucrose, it was 39 min 14 s; for 45%
sucrose, it lasted 6 min 40 s. However, no change in
the aggregate state of the system was recorded as the
sucrose concentration reached 68%. This effect was
probably associated with the concentration features of
the system, or inability to reach the critical temperature
at which the phase transition occurs. Thus, it took the
system four hours to stabilize completely and for the
temperature of the solutions to reach that of the external
environment.
Table 2 shows the values of the obtained criteria
that describe the process of freezing sugar, sugar-milk,
and milk solutions.
Models A4 and B4 were analogues of sweetened
condensed milk with sugar. They demonstrated no liquidsolid
phase transition. However, a visual inspection
revealed a change in the transparency of the solutions.
All the samples had a firm texture, typical of frozen foods.
The nucleation temperature, the cryoscopic temperature,
and the subcooling degree directly depended on the
concentration and the type of the solute. The dairy
component had a strong impact on these indicators. The
freezing time and the phase transition period declined
as the concentration increased.
Table 2. Moisture crystallization criteria in sugar, sugar-milk, and milk solutions.
Таблица 2. Критерии кристаллизации влаги в сахарных, сахарно-молочных и молочных растворах
Variants
of solution models
Indicator
Nucleation
temperature, °С
Cryoscopic
temperature, °С
Subcooling degree Freezing time, s Point phase transition, s
А1 –1.4 ± 0.1 –0.4 ± 0.1 1.0 2827 2922
А2 –5.3 ± 0.1 –2.2 ± 0.1 3.0 2308 2500
А3 –9.9 ± 0.1 –6.4 ± 0.1 3.5 1570 1885
А4 – – – – –
В1 –2.1 ± 0.1 –2.1 ± 0.1 0 2224 2224
В2 –5.0 ± 0.1 –5.0 ± 0.1 0.9 1579 1927
В3 –10.9 ± 0.1 –10.9 ± 0.1 1.3 1276 1635
В4 – – – – –
С1 –0.4 ± 0.1 –0.4 ± 0.1 0 2730 2730
С2 –1.2 ± 0.1 –1.2 ± 0.1 0 2850 2850
С3 –2.6 ± 0.1 –2.6 ± 0.1 0 2280 2280
С4 –4.6 ± 0.1 –4.6 ± 0.1 0 1740 1740
Figure 3. Thermograms of sugar solutions at various concentrations
Рисунок 3. Термограммы сахарных растворов различной концентраци и
–52
–39
–26
–13
0
13
Temperature, ℃
Time, hh:mm:ss
5% 10% 15% 20% 30% 45% 68%
–52
–39
–26
–13
0
13
Temperature, ℃
Time, hh:mm:ss
5% 10% 15% 20% 30% 45% 68%
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Рябова А. Е. [и др.] Техника и технология пищевых производств. 2022. Т. 52. № 3. С. 526–535
Figure 6. Freezing and defrosting curves for milk solutions at various concentrations
Рисунок 6. Типовые кривые замерзания и размораживания молочных растворов различной концентрации
Figure 5. Freezing and defrosting curves for sugar solutions at various concentrations
Рисунок 5. Типовые кривые замерзания и размораживания сахарно-молочных растворов различной
–50
–40
–30
–20
–10
0
10
20
Temperature, ℃
Time, hh:mm:ss
С1 С2 С3 С4
–51
–45
–39
–33
–27
–21
–15
–9
–3
9
3
15
21
Temperature, ℃
Time, hh:mm:cc
В1 В2 В3 В4
–50
–40
–30
–20
–10
0
10
20
Temperature, ℃
Time, hh:mm:ss
С1 С2 С3 С4
–50
–40
–30
20
–10
0
10
20
Temperature, ℃
Time, hh:mm:ss
С1 С2 С3 С4
–50
–40
–30
20
–10
0
10
20
Temperature, ℃
Time, hh:mm:ss
С1 С2 С3 С4
–50
–40
–30
–20
–10
0
10
20
Temperature, ℃
Time, hh:mm:ss
С1 С2 С3 С4
–50
–40
–30
–20
–10
0
10
20
Temperature, ℃
Time, hh:mm:ss
С1 С2 С3 С4
–50
–40
–30
–20
–10
0
10
20
Temperature, ℃
Time, hh:mm:ss
С1 С2 С3 С4
–50
40
30
20
–10
0
10
20
Temperature, ℃
Time, hh:mm:ss
С1 С2 С3 С4
–50
40
30
20
–10
0
10
20
Temperature, ℃
Time, hh:mm:ss
С1 С2 С3 С4
–51
–45
–39
–33
–27
–21
–15
–9
–3
9
3
15
21
Temperature, ℃
Time, hh:mm:cc
В1 В2 В3 В4
–50
–40
–30
–20
–10
0
10
20
Temperature, ℃
Time, hh:mm:ss
С1 С2 С3 С4
21
–51
–45
–39
–33
–27
–21
–15
–9
–3
9
3
15
21
Temperature, ℃
Time, hh:mm:cc
В1 В2 В3 В4
15
9
3
–3
–9
–15
21
–27
–33
–39
–45
–51
Figure 4. Freezing and defrosting curves for sugar solutions at various concentrations
Рисунок 4. Типовые кривые замерзания и размораживания сахарных растворов различной концентрации
–51
–45
–39
–33
–27
–21
–15
–9
–3
9
3
15
21
Temperature, ℃
Time, hh:mm:cc
В1 В2 В3 В4
–50
–40
–30
–20
–10
0
10
20
Temperature, ℃
Time, hh:mm:ss
A1 A2 A3 A4
–50
–40
–20
–10
0
10
20
Temperature, ℃
Time, hh:mm:ss
С1 С2 С3 С4
20
10
0
–10
–20
–30
–40
–50
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Figure 7. Thermograms of analogue models of sweetened condensed milk frozen with solid carbon dioxide
Рисунок 7. Термограммы моделей-аналогов сгущенного молока с сах аром при замораживании твердым диоксидом углерода
–80
–67
–54
–41
–28
–15
0:00:01 0:20:01 0:40:01 1:00:01 1:20:01 1:40:01 2:00:01 2:20:01
Температура, ℃
Время, чч:мм:сс
Air temperature in the chamber
Upper confidence bound
Average analogue model data
Lower confidence bound
–2
–80
–67
–54
–41
–28
–15
0:00:01 0:20:01 0:40:01 1:00:01 1:20:01 1:40:01 2:00:01 2:20:01
Температура, ℃
Время, чч:мм:сс
Air temperature in the chamber
Upper confidence bound
Average analogue model data
Lower confidence bound
–2
–51
–45
–39
–33
–27
–21
–15
–9
–3
9
3
15
21
Temperature, ℃
Time, hh:mm:cc
В1 В2 В3 В4
–50
–40
–30
–20
–10
0
10
20
Temperature, ℃
Time, hh:mm:ss
С1 С2 С3 С4
Figures 3, 4, and 5 visualize the typical freezing
and defrosting curves for sugar, sugar-milk, and milk
solutions, respectively. As the graphs show, when milk
was introduced into the system, it reduced the water
crystallization time, like in sugar solutions. The defrosting
data were particularly remarkable. The phase transition
time during defrosting was 2–2.5 times longer than
during freezing. The defrosting time decreased after
the milk component was introduced into the system,
which resulted in a smoother phase transition. Thus, the
milk component shortened the freezing/defrosting time.
Probably, this phenomenon could be explained by the
extra moisture-binding agents that entered the system, i.e.,
powdered milk components and, in particular, protein.
Models A4 and B4 had a much faster defrosting rate.
As the previous stage revealed no phase transition,
additional studies had to be performed. Solid carbon
dioxide with a temperature of –78.5°C served as a
refrigerant. However, this experiment also demonstrated
no thermostatic plateaus typical for phase transitions
(Fig. 7). The obtained results did not correspond to the
data published by Pavlova in [14]. However, the multiple
repetition of the experiment and the convergence of the
values obtained made it possible to limit the scope of
possible causal relationships to several options:
1. The rate of phase transition in this temperature
range is less than one second. This value corresponds
to the technical parameters of signal recorded by the
device;
2. The technical parameters of the probes generate
errors at the temperature range from –60 to –78.5°C;
3. Phase transitions occur at lower temperatures in
complex polycomponent systems;
4. Diffusion dilemma.
Figure 8. Effect of concentration on cryoscopic temperature
Рисунок 8. Зависимость изменения криоскопической температуры от концентрации растворов
Y2 = –7E–05x3 + 0.0015x2 – 0.0401x
R² = 0.997
Y3 = –4E–05x3 – 0.0011x2 – 0.0061x
R² = 0.9994
Y1 = –8E–06x3 – 0.0015x2 + 0.0098x
R² = 0.9995
–12
–10
–8
–6
–4
–2
0
0 10 30 40 50 60
Temperature, ℃
Concentration of solids, %
20
y = –4E–05x3 –0,0011x2 –0,0061x
R² = 0,9994
y = –7E-05x3 + 0,0015x2 –0,0401x
R² = 0,997
y1 = –8E–06x3 –0.0015x2 +0.0098x
R² = 0.9995
–12
–10
–8
–6
–4
–2
0
0 10 30 40 50 60
Temperature, ℃
Sugar solution (Y1) Milk solution (Y3)
20
Concentration of solids, %
Sugar-milk solution (Y2)
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Figure 8 demonstrates the correlation between the
effect of the concentration of solids on the dynamics of
cryoscopic temperature in the solution. The dependences
were non-linear, with three-power polynomials. Solutions
with ≤ 20% solids showed no significant changes in the
freezing point. Further increase in concentration led to
significant changes related to the nature, concentration,
and possible synergistic effects of the dissolved
components.
Since the thermographic method failed to register
the cryoscopic temperature of the analogue models, we
decided to determine the temperature range when liquid
turns solid. The loss of fluidity depended mostly on the
ambient temperature and the storage time. At –30°C
and ≥ 2 h of storage time, the effect was comparable to
54 min of storage at –35°C (Fig. 9). The appearance of
crystal-like elements and the complete loss of fluidity
under mechanical action were characteristic features
of the structural change in the product. However, all
samples thawed within a few minutes, regardless of
temperature and storage time.
Figure 10 illustrates the differential scanning
calorimetry of a commercial sweetened condensed
milk (State Standard 3168). The solidification occurred
at –82 ... –80°С. The pronounced crystallization and
thawing peaks confirmed the heterogeneity of the system
and the polycrystalline nature of the freezing process.
Conclusion
The research revealed some freezing/defrosting
patterns of sugar, sugar-milk, and milk solutions,
depending on the nature and concentration of the
components dissolved. The cryoscopic temperature
decreased following the increase in the concentration
of solids. In sugar and sugar-milk systems, the freezing
time and the phase transition period decreased as the
concentration characteristics of the system increased.
In whole milk solutions, the freezing time and phase
Figure 10. Differential scanning calorimetry of commercial sweetened condensed milk
Рисунок 10. Дифференциально сканирующая калориметрия промышленного образца сгущенного молока с сахаром
Figure 9. Loss of fluidity after 54 min: a – at –30°С, b – at – 32.5°С, c – at –35°С
Рисунок 9. Визуализация потери текучести исследуемых образцов м оделей аналогов сгущенного молока с сахаром при хранении
в течение 54 мин: a – при –30 °С; b – при –32,5 °С; c – при –35 °С
a b c
–115 –110 –105 –100 –95 –90 –85 –80 –75 –70 –65 –60 –55 –50 –45 –40 –35 –30 –25 –20 –15 –10 –5 °С
–16
–14
–12
–10
–8
–4
–2
0
mW
Lab: Mettler Staree SW 15.00
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transition increased as the concentration rose from
12.5 to 25%. With a further increase in concentration,
they decreased, which was probably due to the
multicomponent composition of the system and the
heat of crystallization. In sweetened condensed milk,
the loss of fluidity occurred at –30°С if the storage
time exceeded 2 h. This result was comparable to a
54-min storage at –35°С. The methods employed failed
to establish the phase transitions in analogue models
of sweetened condensed milk. The research created
prerequisites for a more profound differential scanning
calorimetry of phase transitions in sweetened condensed
dairy products.
Contribution
A.G. Galstyan and A.E. Ryabova developed the
research concept and conducted a formal analysis.
A.G. Galstyan developed the methodology and edited
the manuscript. A.E. Ryabova and V.A. Tolmachev
conducted the experiment and visualized the data.
A.E. Ryabova drafted the manuscript. All the authors
were involved in the study and agreed on the final
version of the manuscript.
Conflict of interest
The authors declare that there is no conflict of interests
regarding the publication of this manuscript.
Критерии авторства
А. Г. Галстян и А. Е. Рябова разработали кон-
цепцию исследования и провели формальный анализ.
А. Г. Галстян разработал методологию, рассмо-
трел и отредактировал рукопись. А. Е. Рябова и
В. А. Толмачев провели эксперимент и визуали-
зировали данные. А. Е. Рябова подготовила чер-
новик рукописи. Все авторы были привлечены к
исследованию, а также ознакомились и согласились
с окончательным вариантом рукописи.
Конфликт интересов
Авторы заявляют об отсутствии конфликта
интересов.
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