Determination of Supercooling Degree, Nucleation and Growth Rates, and Particle Size for Ice Slurry Crystallization in Vacuum

Article Determination of Supercooling Degree, Nucleation and Growth Rates, and Particle Size for Ice Slurry Crystallization in Vacuum

Xi Liu, Kunyu Zhuang, Shi Lin, Zheng Zhang and Xuelai Li *

School of Chemical Engineering, Fuzhou University, Fuzhou 350116, China; [email protected] (X.L.); [email protected] (K.Z.); [email protected] (S.L.); [email protected] (Z.Z.) * Correspondence: [email protected]

Academic Editors: Helmut Cölfen and Mei Pan Received: 7 April 2017; Accepted: 29 April 2017; Published: 5 May 2017

Abstract: Understanding the crystallization behavior of ice slurry under vacuum condition is important to the wide application of the vacuum method. In this study, we first measured the supercooling degree of the initiation of ice slurry formation under different stirring rates, cooling rates and ethylene glycol concentrations. Results indicate that the supercooling crystallization pressure difference increases with increasing cooling rate, while it decreases with increasing ethylene glycol concentration. The stirring rate has little influence on supercooling crystallization pressure difference. Second, the crystallization kinetics of ice crystals was conducted through batch cooling crystallization experiments based on the population balance equation. The equations of nucleation rate and growth rate were established in terms of power law kinetic expressions. Meanwhile, the influences of suspension density, stirring rate and supercooling degree on the process of nucleation and growth were studied. Third, the morphology of ice crystals in ice slurry was obtained using a microscopic observation system. It is found that the effect of stirring rate on ice crystal size is very small and the addition of ethylene glycoleffectively inhibits the growth of ice crystals. The results in this paper can provide theoretical guidance and technical support for the development of vacuum icemakers.

Keywords: ice slurry; supercooling degree; nucleation rate; growth rate; particle size

1. Introduction Thermal energy storage is used to assist in the effective utilization of thermal energy in industrial applications [1–4]. Ice slurry as anenergy storage medium is a very interesting solution thanks to the high energy storage density and fast cooling capacity [5–7]. The most important issue relating to the wide use of ice slurry cooling technology relates to what is the best method of ice slurry production [7]. There are many methods for making ice slurry, including scraped-surface type, supercooling type, direct-injection or direct heat exchange type, fluidized-bed type, and vacuum type [8–12]. Among these methods, vacuum type, which uses aqueous solution as a refrigerant and employs direct contact heat transfer, has received wide attention in recent years. Kim et al. [13] studied the conditions for the formation of ice crystals theoretically by the diffusion-controlled evaporation model and the prediction was proved by experiments. Lugo et al. [14] researched the ice-liquid-vapour equilibria data of ammonia and ethanol aqueous solutions experimentally. The measured data were consistent with the thermodynamic models. Asaoka et al. [15,16] proposed a circulating system to produce ice slurry and studied the vapor-liquid equilibrium data to estimate the coefficient of performance of the system with an ethanol solution. Zhang et al. [17] established a model for the process including flash evaporation and ice making in

Crystals 2017, 7, 128; doi:10.3390/cryst7050128 www.mdpi.com/journal/crystals Crystals 2017, 7, 128 2 of 13 vacuum environment. The influencing factors for the binary ice’s IPF, such as environmental pressure, droplet size and water temperature, were discussed both analytically and experimentally. At present, most of the research interests related to vacuum method are focused on heat and mass transfer inside the liquid, as well as the phase equilibrium measurement and equipment optimization. However, the crystallization thermodynamics and kinetics of ice slurry, including the supercooling degree, the nucleation rate and growth rate, the morphology of ice crystals, have not been accurately understood, which have been the main obstacles to the rapid development and wide application of vacuum method. Therefore, it is necessary to determine the above problems and reveal the crystallization behavior of ice slurry under vacuum condition. The supercooling degree is the driving force for the nucleation and growth of ice crystals. The supercooling degree depends on several operation parameters, such as stirring rate, cooling rate, solution composition, etc. At present, the study of supercooling is mostly conducted under atmospheric pressure [18,19]. The supercooling characteristics of ice nucleation in vacuum environments are rarely reported. Nucleation and crystal growth are the two major steps govern the ice slurry production. Accurate modeling of nucleation and growth is an essential prerequisite to the design and control of a vacuum ice slurry production system. Only a few published papers have reported the crystallization kinetics of ice slurry [20,21], but they had small sample sizes and relied on classical nucleation theory. They are not applicable to the formation of ice slurry produced by vacuum. The shape and the size of ice crystals are very important aspects which should be studied, because they influence the operation of ice slurry system. Ice slurry with larger ice crystals will show a slower melt-off rate and need greater power to pump. Some scientists have conducted researches on particle morphology of ice slurry produced by scraped-surface method or fluidized-bed method [11,22,23]. However, the study of the morphology of ice crystals produced by vacuum method has not been taken seriously. In this work, ethylene glycol aqueous solution served as the ice-making solution, and the supercooling characteristics at different experimental conditions were measured using a vacuum ice slurry production system. The nucleation rate and growth rate of the crystal formation process were discussed in the view of kinetics, and the influence of each parameter on crystallization process was analyzed. At the same time, the morphology of ice crystals was observed, and the influence of stirring rate and initial concentration on the particle size of ice crystals was determined. The objectives of this research are to explore the rules of ice slurry crystallization in vacuum and provide theoretical and technical support for the ice slurry production.

2. Theory

2.1. Nucleation and Growth Rate For nucleation two different mechanism are distinguished; the homogeneous and the heterogeneous nucleation. In homogeneous nucleation embryos are formed internally in the supercooled liquid containing only water molecules. In heterogeneous nucleation a foreign substrate initiates nuclei formation. At present, a number of authors suggest that most primary nucleation in industrial crystallizers is heterogeneous rather than homogeneous and empirical relationships such as [24–28]: a b c B = KN MT NP ∆C (1) where KN is the nucleation rate constant, MT is the suspension density, NP is the stirring rate, ∆C is the driving force of nucleation. In the process of ice slurry production, ∆C equals to supercooling degree ∆t. Equation (1), therefore, can be rewritten as:

a b c B = KN MT NP ∆t (2) Crystals 2017, 7, 128 3 of 13

An empirical correlation is frequently employed to describe the crystal growth rate as a function of the supercooling degree ∆t, as follows:

g G = KG∆t (3) where KG is the growth rate constant.

2.2. Population Balance To evaluate the nucleation and growth kinetics, a population balance model that describes the crystallization process has been employed. The following assumptions are made: (1) growth rate is independent of crystal size and the McCabe’s “∆L rule” is valid; (2) agglomeration and breakage are not signiﬁcant; (3) the volume of the solution is invariable. Hence, the general population balance equation can be expressed as [27,28]: ∂n ∂n + G = 0 (4) ∂t ∂L The kth moment of the population density function can be deﬁned as:

Z ∞ k µk = nL dL (5) 0 where L is the ice crystal size and n is the population density which can be calculated from the follow relations: M ∆V = T i ni 3 (6) ρckvLi ∆Li where ∆Vi is the volume fraction in ith region, Li is the average ice crystal size in the given size range, ∆Li is the width between two crystal size region, ρc is the crystal density, kv is the volume shape factor. By the method of moment transform, the Equation (4) can be transformed from a ﬁrst-order nonlinear partial differential equation to a group of constant differential equations:

dµ 0 = B (7) dt dµ 1 = G (8) µ0dt When the time interval is very short, the relationship between the moment value and the time will accord with the linearity. Thus, the kinetic rate can be expressed as:

∆µ B = 0 (9) ∆t ∆µ G = 1 (10) µ0∆t

3. Materials and Methods

3.1. Materials Ethylene glycol (purity ≥99.0%) was purchased from Sinopharm Chemical Reagent Co., Ltd. (Shanghai, China) Distilled water has served as solvent.

3.2. Measurement of Supercooling Degree A schematic of the experimental apparatus for producing ice slurry is shown in Figure1. The apparatus consists of a vacuum pump, a vacuum chamber, a magnetic stirrer, a vapor condenser, a T Crystals 2017, 7, 128 4 of 13 Crystals 2017, 7, 128 4 of 13

thermocouple (accuracy:(accuracy: ±±0.20.2 K), K), a a pressure transducer (accuracy: ±±0.040.04 mbar), mbar), and and data acquisition systems for recording the temperaturetemperature and pressure. The vacuum pump could deliver a maximum volume ﬂowflow rate of 2 LL·s·s−1 1atat 100 100 kPa kPa and and could could reach reach a a maximum maximum vacuum vacuum of of 6 6 ×× 1010−2 −Pa.2 Pa.

Figure 1. Schematic of ice slu slurryrry production system.

The changes of pressure and temperature versus time during the process of ice slurry The changes of pressure and temperature versus time during the process of ice slurry production production are shown in Figure 2. At the beginning, the aqueous solution evaporated under are shown in Figure2. At the beginning, the aqueous solution evaporated under low-pressure low-pressure conditions, and the remaining solution was cooled as a consequence of the latent heat conditions, and the remaining solution was cooled as a consequence of the latent heat of evaporation. of evaporation. When the temperature dropped below the freezing point (T = T0, p = p0), the aqueous When the temperature dropped below the freezing point (T = T , p = p ), the aqueous solution entered solution entered the supercooling state. After a few minutes, the0 supercooling0 state broke and the ice the supercooling state. After a few minutes, the supercooling state broke and the ice slurry formed slurry formed immediately. Latent heat released by ice enabled the temperature of the solution to immediately. Latent heat released by ice enabled the temperature of the solution to rise to freezing, rise to freezing, and the initiation of formation of ice slurry was monitored by a small jump of and the initiation of formation of ice slurry was monitored by a small jump of temperature and temperature and pressure data. pressure data. The temperature and pressure curves in Figure 2 show that the variation of the two state The temperature and pressure curves in Figure2 show that the variation of the two state parameters is very similar during the ice making process, suggesting that these two parameters can parameters is very similar during the ice making process, suggesting that these two parameters be used to monitor the changes in the state of the solution in the vacuum chamber. The solution in can be used to monitor the changes in the state of the solution in the vacuum chamber. The solution in the chamber was stirred throughout the experiment, so the thermocouple was affected by the strike the chamber was stirred throughout the experiment, so the thermocouple was affected by the strike of of the liquid, which caused temperature variation and fluctuations in the temperature curve. the liquid, which caused temperature variation and fluctuations in the temperature curve. Observation Observation of the pressure curve, on the other hand, showed no random fluctuations. This is of the pressure curve, on the other hand, showed no random fluctuations. This is because the pressure because the pressure monitored by pressure transducer is the gas pressure, which is not affected by monitored by pressure transducer is the gas pressure, which is not affected by the liquid stirring. the liquid stirring. For this reason, pressure is chosen as the characteristic parameter to characterize For this reason, pressure is chosen as the characteristic parameter to characterize the supercooling the supercooling degree of ice crystallization in this work. The minimum pressure during the degree of ice crystallization in this work. The minimum pressure during the pressure relieving process pressure relieving process is defined as relief pressure of supercooling pmin. The pressure at which is defined as relief pressure of supercooling pmin. The pressure at which the ice crystal begins to the ice crystal begins to emerge is defined as phase transition pressure p0. The difference between p0 emerge is defined as phase transition pressure p0. The difference between p0 and pmin, ∆p, is named and pmin, Δp, is named “supercooling crystallization pressure difference”, which is the evaluation “supercooling crystallization pressure difference”, which is the evaluation parameter of supercooling. parameter of supercooling. The freezing behavior of solution shows a certain randomness, it is The freezing behavior of solution shows a certain randomness, it is therefore necessary to repeat the therefore necessary to repeat the same experiment several times under the same conditions. In this same experiment several times under the same conditions. In this study, all experiments performed study, all experiments performed under the same conditions were performed 40 times and averaged under the same conditions were performed 40 times and averaged to ensure the reliability of the results. to ensure the reliability of the results.

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Figure 2. Variations of pressure and temperature during the process of ice slurry production. Figure 2. Variations of pressure and temperature during the process of ice slurry production. Figure 2. Variations of pressure and temperature during the process of ice slurry production.

3.3. Measurement of Crystal Morphology 3.3. Measurement of Crystal Morphology The ice crystals were observed based on a microscopic observation device as shown in Figure 3. The ice crystals were observed based on a microscopic observation device as shown in Figure3. This device was inspired by previous work on ice slurries [23,29,30]. During the observation process, This device was inspired by previous work on ice slurries [23,29,30]. During the observation process, the bottom plate of glass was kept at −2 °C to prevent ice from melting by heat from the backlight the bottom plate of glass was kept at −2 ◦C to prevent ice from melting by heat from the backlight and and environment. All the observation processes were performed within 3 min, so the effect of environment. All the observation processes were performed within 3 min, so the effect of Ostwald Ostwald ripening, particle agglomeration and particle melting could be ignored. The typical image ripening, particle agglomeration and particle melting could be ignored. The typical image of ice slurry of ice slurry crystals is shown in Figure 4. Several images were taken and the total number of ice crystals is shown in Figure4. Several images were taken and the total number of ice crystals for each crystals for each test was at least 400. The images were processed by the image software ImageJ. test was at least 400. The images were processed by the image software ImageJ. Because the ice crystals Because the ice crystals appeared only as 2D-projections in the images, the equivalent circular appeared only as 2D-projections in the images, the equivalent circular diameter of each ice crystal was diameter of each ice crystal was considered its length. This equivalent diameter D of ice crystals was calculatedconsidered using its length. the surface This equivalent area of ice diameter crystal 2D-projectionD of ice crystals Ai, wasas proposed calculated in usinga previous the surface work [26]: area calculated using the surface area of ice crystal 2D-projection Ai, as proposed in a previous work [26]: of ice crystal 2D-projection Ai, as proposed in a previous work [26]: 4Ai D = 4Ai D = r (11) 4πA D = π i (11) π The average crystal diameter was computed using the equivalent diameter of each crystal and the totalThe number average of crystal crystals diameter analyzed: was computed using the equivalent diameter of each crystal and the total number of crystals analyzed: N = 1 N D = N DFeret,i (12) N1 N=1 Feret,i (12) D = N N∑=1 DFeret,i (12) N N=1

Figure 3. Ice crystal observation system. Figure 3. IceIce crystal crystal observation observation system.

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Figure 4. Photograph of the ice crystals in ice slurry. Figure 4. Photograph of the ice crystals in ice slurry. 3.4. Measurement of Crystallization Kinetics 3.4. Measurement of Crystallization Kinetics The crystallization kinetics of ethylene glycol aqueous solution was determined experimentally usingThe the crystallization vacuum ice slurry kinetics production of ethylene system glycol shown aqueous in Figure solution 1. The was stirring determined rates selected experimentally in the usingexperiment the vacuum were ice200, slurry 300, and production 400 rpm. systemThen vacuum shown chamber in Figure was1. The filled stirring with 20 rates mL selectedethylene in theglycol experiment aqueous were solution 200, 300,at different and 400 concentrat rpm. Thenions, vacuum and the chamber vacuum was pump, ﬁlled pressure with 20 mLcollection ethylene glycolsystem aqueous were turned solution on at to different observe concentrations,the pressure change. and the The vacuum pressure pump, jump pressureobserved collection in the system system wereserved turned as an on indicator to observe for thethe pressureoccurrence change. of crysta Thellization. pressure When jump crystallization observed in time the systemreached served the asdefault an indicator measurement for the occurrencetime, the vacuum of crystallization. pump was tu Whenrned off crystallization to allow sampling. time reachedSix samples the were default measurementtaken at the time,same thestirring vacuum rate. pumpDegree was of supercooling, turned off to suspension allow sampling. density Six and samples particle were size takenof ice at thecrystals same stirring were measured rate. Degree for each of supercooling, sample. suspension density and particle size of ice crystals were measuredHere for the each degree sample. of supercooling refers to the difference between the measured temperature and theHere theoretical the degree temperature of supercooling calculated refers at the to the thr differenceee-phase equilibrium between the state. measured The ethylene temperature glycol and theaqueous theoretical solution temperature is nonvolatile, calculated so at thethe three-phasetemperature-pressure equilibrium relationship state. The ethylene of the glycolthree-phase aqueous solutionequilibrium is nonvolatile, can be described so the by temperature-pressure the vapor-solid equilibrium relationship equation of of the ice three-phase [14]. In this equilibrium way, the measured pressure data are substituted into the vapor-solid equilibrium equation of ice to determine can be described by the vapor-solid equilibrium equation of ice [14]. In this way, the measured the phase equilibrium temperature in theory. The measurement of the suspension density was based pressure data are substituted into the vapor-solid equilibrium equation of ice to determine the phase on the energy conservation principle. There was negligible heat loss during the measurement equilibrium temperature in theory. The measurement of the suspension density was based on the process, and the value of the suspension density was computed by measuring the initial and final energy conservation principle. There was negligible heat loss during the measurement process, and the temperatures and masses of the sample as mixed with 20 g hot water at 40 °C. The observation of ice value of the suspension density was computed by measuring the initial and ﬁnal temperatures and crystals was based on the ice crystal observation system,◦ as shown in Figure 3. All parameters and massesstrategies of the used sample for measuremen as mixed witht are 20 summarized g hot water in at Table 40 C. 1. The observation of ice crystals was based on the ice crystal observation system, as shown in Figure3. All parameters and strategies used for measurement are summarizedTable 1. Summary in Table1 of. measurement parameters and strategies.

Table 1.ParameterSummary of measurement parametersStrategy and strategies. system pressure pressure transducer systemParameter temperature T thermocouple Strategy systemice crystal pressure size microscopic pressure observation transducer system suspensionsystem density temperature of ice slurry energy conservation T thermocouple principle icestirring crystal rate size digital-display microscopic observationmagnetic stirrer system suspension density of ice slurry energy conservation principle stirring rate digital-display magnetic stirrer

Crystals 2017, 7, 128 7 of 13 Crystals 2017, 7, 128 7 of 13

4. Results andDiscussion

4.1. Supercoolling Degree The supercoolingsupercooling characteristics of ethyleneethylene glycolglycol aqueousaqueous solutionsolution withwith initialinitial concentrationconcentration of 3% waswas experimentallyexperimentally measured at stirring rates of 100, 200, 300, 400, and 500 rpm, as shownshown in Figure5 5.. At different stirring stirring rates, rates, the the mean mean value value of of the the Δp∆ isp 55.34,is 55.34, 50.36, 50.36, 51.56, 51.56, 49.65, 49.65, 50.34 50.34 Pa and Pa andthe corresponding the corresponding standard standard deviation deviation is 6.02, is 5.87 6.02,, 6.33, 5.87, 5.25 6.33, and 5.25 5.38 and Pa, 5.38 respectively, Pa, respectively, which whichshows showsthat the that stirring the stirring rate does rate not does significantly not signiﬁcantly affect the affect supercooling the supercooling degree of degree ethylene ofethylene glycol aqueous glycol aqueoussolution. solution.The effect The of effectstirring of stirringon the onice thecrystall ice crystallizationization is complicated. is complicated. Stirring Stirring can enhance can enhance heat heattransfer, transfer, maintain maintain the uniformity the uniformity of temperature of temperature inside inside the vacuum the vacuum chambe chamber,r, and andaccelerate accelerate the theprobability probability of molecular of molecular contact contact to toform form critical critical nucleus nucleus in in certain certain size size that that can can promote the generation ofof iceice crystals; crystals; however, however, an an extra-high extra-high mixing mixing rate rate can resultcan result in excessive in excessive shear shear forces, forces, and it isand possible it is possible to accelerate to accelerate the crushing the ofcrushing the critical of the nuclei, critical reducing nuclei, the reducing possibility the of possibility the formation of the of criticalformation nuclei, of critical which maynuclei, be detrimentalwhich may to be crystal detrimental nucleation to andcrystal increase nucleation the supercooling and increase degree. the Saitosupercooling et al. studied degree. the Saito effects et al. of externalstudied the factors effects on of supercooling external factors degree on [supercooling31]. Results showed degree [31]. that stirring,Results showed vibration, that friction, stirring, and vibration, forced convection friction, and in forced water hadconvection little effect in water on its had supercooling. little effect Theseon its resultssupercooling. are consistent These results with the are ﬁndings consistent of thiswith work. the findings of this work.

Figure 5. Effects of stirring rate on supercooling crystallization pressure difference.difference.

The cooling rate is defined as the ratio of the Δp over the elapsed time in supercooling state. The cooling rate is deﬁned as the ratio of the ∆p over the elapsed time in supercooling state. During the experiment, the stirring rate was maintained at 300 rpm, and supercooling degree of the During the experiment, the stirring rate was maintained at 300 rpm, and supercooling degree of ethylene glycol aqueous solution at different cooling rates was measured, as shown in Figure 6. the ethylene glycol aqueous solution at different cooling rates was measured, as shown in Figure6. When the cooling rate increased, the Δp increased. This is because when the cooling rate was fast, the When the cooling rate increased, the ∆p increased. This is because when the cooling rate was fast, solution that was already supercooled did not produce nuclei in time. The delay in the nuclei the solution that was already supercooled did not produce nuclei in time. The delay in the nuclei precipitation requires an even lower temperature for ice crystallization and widens the subcooled precipitation requires an even lower temperature for ice crystallization and widens the subcooled region. Okawa et al. tested the characteristics of ice formation of supercooled water on metal plate region. Okawa et al. tested the characteristics of ice formation of supercooled water on metal plate under ambient pressure [18]. Results showed that the degree of supercooling at 2.0 K·min−1 was under ambient pressure [18]. Results showed that the degree of supercooling at 2.0 K·min−1 was much much larger than that at 0.2 K·min−1. These results are consistent with our experiment. larger than that at 0.2 K·min−1. These results are consistent with our experiment.

Crystals 2017, 7, 128 8 of 13 Crystals 2017, 7, 128 8 of 13

Crystals 2017, 7, 128 8 of 13

FigureFigure 6. 6.Effects Effects of of cooling cooling raterate onon supercoolingsupercooling crystallization crystallization pressure pressure difference. difference.

The supercoolingFigure 6. Effects characteristics of cooling rateof ethylene on supercooling glycol aqueouscrystallization solution pressure of different difference. concentrations wereThe measured supercooling respectively characteristics while maintaining of ethylene the glycol stirring aqueous rate at solution300 rpm.of The different results concentrationsare shown in The supercooling characteristics of ethylene glycol aqueous solution of different concentrations wereFigure measured 7. As shown respectively in the whilefigure, maintainingthe relationsh theip stirringbetween ratethe atwidth 300 rpm.of supercooled The results region are shownand were measured respectively while maintaining the stirring rate at 300 rpm. The results are shown in incooling Figure7 rate. As showed shown inthe the same ﬁgure, trend the at relationshipdifferent cooling between rates. the At widththe same of supercooledcooling rate, regionthe Δp andof Figure 7. As shown in the figure, the relationship between the width of supercooled region and coolingethylene rate glycolaqueous showed the samesolution trend decreased at different as the cooling initial concentration rates. At the of same ethylene cooling glycol rate, increased. the ∆p of cooling rate showed the same trend at different cooling rates. At the same cooling rate, the Δp of ethyleneFor example, glycolaqueous when the solution cooling decreased rate was 20.25 as the Pa·min initial− concentration1, the Δp of the of ethylene ethylene glycol glycol aqueous increased. ethylene glycolaqueous solution decreased as the initial concentration of ethylene glycol increased. Forsolution example, with when initial the concentration cooling rate wasof 1% 20.25 wasPa 56·.81min Pa.−1 ,When the ∆ ptheof initial the ethylene concentration glycol aqueouswas 7%, the solution Δp For example, when the cooling rate was 20.25 Pa·min−1, the Δp of the ethylene glycol aqueous withdropped initial concentrationto 36.91 Pa, a decrease of 1% was of 35.03%. 56.81 Pa. Therefore, When the a higher initial initial concentration concentration was 7%,of ethylene the ∆p droppedglycol solution with initial concentration of 1% was 56.81 Pa. When the initial concentration was 7%, the Δp aqueous solution results in a smaller Δp, a narrower supercooled region, and higher unpredictability todropped 36.91 Pa, to a decrease36.91 Pa, a of decrease 35.03%. of Therefore, 35.03%. Therefore, a higher initiala higher concentration initial concentration of ethylene of ethylene glycol aqueousglycol of the formation of ice crystals. In this way, in view of favoring the control of crystal growth, the solutionaqueous results solution in aresults smaller in a∆ smallerp, a narrower Δp, a narrower supercooled supercooled region, region, and higher and higher unpredictability unpredictability of the solution concentration should be kept as low as possible. formationof the formation of ice crystals. of ice crystals. In this way,In this in way, view in of view favoring of favoring the control the control of crystal of crystal growth, growth, the solution the concentrationsolution concentration should be should kept as be low kept as as possible. low as possible.

Figure 7. Effects of ethylene glycol concentration on supercooling crystallization pressure difference. Figure 7. Effects of ethylene glycol concentration on supercooling crystallization pressure difference. Figure 7. Effects of ethylene glycol concentration on supercooling crystallization pressure difference.

Crystals 2017, 7, 128 9 of 13 Crystals 20172017,, 77,, 128128 9 of 13 4.2. Equations of Nucleation Rateand Growth Rate 4.2. Equations of Nucleation Rateand Growth Rate 4.2. Equations of Nucleation Rateand Growth Rate The kinetic parameters of nucleation and growth are obtained by multiple regression analysis The kinetic parameters of nucleation and growth are obtained by multiple regression analysis of allThe experimental kinetic parameters data, and of nucleationthe equations and of growth nucleation are obtained rate and by growth multiple rate regression are established analysis as of of all experimental data, and the equations of nucleation rate and growth rate are established as follows:all experimental data, and the equations of nucleation rate and growth rate are established as follows: follows: 10 −1.465 −0.641 0.517 B = 2.922×1010 M −−1.465N −− 0.641Δt 0.517 R2 = 0.934 (13) B ==2.922 ××10 10MTT 1.465NP 0.641 ∆t0.517 R2 = 0.934 (13) B 2.922 10 MT NP Δt R = 0.934 (13)

−55 4.0364.036 22 (14) GG==1.411.41××1010− Δ∆tt RR = 0.9330.933 (14) G = 1.41×10 5 Δt 4.036 R2 = 0.933 (14) A comparison of of the the regression regression values values from from mo modeldel and and the the values values measured measured in experiments in experiments for A comparison of the regression values from model and the values measured in experiments for thefor theice nucleation ice nucleation rate rate and and growth growth rate rate is shown is shown in Figures in Figures 8 and8 and 9, 9respectively., respectively. As As shown shown in inthe the ice nucleation rate and growth rate is shown in Figures 8 and 9, respectively. As shown in the figure,the ﬁgure, the thedata data points points are are evenly evenly distributed distributed on on both both sides sides of of the the diagonal, diagonal, indicating indicating that the figure, the data points are evenly distributed on both sides of the diagonal, indicating that the established kinetickinetic model model can can truthfully truthfully describe describe the nucleationthe nucleation and growthand growth kinetics kinetics of the iceof crystals.the ice established kinetic model can truthfully describe the nucleation and growth kinetics of the ice crystals.Some individual Some individual data points data deviate points deviate from the from diagonal, the diagonal, probably probably because because of the ignoranceof the ignorance of the crystals. Some individual data points deviate from the diagonal, probably because of the ignorance ofagglomeration, the agglomeration, Oswald Oswald ripening, ripening, and crushing and crushing behavior behavior of ice crystalsof ice crystals in kinetics in kinetics analysis. analysis. of the agglomeration, Oswald ripening, and crushing behavior of ice crystals in kinetics analysis.

Figure 8. Comparison of nucleation rate between experimental values and regressed values. Figure 8. Comparison of nucleation rate between experimental values and regressed values.values.

Figure 9. Comparison of growth rate between experimental values and regressed values. Figure 9. Comparison of growth rate between experimentalexperimental values and regressed values.values. As shown in Equation (13), the exponent of stirring rate in the nucleation rate equation is −0.641, As shown in Equation (13), the exponent of stirring rate in the nucleation rate equation is −0.641, which is less than zero, indicating that the higher stirring rate results in the lower nucleation rate in which is less than zero, indicating that the higher stirring rate results in the lower nucleation rate in

Crystals 2017, 7, 128 10 of 13

As shown in Equation (13), the exponent of stirring rate in the nucleation rate equation is −0.641, which is less than zero, indicating that the higher stirring rate results in the lower nucleation rate in Crystals 2017, 7, 128 10 of 13 the stirring range, i.e., the higher rate of stirring inhibits the nucleation of ice crystals. This is because whenthe stirring the stirring range, strength i.e., the ishigher too strong, rate of largestirring grains inhibits can the break nucleation into many of ice small crystals. particles This is whose because size doeswhen not the meet stirring the critical strength radius is too for strong, nucleation, large grai therebyns can reducingbreak into the many nucleation small particles rate. The whose exponent size ofdoes suspension not meet density the critical is − 1.465,radius whichfor nucleation, is less than thereby zero, reducing indicating the thatnucleation the increase rate. The of suspensionexponent densityof suspension did not facilitatedensity is the −1.465, nucleation which ofis iceless crystals. than zero, indicating that the increase of suspension densityAs the did driving not facilitate force of the the nucleation formation of of ice ice crystals. crystals, the degree of supercooling of solution has an importantAs the effect driving on the force nucleation of the formation and growth of ice of crystals, ice crystals. the degree The exponent of supercooling of supercooling of solution degree has inan the important equation ofeffect nucleation on the nucleation rate is 0.517, and which growth is largerof ice thancrystals. zero, The indicating exponent that of supercooling the increase of supercoolingdegree in the can equation increase theof nucleati nucleationon rate rate is considerably. 0.517, which This is larger result isthan consistent zero, indicating with the theoreticalthat the analysis,increase i.e., of supercooling the larger the can supercooling, increase the nucleation the faster therate nucleation.considerably. In This general, result theis consistent kinetic order with of primarythe theoretical nucleation analysis, is close i.e., to the 10, whichlarger the is much superc largerooling, than the thefaster kinetic the nucleation. order obtained In general, in this the work (0.517),kinetic suggesting order of thatprimary the mechanismnucleation is of close nucleation to 10, iswhich secondary is much contact larger nucleation. than the Askinetic shown order from Equationobtained (14), in this the icework crystal (0.517), growth suggesting rate increased that the alongmechanism with theof nucleation degree of supercooling,is secondary contact and it is proportionalnucleation. toAs the shown 4.036th from power Equation of supercooling. (14), the ice crystal However, growth the rate nucleation increased rate along is proportional with the degree to the 0.517thof supercooling, power of supercooling, and it is proportional which suggests to the 4.036th that thepower impact of supercooling. of supercooling However, on the the nucleation nucleation rate rate is proportional to the 0.517th power of supercooling, which suggests that the impact of is much weaker than on the growth rate. supercooling on the nucleation rate is much weaker than on the growth rate. 4.3. Ice Crystal Size 4.3. Ice Crystal Size The average particle size of ice crystals was observed in 3% ethylene glycolaqueous solution at The average particle size of ice crystals was observed in 3% ethylene glycolaqueous solution at stirring rates of 200, 300 and 400 rpm, respectively. The results are shown in Figure 10. Under different stirring rates of 200, 300 and 400 rpm, respectively. The results are shown in Figure 10. Under stirring rates, the average particle size of ice crystals is 45.95, 44.04 and 44.18µm with a standard different stirring rates, the average particle size of ice crystals is 45.95, 44.04 and 44.18μm with a deviation of 6.89, 7.08 and 6.55 µm, respectively. Obviously, the average particle size of ice crystalsis standard deviation of 6.89, 7.08 and 6.55 μm, respectively. Obviously, the average particle size of ice lesscrystalsis affected less by affected the stirring by the rate. stirring In theory, rate. In the theory, mixing the breaks mixing the breaks ice crystals the ice crystals into smaller into smaller particles. Meanwhile,particles. Meanwhile, these existing these ice crystalsexisting areice crystals subject toare agglomeration subject to agglomeration and Ostwald and ripening Ostwald effect, ripening which increaseeffect, thewhich size increase of ice crystals. the size Whenof ice thecrystals. crushing When effect the is crushing equivalent effect to theis equivalent agglomeration to the and Ostwaldagglomeration ripening and effect, Ostwald the average ripening particle effect, the size average of ice crystalsparticle size is generally of ice crystals not changing is generally with not the stirringchanging rate. with the stirring rate.

Figure 10. Effects of stirring rate on average particle size of ice crystals. Figure 10. Effects of stirring rate on average particle size of ice crystals. The average particle size of ice crystals was observed in 1%, 3% and 5% ethylene glycol aqueous solutionThe average respectively particle and size the of results ice crystals are shown was in observed Figure 11. in 1%,The 3%average and 5%particle ethylene size of glycol ice crystals aqueous solutiondecreased respectively significantly and alongside the results the are initial shown concentration in Figure 11 of. Theethylene average glycol. particle The characteristics size of ice crystals of the particle size of ice crystals in the ice slurry prepared by the scraped-surface method have been addressed in previous works, and the particle size of ice crystals was also found to decrease as concentration increased. This phenomenon can be explained as follows: the addition of ethylene

Crystals 2017, 7, 128 11 of 13 decreased signiﬁcantly alongside the initial concentration of ethylene glycol. The characteristics of the particle size of ice crystals in the ice slurry prepared by the scraped-surface method have been

Crystalsaddressed 2017, 7 in, 128 previous works, and the particle size of ice crystals was also found to decrease11 of as13 concentration increased. This phenomenon can be explained as follows: the addition of ethylene glycol reduces the diffusion coefficient coefﬁcient of water molecules in the aqueous solution. At At the the same same time, time, the hydroxyl groups contained in the ethylene glyc glycolol molecule can form hydrogen bonds with the water moleculesmolecules andand break break the the hydrogen hydrogen bonds bonds between between water water molecules. molecules. In this In way,this ethyleneway, ethylene glycol glycolcan inhibit can inhibit the growth the growth of ice crystals of ice crystals to a certain to a ce extentrtain andextent reﬁne and the refine particles. the particles. The greater The thegreater content the contentof ethylene of ethylene glycol, theglycol, more the pronounced more pronounced the inhibitory the inhibitory effect is. effect is.

Figure 11. EffectsEffects of of initial initial concentration on av averageerage particle size of ice crystals.

5. Conclusions 5. Conclusions A systematic investigation is carried out to determine the thermodynamics and kinetics A systematic investigation is carried out to determine the thermodynamics and kinetics behavior behavior of ice slurry crystallization in vacuum. The following conclusions can be drawn from the of ice slurry crystallization in vacuum. The following conclusions can be drawn from the experiments: experiments: (1) (1)A newA new term, term, “supercooling “supercooling crystallization crystallization pressure pressure difference” difference” oror ∆Δpp,, waswas establishedestablished to characterizecharacterize the supercooling the supercooling degree. degree. In addition, In addition, the effect the of effectseveral of parameters several parameters including including additive concentration,additive concentration,cooling rate, coolingand stirring rate, andrate stirring on the rate instantaneous on the instantaneous supercooling supercooling degree during degree crystalduring nucleation crystal under nucleation vacuum under environment vacuum environment were studied. were These studied. results These show results that show the thatstirring the rate hasstirring little rateeffect has on little supercooling, effect on supercooling,the increase of the cooling increase rate of causes cooling the rate increase causes of the supercooling increase of degree,supercooling and increasing degree, initial and concentration increasing initial can reduce concentration the supercooling can reduce degree. the supercooling degree. (2) (2)The The kinetic kinetic mechanism mechanism underlyingunderlying the nucleation nucleation process process of ofice icecrystals crystals was wasillustrated. illustrated. The equationsThe equationsof nucleati ofon nucleation rate and growth rate and rate growth were established. rate were established. The study found The study that foundthe increase that the of suspensionincrease density of suspension and stirring density rate andcould stirring not impr rateove could the nucleation not improve of theice nucleationcrystals. Meanwhile, of ice crystals. the opticalMeanwhile, method of theaccele opticalrating method nucleation of accelerating and growth nucleation is to increase and the growth degree is toof increasesupercooling. the degree (3)of supercooling.Stirring rate has a negligible effect on the average particle size of ice crystals. Ethylene glycol can(3) inhibitStirring the rate growth has a of negligible crystal to effect a certain on the extent average and particle reduce sizethe average of ice crystals. particle Ethylene size. glycol can Summarizing,inhibit the growth the ofresearch crystal toof athis certain article extent reve andals reducethe supercooling the average particlecondition size. of ice slurry crystallization and the rules of nucleation and growth of ice crystals, as well as enriches the morphologySummarizing, study of the ice researchcrystals. ofTherefore, this article this revealsstudy will the be supercooling helpful in the condition design and of control ice slurry of industrialcrystallization ice making. and the rules of nucleation and growth of ice crystals, as well as enriches the morphology study of ice crystals. Therefore, this study will be helpful in the design and control of industrial Acknowledgments:ice making. We gratefully acknowledge the support of National Natural Science Foundation of China (Nos. J1103303 and 51602054) and Program for Young Teacher Education and Research of Fujian Province (No. JA14053).

Author Contributions: Xi Liu conceived and designed the experiments; Kunyu Zhuang and Zheng Zhang performed the experiments; Shi Lin analyzed the data; Xi Liu wrote the paper; Xuelai Li modified the article.

Conflicts of Interest: The authors declare no conflict of interest.

Crystals 2017, 7, 128 12 of 13

Acknowledgments: We gratefully acknowledge the support of National Natural Science Foundation of China (Nos. J1103303 and 51602054) and Program for Young Teacher Education and Research of Fujian Province (No. JA14053). Author Contributions: Xi Liu conceived and designed the experiments; Kunyu Zhuang and Zheng Zhang performed the experiments; Shi Lin analyzed the data; Xi Liu wrote the paper; Xuelai Li modified the article. Conflicts of Interest: The authors declare no conflict of interest.

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