IntroductionSweetened condensed milk is a strategic high-energyfood product because it is rich in milk and sucrose [1–6].It is especially popular in the Business-to-Consumersegment and highly applicable in the daily diet. Itsuse patterns in the industrial sector are also extremelydiversified, the main consumers being the confectioneryindustry and the ice-cream production [7–13]. Sweetenedcondensed milk has a high nutritional value and a longshelf life, which explains why this product has becomean integral part of the state food reserve, humanitarianaid, dry rations, etc. [4, 7, 11]. Regions with no dairyfarming of their own are stable consumers of sweetenedcondensed milk. The indigenous peoples of the RussianArctic are known to depend on sweetened condensedmilk because they have to eat a lot of high-carbohydratefoods [6]. The air temperature in the region can fall muchbelow –40°C. As a result, consumers cannot but violate528Ryabova A.E . et al. Food Processing: Techniques and Technology. 2022;52(3):526–535the recommended storage conditions of 0–10°C. However,industry experts put stress on the universality of theuse of sweetened dairy products, regardless of climaticconditions and geographical location, which explainsthe relevance of research on their low-temperaturestorage.Our review of scientific and technical publicationsrevealed no systematic data on the freezing point ofsweetened condensed milk and its subsequent storage atfreezing temperatures [14–19]. The only publication thatmentioned low-temperature storage of condensed milkwas that by Pavlova, where the cryoscopic temperatureof fresh sweetened condensed milk ranged from –26to –29°C [14]. When the product reaches the cryoscopictemperature, moisture begins to crystallize. The resultingcrystals of various shapes can trigger the abiogenicdegradation of macrocomponents, which implies adecrease in storage stability [20–23]. Low storagetemperature also reduces the rate of biochemical reactions.In theory, the freezing process for simple solutionsmeans that the stability of one phase ends at a certainpoint that corresponds to a particular set of systemvariables. In practice, point phase transitions areabstractions that imply infinite ideal and defect-freesystems [24]. In real systems, they are a priori blurred.The diffusion dilemma consists in determining the rangeof characteristic values. In some cases, this diffusion canbe so weak that the point phase transition stops beingan abstraction. In other cases, the phase transition canbe so blurred that its limits are impossible to determine.Therefore, no boundary exists between phase transitionsof the first and second levels. For instance, point phasetransition can be determined for the system of water –extra pure sucrose but not for the system of water – foodgrade sucrose – milk powder, for which the probabilityof a point phase transition vanishes as the concentrationof the components increases.The present research objective was to analyze thechange in the aggregate state of analogue models ofsweetened condensed milk in the temperature rangefrom +20 to –50°C and to determine its cryoscopictemperature.Study objects and methodsThe research was conducted at the Laboratory ofCanned Dairy Products of the All-Russian Dairy ResearchInstitute.The study featured sugar, sugar-milk, and milksolutions of various concentrations, whole milk powder,Table 1. Formulation of sugar-milk solutionsТаблица 1. Рецептурный состав сахарно-молочных растворовComponent Variants of solution modelsSucrose solutionА1 А2 А3 А4Sugar, g 15.0 30.0 45.0 68.0Distilled water, g 85.0 70.0 55.0 32.0Sugar-milk solutionВ1 В2 В3 В4Whole milk powder, g 28,5Distilled water, g 85.0 70.0 55.0 32.0Sugar, g 15.0 30.0 45.0 68.0Solids, % 33.9 45.5 57.2 75.1Whole milk solutionС1 С2 С3 С4Whole milk powder, g 12.5 25.0 37.5 50.0Distilled water, g 87.5 75.0 62.5 50.0Figure 1. Experimental stand for determining thecryoscopic temperatureРисунок 1. Экспериментальный стенд для определениякриоскопической температуры529Рябова А. Е. [и др.] Техника и технология пищевых производств. 2022. Т. 52. № 3. С. 526–535and 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 concentrationof 12.5, 25, 37.5, and 50%. They were prepared bydissolving a certain mass of sucrose and whole milkpowder in a given amount of water at 25 and 40°C,respectively. The calculations ignored the moisturecontent in the powder.To assess the effect of the milk solid concentrationon freezing and defrosting, the sugar-milk solutionswere obtained by restoring the whole milk powder at40°C for 20 min, followed by adding sugar according toState Standard 33222-2015 (Table 1). The whole milkpowder was produced according to State Standard 33629-2015: 96.46% solids, 26% fat, 26% protein, solubilityindex = 0.1 mL of crude residue. The low saturation ofthe solution was maintained by the controlled mixingrate of 27 min–1 during the dissolution process.All the solution samples weighed 35 g. They werepoured into plastic flasks and sealed hermetically withlids with integrated temperature probes (Fig. 1).The solutions were frozen in a low-temperaturelaboratory freezer Vestfrort VT 327 (Denmark)at –50 ± 1°C. Solid carbon dioxide in thermally insulatedcontainers made it possible to obtain temperatures as lowas –78.5 ± 0.5°C. The temperature was recorded everysecond using a combined Testo 176T4 meter (Germany).The device had four waterproof food probes made ofK-type stainless steel (NiCr-Ni) with boundary valuesfrom –60 to –400°C. The samples were stored at thespecified temperature. After they were taken out of thefreezer, they thawed at 22 ± 1°C. Instrument readingsand data export to Microsoft Excel for analysis andvisualization were processed using the Testo-ComSoftBasic software.The cryoscopic temperature was determinedthermographically based the temperature curveplateau [25].The fluidity of sweetened condensed milk analoguemodels was determined by freezing, followed byretrievability and visual assessment of the probesat –25 ... –50°C under refrigerator conditions.The thawing kinetics of the analogue models wasstudied using a DSC822e Mettler Toledo differentialscanning calorimeter under conditions of dynamic heatingat a constant rate (https://www.mt.com). The resultswere processed using the STARe software.Results and discussionWe divided the freezing process into three successivestages to ensure the terminological uniformity (Fig. 2):– pre-freezing stage: the period of time between the startof freezing and the cryoscopic temperature (freezingpoint). At this stage, the system is supercooled to thenucleation temperature to trigger the nucleation ofice crystals. The release of latent crystallization heatcorresponds to the start of the thermostatic plateau;– freezing stage: the temperature at the considered area ofthe product is almost constant because the heat removalmakes a large amount of water turn into ice, i.e., phasetransformation;– decline to storage temperature: most of the water hasfrozen, and the temperature decreases to the requiredend temperature [26].At the first stage, we determined how the time ofrational low-temperature storage of solutions affectedtheir aggregation state. The main criterion for determiningthe exposure time in the dynamic temperature – time –concentration system was to register all the stages ofthe freezing process. Figure 3 shows the data for sugarFigure 2. Freezing processРисунок 2. Схематическое представление процесса замораживанияTemperature, ℃Time, minPre-freezingstageDecline t Freezing stage o storage temperatureNucleationtemperatureSubcoolingdegreeCryoscopictemperatureThermostaticplateau530Ryabova A.E . et al. Food Processing: Techniques and Technology. 2022;52(3):526–535solutions. Milk and sugar-milk solutions underwentthe same procedure.The onset of moisture crystallization processcorrelated 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 dependenton the concentration of solids. The crystallizationtime decreased in proportion to the concentration ofsucrose: for 5% sucrose, it was 39 min 14 s; for 45%sucrose, it lasted 6 min 40 s. However, no change inthe aggregate state of the system was recorded as thesucrose concentration reached 68%. This effect wasprobably associated with the concentration features ofthe system, or inability to reach the critical temperatureat which the phase transition occurs. Thus, it took thesystem four hours to stabilize completely and for thetemperature of the solutions to reach that of the externalenvironment.Table 2 shows the values of the obtained criteriathat describe the process of freezing sugar, sugar-milk,and milk solutions.Models A4 and B4 were analogues of sweetenedcondensed milk with sugar. They demonstrated no liquidsolidphase transition. However, a visual inspectionrevealed 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 theconcentration and the type of the solute. The dairycomponent had a strong impact on these indicators. Thefreezing time and the phase transition period declinedas 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 растворахVariantsof solution modelsIndicatorNucleationtemperature, °СCryoscopictemperature, °СSubcooling degree Freezing time, s Point phase transition, sА1 –1.4 ± 0.1 –0.4 ± 0.1 1.0 2827 2922А2 –5.3 ± 0.1 –2.2 ± 0.1 3.0 2308 2500А3 –9.9 ± 0.1 –6.4 ± 0.1 3.5 1570 1885А4 – – – – –В1 –2.1 ± 0.1 –2.1 ± 0.1 0 2224 2224В2 –5.0 ± 0.1 –5.0 ± 0.1 0.9 1579 1927В3 –10.9 ± 0.1 –10.9 ± 0.1 1.3 1276 1635В4 – – – – –С1 –0.4 ± 0.1 –0.4 ± 0.1 0 2730 2730С2 –1.2 ± 0.1 –1.2 ± 0.1 0 2850 2850С3 –2.6 ± 0.1 –2.6 ± 0.1 0 2280 2280С4 –4.6 ± 0.1 –4.6 ± 0.1 0 1740 1740Figure 3. Thermograms of sugar solutions at various concentrationsРисунок 3. Термограммы сахарных растворов различной концентраци и–52–39–26–13013Temperature, ℃Time, hh:mm:ss5% 10% 15% 20% 30% 45% 68%–52–39–26–13013Temperature, ℃Time, hh:mm:ss5% 10% 15% 20% 30% 45% 68%531Рябова А. Е. [и др.] Техника и технология пищевых производств. 2022. Т. 52. № 3. С. 526–535Figure 6. Freezing and defrosting curves for milk solutions at various concentrationsРисунок 6. Типовые кривые замерзания и размораживания молочных растворов различной концентрацииFigure 5. Freezing and defrosting curves for sugar solutions at various concentrationsРисунок 5. Типовые кривые замерзания и размораживания сахарно-молочных растворов различной–50–40–30–20–1001020Temperature, ℃Time, hh:mm:ssС1 С2 С3 С4–51–45–39–33–27–21–15–9–3931521Temperature, ℃Time, hh:mm:ccВ1 В2 В3 В4–50–40–30–20–1001020Temperature, ℃Time, hh:mm:ssС1 С2 С3 С4–50–40–3020–1001020Temperature, ℃Time, hh:mm:ssС1 С2 С3 С4–50–40–3020–1001020Temperature, ℃Time, hh:mm:ssС1 С2 С3 С4–50–40–30–20–1001020Temperature, ℃Time, hh:mm:ssС1 С2 С3 С4–50–40–30–20–1001020Temperature, ℃Time, hh:mm:ssС1 С2 С3 С4–50–40–30–20–1001020Temperature, ℃Time, hh:mm:ssС1 С2 С3 С4–50403020–1001020Temperature, ℃Time, hh:mm:ssС1 С2 С3 С4–50403020–1001020Temperature, ℃Time, hh:mm:ssС1 С2 С3 С4–51–45–39–33–27–21–15–9–3931521Temperature, ℃Time, hh:mm:ccВ1 В2 В3 В4–50–40–30–20–1001020Temperature, ℃Time, hh:mm:ssС1 С2 С3 С421–51–45–39–33–27–21–15–9–3931521Temperature, ℃Time, hh:mm:ccВ1 В2 В3 В41593–3–9–1521–27–33–39–45–51Figure 4. Freezing and defrosting curves for sugar solutions at various concentrationsРисунок 4. Типовые кривые замерзания и размораживания сахарных растворов различной концентрации–51–45–39–33–27–21–15–9–3931521Temperature, ℃Time, hh:mm:ccВ1 В2 В3 В4–50–40–30–20–1001020Temperature, ℃Time, hh:mm:ssA1 A2 A3 A4–50–40–20–1001020Temperature, ℃Time, hh:mm:ssС1 С2 С3 С420100–10–20–30–40–50532Ryabova A.E . et al. Food Processing: Techniques and Technology. 2022;52(3):526–535Figure 7. Thermograms of analogue models of sweetened condensed milk frozen with solid carbon dioxideРисунок 7. Термограммы моделей-аналогов сгущенного молока с сах аром при замораживании твердым диоксидом углерода–80–67–54–41–28–150:00:01 0:20:01 0:40:01 1:00:01 1:20:01 1:40:01 2:00:01 2:20:01Температура, ℃Время, чч:мм:ссAir temperature in the chamberUpper confidence boundAverage analogue model dataLower confidence bound–2–80–67–54–41–28–150:00:01 0:20:01 0:40:01 1:00:01 1:20:01 1:40:01 2:00:01 2:20:01Температура, ℃Время, чч:мм:ссAir temperature in the chamberUpper confidence boundAverage analogue model dataLower confidence bound–2–51–45–39–33–27–21–15–9–3931521Temperature, ℃Time, hh:mm:ccВ1 В2 В3 В4–50–40–30–20–1001020Temperature, ℃Time, hh:mm:ssС1 С2 С3 С4Figures 3, 4, and 5 visualize the typical freezingand defrosting curves for sugar, sugar-milk, and milksolutions, respectively. As the graphs show, when milkwas introduced into the system, it reduced the watercrystallization time, like in sugar solutions. The defrostingdata were particularly remarkable. The phase transitiontime during defrosting was 2–2.5 times longer thanduring freezing. The defrosting time decreased afterthe milk component was introduced into the system,which resulted in a smoother phase transition. Thus, themilk component shortened the freezing/defrosting time.Probably, this phenomenon could be explained by theextra 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 carbondioxide with a temperature of –78.5°C served as arefrigerant. However, this experiment also demonstratedno thermostatic plateaus typical for phase transitions(Fig. 7). The obtained results did not correspond to thedata published by Pavlova in [14]. However, the multiplerepetition of the experiment and the convergence of thevalues obtained made it possible to limit the scope ofpossible causal relationships to several options:1. The rate of phase transition in this temperaturerange is less than one second. This value correspondsto the technical parameters of signal recorded by thedevice;2. The technical parameters of the probes generateerrors at the temperature range from –60 to –78.5°C;3. Phase transitions occur at lower temperatures incomplex polycomponent systems;4. Diffusion dilemma.Figure 8. Effect of concentration on cryoscopic temperatureРисунок 8. Зависимость изменения криоскопической температуры от концентрации растворовY2 = –7E–05x3 + 0.0015x2 – 0.0401xR² = 0.997Y3 = –4E–05x3 – 0.0011x2 – 0.0061xR² = 0.9994Y1 = –8E–06x3 – 0.0015x2 + 0.0098xR² = 0.9995–12–10–8–6–4–200 10 30 40 50 60Temperature, ℃Concentration of solids, %20y = –4E–05x3 –0,0011x2 –0,0061xR² = 0,9994y = –7E-05x3 + 0,0015x2 –0,0401xR² = 0,997y1 = –8E–06x3 –0.0015x2 +0.0098xR² = 0.9995–12–10–8–6–4–200 10 30 40 50 60Temperature, ℃Sugar solution (Y1) Milk solution (Y3)20Concentration of solids, %Sugar-milk solution (Y2)533Рябова А. Е. [и др.] Техника и технология пищевых производств. 2022. Т. 52. № 3. С. 526–535Figure 8 demonstrates the correlation between theeffect of the concentration of solids on the dynamics ofcryoscopic temperature in the solution. The dependenceswere non-linear, with three-power polynomials. Solutionswith ≤ 20% solids showed no significant changes in thefreezing point. Further increase in concentration led tosignificant changes related to the nature, concentration,and possible synergistic effects of the dissolvedcomponents.Since the thermographic method failed to registerthe cryoscopic temperature of the analogue models, wedecided to determine the temperature range when liquidturns solid. The loss of fluidity depended mostly on theambient temperature and the storage time. At –30°Cand ≥ 2 h of storage time, the effect was comparable to54 min of storage at –35°C (Fig. 9). The appearance ofcrystal-like elements and the complete loss of fluidityunder mechanical action were characteristic featuresof the structural change in the product. However, allsamples thawed within a few minutes, regardless oftemperature and storage time.Figure 10 illustrates the differential scanningcalorimetry of a commercial sweetened condensedmilk (State Standard 3168). The solidification occurredat –82 ... –80°С. The pronounced crystallization andthawing peaks confirmed the heterogeneity of the systemand the polycrystalline nature of the freezing process.ConclusionThe research revealed some freezing/defrostingpatterns of sugar, sugar-milk, and milk solutions,depending on the nature and concentration of thecomponents dissolved. The cryoscopic temperaturedecreased following the increase in the concentrationof solids. In sugar and sugar-milk systems, the freezingtime and the phase transition period decreased as theconcentration characteristics of the system increased.In whole milk solutions, the freezing time and phaseFigure 10. Differential scanning calorimetry of commercial sweetened condensed milkРисунок 10. Дифференциально сканирующая калориметрия промышленного образца сгущенного молока с сахаромFigure 9. Loss of fluidity after 54 min: a – at –30°С, b – at – 32.5°С, c – at –35°СРисунок 9. Визуализация потери текучести исследуемых образцов м оделей аналогов сгущенного молока с сахаром при хранениив течение 54 мин: a – при –30 °С; b – при –32,5 °С; c – при –35 °Сa 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–16–14–12–10–8–4–20mWLab: Mettler Staree SW 15.00534Ryabova A.E . et al. Food Processing: Techniques and Technology. 2022;52(3):526–535transition increased as the concentration rose from12.5 to 25%. With a further increase in concentration,they decreased, which was probably due to themulticomponent composition of the system and theheat of crystallization. In sweetened condensed milk,the loss of fluidity occurred at –30°С if the storagetime exceeded 2 h. This result was comparable to a54-min storage at –35°С. The methods employed failedto establish the phase transitions in analogue modelsof sweetened condensed milk. The research createdprerequisites for a more profound differential scanningcalorimetry of phase transitions in sweetened condenseddairy products.ContributionA.G. Galstyan and A.E. Ryabova developed theresearch concept and conducted a formal analysis.A.G. Galstyan developed the methodology and editedthe manuscript. A.E. Ryabova and V.A. Tolmachevconducted the experiment and visualized the data.A.E. Ryabova drafted the manuscript. All the authorswere involved in the study and agreed on the finalversion of the manuscript.Conflict of interestThe authors declare that there is no conflict of interestsregarding the publication of this manuscript.Критерии авторстваА. 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 иВ. А. Толмачев провели эксперимент и визуали-зировали данные. А. Е. Рябова подготовила чер-новик рукописи. Все авторы были привлечены кисследованию, а также ознакомились и согласилисьс окончательным вариантом рукописи.Конфликт интересовАвторы заявляют об отсутствии конфликтаинтересов.