Crystal networks, partial coalescence, and rheological properties of milk fat fraction model systems

This study aimed to investigate the crystal network of bulk milk fat fractions and the partial coalescence, and the rheological properties of their oil-in-water (O/W) emulsions. Different milk fat fraction model systems were compared for their physicochemical properties, crystallization kinetics, and fat crystal networks across a range of temperatures. The extent of partial coalescence and rheological properties of the O/W emulsion prepared by different milk fat fractions were further analyzed. The results demonstrated that the ratio be-tween saturated fatty acids (SFA) and unsaturated fatty acids and triacylglycerides (TAG) influenced the melting thermal behaviors, solid fat contents (SFC), and crystal networks of various milk fat fractions, which in turn influenced the partial coalescence and rheological characteristics of their O/W emulsions. Moreover, an excellent fit of the trend line confirmed that hardness increased exponentially with SFC. Trisaturated TAG in fractions with high melting points (HMF) such as milk fat fraction MF45, whose clarification temperature was 45°C, enriched long-chain SFA (saturated: unsaturated fatty acid = 2.2:1). We found that MF45 achieved higher SFC and hardness in the range of 0 to 40°C and, ultimately, formed a well-defined microstructural network with thick, rod-like crystals. Further, TAG in fractions with low melting points (LMF) such as MF10, whose clarification temperature was 10°C, were enriched with short-chain and unsaturated fatty acids (saturated: unsaturated fatty acid = 1.5:1), and a disordered crystal network in MF10, composed of randomly arranged, translucent platelets, was detected. Although fat globules of HMF and LMF were stabilized against coalescence, this could be attributed to a variety of mechanisms involving SFC, liquid fat, protective film around the fat globule, and minor lipids. According to the rheological profiles, all O/W emulsions exhibited weak viscoelastic


INTRODUCTION
Due to its broad chemical composition, milk fat is one of the most complex edible fats, used in a wide range of bakery and confectionery products (Méndez-Velasco and Goff, 2011;Nicholson et al, 2022).The majority of milk fat is composed of triacylglycerides (TAG), which account for more than 98% of total milk fat.Milk fat contains over 400 fatty acids (FA), from which thousands of TAG species can be formed through random combinations (Jensen et al., 1991;Wang et al., 2019;Staniewski et al., 2021).Therefore, milk fat has a broad melting and crystallization temperature range, typically between −40 and 40°C.The complex thermal and crystallization behavior influences a broad range of physiochemical and rheological properties of milk fat-based products (Ramel and Marangoni, 2017).By separating milk fat into fractions with varying melting points, as determined by the distribution of FA in TAG molecules, the range of applications for milk fat can be expanded.Multistep dry fractionation has led to significant changes in the thermal profiles of the obtained fractions, which can be used to provide structure and particular functionality in a variety of food applications, including baked goods, cold-spreadable butter, pourable frying oils, cocoa butter replacement in chocolate and ice cream, and more (Hartel, 1996).The use of fractions with high melting points (HMF) to prevent bloom formation in chocolate has been clearly approved (Ramel and Marangoni, 2016).
It is therefore important to characterize the crystal networks, partial coalescence, and rheological properties of various fractions at different crystallization temperatures to be able to create a database of different crystallization behaviors and physicochemical properties for different product applications.
The development of fat crystals is a highly complex nonlinear process (i.e., polymorphic transformations; Sato, 1993), and the various polymorphic forms have distinct differences in crystal structure and temperature resistance (Lopez and Ollivon, 2009;Chen et al., 2021).Therefore, to create plastic fats with hard solid or gel-like properties, the formation of a fat crystal network is essential.This network can be considered a colloidal aggregate and represented as an aggregate of fat crystals.The partial coalescence of fat globules may be partially explained by the behavior of fat crystals (Thiel, 2020).Fat crystallization behavior in oil-inwater (O/W) emulsions has been found to depend on the ratio of palmitic acid to oleic acid (Tanaka et al., 2010).High melting-point FA that were abundant in the fat phase crystallized near the interface, whereas low melting-point FA accumulated in the liquid state closer to the globule's center (Miura et al., 2002).Coalescence generally necessitates the protrusion of large crystals to the globule's exterior, whereas small crystals contained within the globule do not easily initiate globule destabilization (Munk and Andersen, 2015).To completely comprehend and eventually anticipate the macroscopic properties of plastic fats, it is necessary to characterize and define the different levels of the structure and their relationships to the macroscopic properties (Marangoni and Tang, 2008).
The rheological properties of milk fat are significantly influenced by TAG and FA composition and the crystallization/melting temperature, which must be maintained throughout the production (Omar et al., 2015).By measuring the storage modulus (G′) and loss modulus (Gʺ) at a fixed temperature or time, smallamplitude oscillatory rheology can be used to ascertain the rheological properties without interfering with the formation of a fat network during crystallization.This demonstrates the correlation between solid-like and liquid-like properties (Wright et al., 2001).Solidification kinetics of fat systems have been studied using small-amplitude oscillatory rheology, and the effects of crystallization conditions can be compared using G′ values.A high-equilibrium G′ corresponds to a final crystal network with high hardness (Rigolle et al., 2015).Numerous attempts have been made to determine the relationship between the crystal networks and their texture properties.Still, it is crucial to continue developing and refining the relationship between crystal networks, partial coalescence, and rheological properties.
In this study, the crystallization kinetics, crystal network, and texture properties of milk fat fractions subjected to various temperatures were systematically evaluated in accordance with their chemical composition and thermal properties.The relationships between solid fat content (SFC) and log Gʹ, as well as between SFC and hardness, were established to further investigate the influence mechanisms under microstructure, partial coalescence, and rheology properties of milk fat fractions in O/W emulsion.This will help us comprehend the intricate crystallization behavior of milk fat-based products.

MATERIALS AND METHODS
Because no human or animal subjects were used, this analysis did not require approval by an Institutional Animal Care and Use Committee or Institutional Review Board.

Materials
Unfractionated milk fat (UMF) was obtained from Grassland Dairy (Greenwood, WI), and milk fat fractions with different melting points at 99.96 wt/wt were obtained from Nutrical (Mexico City, Mexico).All other reagents and solvents were of analytical or chromatographic grade to suit the analytical requirements.
The chemical compositions of the multiple milk fat fractions are summarized in Table 1.The FA species were identified using the retention time of FAME standard, prepared according to AOCS Official Method Ce 2-66 (AOCS, 2017) and then analyzed using GC equipped with a flame ionization detector (Agilent) and a DB-WAX capillary column (30 m × 0.25 mm × 0.25 μm; Agilent Technologies, Santa Clara, CA).The injection port and detector temperatures were both set at 200°C.The column was first heated to 40°C, maintained for 3 min, and then programmed at 5°C/ min to reach 120°C.By comparing the retention times of FAME peaks against those of a standard FAME mixture, FAME peaks were identified.
The TAG were separated using ultra HPLC with a Waters 1525 binary pump (Milford, MA).An API 4500 QTRAP mass spectrometer (Applied Biosystems, MDS SCIEX) with an electrospray ion source was connected to the ultra HPLC system for MS analysis.All experiments were conducted in positive ionization mode.The peak areas of individual TAG analyzed with the QTRAP 4500 system (Applied Biosystems SCIEX, Framingham, MA) were collected and used to calculate the concentrations (Wang et al., 2019).Measurements were taken from each triplicate sample.Based on their clarification temperatures (Figure 1A), the 7 milk fat fractions were categorized as MF5, MF10, MF20, and so on (e.g., MF5 is the milk fat fraction with a clarification temperature of 5°C).Fractions with low melting points (LMF) comprised MF5 and MF10; fractions with medium melting points (MMF) comprised MF20, MF25,and MF30;and HMF comprised MF40 and MF45.

O/W Emulsion Preparation
Various milk fat fractions and water phases (deionized water with 0.4 wt/wt xanthan gum) were heated to 80°C in a water bath to constitute the O/W emulsions.The O/W emulsion was homogenized using a mixer homogenizer (Omni International) at 4,000 rpm for 2 min.The final emulsion consisted of 36% wt/wt bulk fat.The O/W emulsions were aged for 24 h at 4°C before being measured and analyzed.Emulsions were made in triplicate for each experimental parameter investigated.

Characterization of Bulk Milk Fat
Melting Thermal Behavior.The melting behavior of the milk fat fractions was analyzed using differential scanning calorimetry (DSC; Perkin Elmer Inc., Shelton, CT).Each sample (10 μg) was sealed in hermetic alodine-aluminum pans (Perkin Elmer Inc.), and an empty pan was used as a reference.The DSC sample pans were successively subjected to the following thermal treatments: (1) heating to 80°C and holding for 2 min to ensure complete melting, (2) maintaining the sample at −15°C for 2 min, and (3) heating at 5°C/ min to 50°C.The DSC was calibrated with indium at a heating rate of 5°C/min.Nitrogen was used to purge the system (Tomaszewska-Gras, 2013).Measurements were performed on each triplicate sample.
Solid Fat Content.The SFC of the different bulk milk fat fractions were determined using time-domain nuclear magnetic resonance on the Bruker Minispec following the AOCS Official Method Cd 16b-93 (Billerica, MA; AOCS, 2022).The samples were weighed into nuclear magnetic resonance tubes and melted for 30 min at 80°C, held for 90 min at 0°C, and maintained for 30 min at each chosen measurement temperature (5, 10, 15, 20, 25, 30, 45, and 40°C).Measurements were performed on each triplicate sample (Wang et al., 2021).
Crystallization kinetics of the different bulk milk fat fractions were analyzed at 4 different isothermal crystallization temperatures: 5, 15, 25, and 35°C (Meng et al., 2011).Solid fat content readings were taken at regular intervals.Data were analyzed using Origin 8.0 (OriginLab Corporation).Isothermal Avrami kinetics addresses the entire crystallization procedure, including nucleation and growth (Wang et al., 2019).The Avrami equation is given as follows: in which f is the SFC amount at time t during crystallization; K is the crystallization rate constant; n is the Avrami exponent (a constant); K and n are calculated from the intercept and slope obtained by plotting ln[− ln(1 − f)] against lnt.The entire rate of crystallization is given by Equation [2]: where t 1/2 is the half-time of crystallization, the time required to complete half of the crystallization process.
Hardness.The hardness of the different bulk milk fat fractions was measured using a TA-XT2 texture analyzer (Texture Technologies Corp.) equipped with an aluminum cylinder probe (4-mm diameter).Ten grams of sample was placed in glass containers and heated to 80°C for 30 min to ensure complete melting.The samples were then immediately transferred to temperature-controlled water baths and stored for 24 h.The distance and speed of penetration were 5 mm and 1 mm/s, respectively.Before each measurement on stored samples, the probe was pre-cooled in the refrigerator (Watanabe et al., 2021).Measurements were taken from each triplicate sample.
Fat Crystal Network Microstructure.Observing the microstructure of the fat crystal network required a Nikon Eclipse FN1 microscope (Melville, NY) with a polarized light magnification of 20× (Nikon DS-Fi2) and a Digital Microinjection System (Sutter Instrument Co., Novato, CA; Tang and Marangoni, 2006).Bulk milk fat fractions and O/W emulsions were melted (80°C, 30 min) and placed on microscope slides.On each glass slide, without a coverslip, these samples were allowed to cool and crystallize freely so that the structure of the fat crystal network could be observed without confinement effects.The slides were chilled for 1 h at 5°C in a refrigerator and then allowed to crystallize for 48 h at the same temperature.The liquid phase appeared black, and the solid phase appeared white in polarized light.Controlling the temperature (5, 15, 25,  and 35°C) was a specially constructed plate equipped with a cold-heat system (Linkam THMSG600).Observations were performed on each triplicate sample.
Temperature Sweep Rheology.On a Discovery HR-2 hybrid rheometer (TA Instruments, New Castle, DE), bulk fat fractions were transferred to the crosshatched plate.After trimming any unnecessary sample, the upper parallel plate (20 mm in diameter) was slowly lowered onto the sample.To determine the elastic (G′) moduli of bulk milk fat fractions in the linear viscoelastic region, small deformation rheological tests were conducted from 5°C to 45°C at a rate of 0.5°C/ min and a strain of 0.1% (linear viscoelastic region).The G′ and loss (Gʺ) moduli were measured at 10.0 rad/s (Freire, 2020).Measurements were taken on each triplicate sample.
Fat Globule Partial Coalescence.Micromanipulation was used to study the coalescence behavior of different milk fat fraction model systems by manually bringing 2 fat globules into contact with each other.The micromanipulation apparatus included a Nikon Eclipse FN1 microscope (Melville, NY) and a Nikon DS-Fi2 camera combined with a digital microinjection system (Sutter Instrument Co., Novato, CA).Fire-polished borosilicate glass capillary tubes were used to make micromanipulator tips (10 cm in length).Emulsions were made from various milk fat fractions and placed in a glass petri dish that fit underneath the microscope lens.The 2 pipettes were lowered into the petri dish, where they could be moved in the X, Y, and Z directions using the Sutter MPC-200 multi-manipulator controller.The manipulators were used to attach the fat globules (about 50 μm in diameter) to the pipette tips via the microinjection unit, and the fat globules were then gently brought into contact with each other to allow coalescence.Nikon NIS Elements software was used to monitor all events in real time (Wang et al., 2021).Observations were performed in triplicate.
Interfacial Tension.The interfacial tension between the oil and water phases was measured using the pendant drop method on a ThetaLite optical tensiometer (Biolin Scientific, Västra Frölunda, Sweden).The tensiometer was equipped with OneAttension software, which recorded real-time interfacial tension measurements using the Young-Laplace equation (Thiel et al., 2016).The melted bulk fat fractions were placed in cuvettes.Then, a syringe containing the aqueous phase was used to inject a droplet into the oil-filled cuvette, from which the interfacial tension was measured in triplicate for each system.
Apparent Viscosity.The apparent viscosities of O/W emulsions with different milk fat fractions at 5, 15, 25, and 35°C were measured using a Discovery HR-2 hybrid TA Instruments rheometer (New Castle, DE) equipped with bob and cup geometry.The shear rate was linearly increased from 0.1 s −1 to 300 s −1 , yielding 20 viscosity data points.Before measurement, all samples were equilibrated for 60 s (Wang et al., 2021).Measurements were taken on each triplicate sample.
Data Analysis.One-way ANOVA was performed using IBM SPSS 21 (IBM SPSS Inc., Chicago, IL).A P < 0.05 difference was considered significant.

Melting Thermal Behavior of Bulk Fat Fractions
By analyzing the melting thermal and hardness profiles, it is possible to determine the suitability of milk fat fractions for a particular application (Geary and Hartel, 2017;Nguyen et al., 2020).The melting thermograms in Figure 1A show that the peak temperature and the number of endotherm peaks varied with the thermal properties and chemical compositions of the different milk fractions.It is evident that the clarification temperature gradually shifted toward a higher temperature from MF5 to MF45, and the melting limits became much broader and skewed, developing a pronounced leading shoulder on the right side.The higher clarification temperature could be attributed to an increase in the trisaturated (S3) TAG or monounsaturated TAG.Only a fully resolved peak was present in MF5 and MF10, which might indicate the removal of high-melting TAG.The melting thermogram of LMF and HMF illustrates that their endotherm represented clarification temperatures of 6.68 ± 1.12°C and 13.04 ± 2.05°C for MF5 and MF10, and 41.16 ± 1.05°C and 43.99 ± 2.01°C for MF40 and MF45, respectively.Both MF5 and MF10 are rich in short-chain and unsaturated FA and have lower melting points than MF40 and MF45 (Table 1), which enriched the long-chain and SFA and the S3 TAG.
Figure 1B and C show the results of SFC and hardness tests conducted at temperatures ranging from 0 to 45°C.We found that MF45 displayed higher heat resistance (SFC between 20 and 30°C) than other fractions.The SFC values of all fractions, with the exception of MF5 and MF10, were between 50 and 70% at 0°C and decreased almost linearly between 5 and 15°C.Between 15 and 40°C, the SFC profiles of UMF appeared concave or inwardly inflected.Figure 1C shows that hardness decreased gradually with increasing temperature, with a steep decrease between 15 and 25°C.All fractions displayed varying hardness tendencies; MF5 had the lowest hardness at 0°C, measuring 40.07 ± 1.40 g, whereas MF10 was 4 times harder (191.27 ± 4.85 g).In addition, MF40 and MF45 were both greater than 800 g at the same temperature.At 25°C and above, no other hardness values aside from MF40 and MF45 were measured, indicating that these fractions lacked heat resistance.Although some solid fat remained in MF25 and MF30 at 25°C (Figure 1B), they were too soft to determine their hardness, indicating that their crystal networks melted at room temperature.Both MF40 and MF45 appeared to be in a similar situation, as the lowest temperature at which no hardness was detected was 5°C lower than the temperature at which the SFC was approximately 0, indicating that solid fat remained in the bulk fat system even though the fat crystal network was no longer intact and unable to withstand mechanical stress.
Furthermore, laboratory measurements revealed a direct correlation between SFC and hardness.Figure 1D shows the correlation between hardness values and SFC, which could represent various typical network structures.As expected, an excellent fit (R 2 = 0.98) of the trend line of the experimental data confirmed that hardness increased with SFC, which is consistent with Wright et al. (2001) and Narine and Humphrey (2004).With an increase in SFC, hardness increases exponentially.This variation in hardness (within the increasing trend) is due to variations in structures formed during crystallization, as 2 fat samples with the same SFC value can have very different crystal structures and microstructures, as shown in Figure 1B and C and Figure 4. We found that UMF and MF40 (SFC around 60%), as well as MF25 and MF30 (SFC around 40%), had similar SFC values at 5°C, respectively, but their microstructures were different.The microstructural characteristics of polymorphism, crystal shape, bridge type, and relative strength of intracrystalline connections and intercrystalline links (Shi et al., 2005) all play roles in the differences in textural properties for the various fractions of milk fat.

Crystallization Kinetics
The isothermal crystallization process is critical for predicting fat functionality at various manufacturing phases and reveals the plasticity of the fat (Stahl et al., 2017).Figure 2 shows the isothermal crystallization curves for different milk fat fractions at 5, 15, 25, and 35°C, respectively.All fractions first crystallized and then displayed equilibrium with increased time.We found that MF45 had the highest SFC at any temperature, whereas MF5 was the lowest.Other fractions and UMF exhibited hyperbolic curves against time at 5°C, and their SFC ranged from 50 to 80%.Namely, crystallization was rapid, followed by equilibrium in SFC.Only MF40 and MF45 had hyperbolic curves at 15°C, and their SFC was 50 to 60%.In contrast, MF25 and MF30 showed sigmoidal curves, with an induction time without fat crystallization followed by faster crystallization (Herrera et al., 1999;Meng et al., 2011).However, as the temperature increased to 25°C, there were no remaining crystals other than MF40, MF45, and UMF, and MF40 and MF45 with 40% to 50% SFC maintained hyperbolic curves, and UMF with 20% SFC maintained a sigmoidal curve, respectively.At 35°C, all fractions melted completely (data not shown), except for MF45, which contained a minimal number of crystals and an SFC below 30%.
Their chemical composition readily explains the distinctions in isothermal crystallization between the various fractions (Table 1).The LMF (MF5 and MF10) had higher concentrations of unsaturated and shortchain SFA with lower melting points, and the ratio between saturated and unsaturated FA was 1.4 to 1.5:1.In contrast, the melting points of long-chain SFA are higher, and these were abundant in HMF (MF40 and MF45), with ratios between saturated and unsaturated FA of 2.1 to 2.2:1.Additionally, MF5 and MF10 were enriched in unsaturated TAG, whereas MF40 and MF45 contained higher concentrations of S3 TAG.Therefore, their SFC was higher than that of UMF, indicating that fractionation significantly altered the chemical composition, hence melting behavior, resulting in significant changes in the physical properties.These results corresponded to trends observed in earlier studies (Tomaszewska-Gras, 2013;Wang et al., 2019).
The crystallization kinetics of multiple milk fat fractions are clarified by fitting isothermal curves to the Avrami model (Eq.[1] and [2]) using a nonlinear regression package.Table 2 shows the Avrami exponent (n), Avrami constant (K), and the half-time of crystallization (t 1/2 ) for all fractions at various temperatures.Some isothermal curves were omitted because their crystallization kinetics at the specific temperatures were too slow to provide an acceptable fit (curves in Figures 2B, C, and D).The equation fitted the data well throughout the entire isothermal crystallization range (R 2 = 0.983-0.998 in all cases).
At the above-mentioned critical temperatures, the Avrami model predicts different crystal nucleation as instantaneous or sporadic and growth mechanisms that occur either as rods, disks, or spherulites based on variations in the n values (Avrami, 1940(Avrami, , 1941;;Cheong et al., 2009;Porter et al., 2009;Ergun et al., 2015).In Table 2, at 5°C, n values ranged from 0.12 ± 0.01 (MF45) to 0.52 ± 0.01 (MF5), with K values ranging Wang et al.: CRYSTAL NETWORK OF BULK MILK FAT FRACTIONS from 0.01 ± 0.00 (MF5) to 0.68 ± 0.01 (MF45), indicating a distinct fat crystallization mechanism.Generally, higher n and lower K values are associated with a slower crystallization rate and a nucleation process with a longer induction time.However, this could result in larger but fewer crystals (Meng et al., 2011;Fredrick et al., 2013).Not surprisingly, the K values of the HMF (MF40 and MF45) were greater (P < 0.05) than those of the other fractions at the same temperature, indicating that crystallization occurred more rapidly with a higher SFC.As the temperature increased, the n value for MF45 increased from 0.12 ± 0.01 (5°C) to 2.16 ± 0.23 (35°C), indicating that fat crystals grew from rodlike form into the spherulitic form at varying degrees of supercooling.The similarity between the UMF and MF30 Avrami exponents at 5°C suggests similar growth modes.
The t 1/2 value represents the time required to complete half of the crystallization process (Meng et al., 2011;Wang et al., 2019).Our study discovered that higher temperatures caused t 1/2 values to be significantly higher.Consequently, the crystallization curves appeared more sigmoidal.At 5°C, the t 1/2 value of MF45 was 1.00 ± 0.01 min, based on a hyperbolic curve, whereas at 35°C the t 1/2 value was approximately 14.80 ± 0.23 min, based on a sigmoidal curve (Figure 2).The increase in t 1/2 as a function of increased temperatures reflected the decrease in K under these conditions.Similar to MF40 and MF45, the crystallization behavior of HMF improved at higher temperatures.

Fat Crystal Network
The microstructure of the fat crystal network of various milk fat fractions was studied using polarized light microscopy.Micrographs of milk fat fractions at different temperatures showed strikingly different crystal network characteristics (Figure 3).Milk fat fractions formed crystal networks of polycrystalline clusters.Some fractions are not shown because they had almost completely melted and were difficult to observe under the microscope.
The micrographs show that as the temperature increased, the size and number of these crystal clusters decreased until they separated from their nearest neighbors.The network would collapse, and the cluster size would decrease as the crystals continued to melt.At 5°C, the clusters of MF45 were thicker and displayed a fine, rod-like granular texture, in contrast to the crystals observed at 35°C, which showed more numerous small clusters.This substantial alteration in the "melting structure" of the fat crystal network should also account for the dramatic decrease in hardness at 35°C (Figure 1C).According to X-ray diffraction analysis (data not shown), these crystals are mainly β′ form.
We found that MF45 showed cluster combinations composed of an aggregation of smaller crystalline microstructural elements and a dense core surrounded by less densely packed crystals at 5°C.In comparison, the clusters in MF40 decreased in size and increased in number.The fat crystal networks of UMF and MF10 consisted of randomly arranged, translucent platelets with a diameter of approximately 10 μm that may be mainly α form (X-ray diffraction data not shown).In contrast to the other fractions, MF20 showed large and plate-like formed networks, whereas MF5 had almost no crystals.
Notable differences exist between the distribution patterns of crystals and clusters in the various milk fat fractions, due to the TAG types and content.As a result, the morphology and distribution of the clusters at the micro-scale level will change over time.The highly ordered crystal stacks formed, as in MF45 enriched in S3 and monounsaturated TAG, resulted in firmer, rod-like crystal nuclei.Then, initial nucleation centers grew into larger crystal clusters.The clusters then aggregated in a mass-and heat transfer-limited aggregation process to form a microstructural network with a defined structural and spatial distribution of fat crystals.In contrast, MF20 was composed of more monosaturated-di-unsaturated and tri-unsaturated TAG, and as a result, its crystal network was weaker and more plate-like.
Figure 4 shows the micrographs of milk fat fractions in O/W emulsion at different temperatures to better understand the fat crystal network structure state under various conditions.At 5°C, the fat globules of each fraction exhibited varying degrees of crystallization, and the crystallization was strong and structured, as shown in Figure 4.The fat globules of MF45 with the highest degree of crystallization were bright, welldefined, homogeneously distributed, and of uniform size.The MF40 fat globules were relatively smaller, and crystals did not completely fill the space within the fat globules.The MF30 fat globules contained only a few sporadic crystals, whereas MF25 fat globule crystals were barely discernible.Due to the unsaturated FA in the molecular structure of the tri-unsaturated and monosaturated-di-unsaturated TAG being abundant in MF5 and MF10, packing into a crystalline structure is extremely difficult.Hence, even at 5°C, no discrete crystal network in the O/W emulsion was observed.
With increasing temperature, UMF, MF25, and MF30 fat globules melted more readily than MF40 and MF45.At 25°C, fat globule partial coalescence or coalescence appeared in MF25, MF30, and MF40, and fat globule aggregates appeared in MF45.Only small crystals remained in UMF and MF25.At 35°C, we observed no visible crystals in UMF, MF25, and MF30.The MF45 fat globules coalesced poorly, with no fat globule profile.

Rheology Properties: Temperature Sweep
The storage modulus (G′) is used to represent crystallization/melting behavior and subsequent aggrega- tion of milk fat crystals.Figure 5A shows the G′ as a function of temperature from 5°C to 40°C of different milk fat fraction systems.
The G′ values of milk fat fractions are a measure of their elasticity, or solid-like character, indicating the ability to store energy while maintaining structural integrity (Munk et al., 2013).The G′ values of each sample decreased with increasing temperature, due to melting behavior and crystal network collapse.Loss modulus (Gʺ), a measure of the liquid-like character of milk fat and the ability to dissipate energy, displayed the same trends with increasing temperature (data not shown), and Gʺ values of all fractions were lower than G′, indicating that gel-like properties (crystal networks) dominated the viscoelastic behavior.The network of fat crystals contained both liquid oil and semisolid (i.e.,    partially crystallized) fat.The relative amount of liquid oil distributed to the surface area of crystals influenced the macroscopic rheological characteristics of the fat crystal network.When the liquid-filled space was large, there was less resistance (low G′) to movement, and the crystal network was flexible and soft.All curves, except that of MF5, exhibited 3-step melting behavior; that is, an approximate plateau between −5°C and the critical temperature of each fraction (from 0.5°C for MF10 to 20.5°C for MF45), followed by a rapid decrease as the temperature increased above the critical temperature, indicating that the crystal network collapsed as the fat fractions melted.Finally, the curves flattened out, indicating that the network structure disintegrated to the point where it ceased to change.
The G′ values of MF5 and MF10 were lower than those of other fractions at lower temperatures (0 to −5°C), indicating that their crystal networks were weaker even at these temperatures.At the plateau, the G′ values of UMF, MF40, and MF45 at around 1 × 10 6 Pa, were greater than those of other samples at the same temperature, indicating that the large and rigid crystals strengthen the networks more effectively, which were consistent with the microstructures (Figures 3 and 4).Because milk fat is a mixture of multiple melting fractions, the curve slope of UMF was the largest, indicating that the melting range of UMF was wider, which was consistent with the SFC curve (Figure 1B).From plots of G′ against SFC (Figure 5B) for the bulk fat fractions studied, it was obvious that a good exponential relationship (R 2 = 0.910) existed between log G′ and SFC.The SFC was found to increase faster when log G′ was greater, indicating that the highly organized and more tightly packed fat crystal network achieved higher SFC.

Partial Coalescence
The partial coalescence of fat globules is a type of emulsion instability that shares some characteristics with flocculation but is not the same as that process.Partial coalescence is the process by which 2 fat globules merge into 1 larger fat globule and their original structure disappears when the interfacial and elastic energy balance each other at an intermediate state (Thiel et al., 2016).The chemical composition, SFC, mechanical shear, and fat globule membrane structure all influence the degree of partial coalescence.Micromanipulation methods can be used to observe the entire coalescence process, from the initial contact of 2 fat globules to a stabilized end structure (Thiel et al., 2016;Wang et al., 2021).Each O/W emulsion was formulated with different milk fat fractions (except UMF), selected to illustrate the varying degrees of coalescence between 2 fat globules, as shown in Figure 6.
Except for MF25 and MF30, total stability against coalescence was evident in the UMF and other bulk milk fat fractions.Namely, the 2 fat globules retained their original structure when they were brought into contact with each other.The fat globules of UMF, MF40, and MF45 were covered in crystals, and their SFC were 14.31 ± 2.43%, 32.59 ± 2.07%, and 38.29 ± 1.11% (Figure 1B), respectively.As a result of the high SFC, these 2 fat globules stuck to each other and stayed that way, and the fat globules were so rigid that there was not enough liquid fat to wet the O/W surface, which ultimately stabilized them against coalescence.Partial coalescence occurred when the dispersed fat had intermediate SFC (10-50% SFC), indicating sufficient liquid fat (Boode et al., 1993).Based on completely solid fat, coalescence would not be present (Munk and Andersen, 2015).
However, even when excessive force was applied, the fat globules of MF5, MF10, and MF20 did not begin to coalesce, despite extreme shape deformation, and then returned to their original spherical shape as the force was removed.This is consistent with the findings of Thiel et al. (2016), who demonstrated that the formation of a thick film around a droplet of methylcellulose stabilized the fat globule against coalescence.Xanthan gum also seems to be an excellent stabilizer, forming a protective film around the fat globule when almost no crystals were present, thus preventing partial coales- cence at the O/W interface.Another reason could be that LMF have more minor lipids such as diacylglycerols (DAG), particularly 1,2-DAG, monoacylglycerols, and cholesterol (Sherbon, 1974;Metin, 1997).Minor lipids can act as emulsifiers, absorbing into the surface of fat globules to form a protective barrier and reducing the interfacial tension of the fat globule membrane to prevent coalescence (Wright et al., 2000).As expected, Figure 7 showed that the interfacial tension of LMF (MF5 and MF10) was much lower than that of MMF and HMF (P < 0.05).Further, MF40 and MF45 had the highest interfacial tension.Apparently, surfaceactive species seem to be concentrated in the LMF.
It is evident that the partial coalescence of 2 fat globules became pronounced for MF25 and MF30 when SFC was less than 10% (Figure 1B).Due to the partial crystallization of the fat globules and the ability of the crystallization spines on the fat globule membrane to pass through the neighboring fat globules, the liquid could wet the neighboring fat globules, allowing them to coalesce partially.In this case, HMF and could not coalesce when SFC >15% or <1% at room temper-ature, respectively, whereas MMF partially coalesced when SFC was around 10%.

Apparent Viscosity
At critical shear rates, semisolid fat, which includes milk fat-based products such as whipping cream and ice cream, is substantially shear-thinning (Stokes and Telford, 2004).Figure 8 shows the apparent viscosity curves for O/W emulsion prepared with various milk fat fractions as a function of shear rate.
In Figure 8, as expected, as the shear rate increased from 0.01 s −1 to 300 s −1 , the apparent viscosity decreased in all fractions, indicating shear-thinning behavior.The increased shear rate distorted the interaction between the fat crystals, resulting in disruption and a decrease in apparent viscosity.The apparent viscosity of all fractions decreased with temperature, likely due to weaker fat crystal networks.For example, UMF viscosity was 10 Pa•s at 5°C, 1 Pa•s at 25°C, and 0.1 Pa•s at 35°C.At 5°C, no trends appeared in the viscosity curves of MF40 and MF45, possibly because the crystal network was too solid to display the viscosity property.At 15°C, the more stable crystal network resulted in higher apparent viscosity, as the fat crystals of MF40 and MF45 were firmer and spherulitic, and their SFC was higher, whereas MF5 and MF10 had the lowest apparent viscosity of all fractions, possibly because of its weaker networks.This finding confirms that greater shear-thinning behavior and viscosity occurred in firmer crystal networks than in weaker ones.

CONCLUSIONS
This study deepened our understanding of the fat crystal networks, rheological properties, and partial coalescence of multiple milk fat fractions at varying temperatures.Because of differences in chemical composition, noticeable differences occurred in crystallization kinetics, SFC, hardness, and morphology of the fat network, resulting in differences in the extent of partial coalescence and rheological properties of the O/W emulsion.We found that HMF with more SFA and S3 TAG crystallized faster, forming well-distributed, rod-like granular crystals, and crystals remained in the O/W emulsion to preserve the shape integrity of fat globules even at higher temperatures (35°C).The G′ values and apparent viscosity of O/W emulsions made by HMF were higher than those of other fractions because the more "gel-like" and highly organized crystal network with higher SFC had relatively higher hardness.When the SFC was greater than 15% at room temperature, no partial coalescence of the fat globule of HMF occurred.This study improves understanding and control of the physicochemical properties of milk fats and fat-based products, as well as data support for raw material fat selection and new product development.

Figure 1 .
Figure 1.Differential scanning calorimetric melting thermograms (A), solid fat content (SFC, B), hardness profiles of milk fat fractions (C), and the relationship between SFC and hardness (D).Tc = clarification temperature (final melting temperature).UMF = unfractionated milk fat; MF = milk fat fraction, with clarification temperature (e.g., MF5 is milk fat fraction with clarification temperature of 5°C).Error bars represent the SD of triplicate experiments.Endo: endotherm.

Figure 5 .
Figure 5. Storage modulus (G′) versus temperature of different milk fat fraction systems (A) and relationship between G′ and solid fat content (B).The inflection point, marked in red, is the temperature at which the crystal network began to collapse.UMF = unfractionated milk fat; MF = milk fat fraction, with clarification temperature (e.g., MF5 is milk fat fraction with clarification temperature of 5°C).Error bars represent the SD of triplicate experiments.

Figure 6 .
Figure 6.Final structures observed between 2 fat globules formulated to different milk fat fractions at room temperature, with schematic representation of partial coalescence.UMF = unfractionated milk fat; MF = milk fat fraction, with clarification temperature (e.g., MF5 is milk fat fraction with clarification temperature of 5°C).
Figure 7. Interfacial tension in model systems composed of the aqueous phase and milk fat fractions at room temperature.UMF = unfractionated milk fat; MF = milk fat fraction, with clarification temperature (e.g., MF5 is milk fat fraction with clarification temperature of 5°C).Error bars represent the SD of triplicate experiments.Different letters (a-f) above the data points indicate significant differences (P < 0.05) among different milk fractions.

Figure 8 .
Figure 8.The apparent viscosity of oil-in-water emulsion with different milk fat fractions at (A) 5°C, (B) 15°C, (C) 25°C, and (D) 35°C.UMF = unfractionated milk fat; MF = milk fat fraction, with clarification temperature (e.g., MF5 is milk fat fraction with clarification temperature of 5°C).Error bars represent the SD of triplicate experiments.
Wang et al.: CRYSTAL NETWORK OF BULK MILK FAT FRACTIONS

Table 1 .
Wang et al.: CRYSTAL NETWORK OF BULK MILK FAT FRACTIONS Basic chemical compositions of milk fat fractions 1

Table 2 .
Wang et al.:CRYSTAL NETWORK OF BULK MILK FAT FRACTIONS Avrami exponent (n), Avrami constant (K), and half-time of crystallization (time required to complete half of the crystallization process; t 1/2 ) for milk fat fractions 1 1 UMF = unfractionated milk fat.MF = milk fat fraction, with clarification temperature (e.g., MF5 is milk fat fraction with clarification temperature of 5°C).Values shown are mean ± SD, n = 3.