International Dairy Journal 85 (2018) 105e111
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Time consolidation of skim milk powder near the glass transition temperature Frank Schulnies*, Thomas Kleinschmidt €then, Germany Anhalt University, Applied Biosciences and Process Engineering, Bernburger Str. 55, D-06366 Ko
a r t i c l e i n f o
a b s t r a c t
Article history: Received 15 March 2018 Received in revised form 15 May 2018 Accepted 15 May 2018 Available online 15 June 2018
Time consolidation (caking) of skim milk powder was studied at 35% relative humidity and different temperatures and consolidation stresses using a ring shear tester. Unconﬁned yield strength developed linearly with storage time. The storage time until the powder formed hard lumps (caking time) was lower when storage temperature and consolidation pressure were increased. Even a slight increase in storage temperature near the glass transition temperature resulted in a drastic decrease of storage stability. For example, when the skim milk powder was stored 2.5 C below the glass transition temperature, the caking time was 110 h. In contrast, an increase in storage temperature of 4 C reduced the caking time by 80% to only 18 h. The caking time increased markedly when the storage temperature was more than 3 C below the glass transition temperature of the skim milk powder. © 2018 Elsevier Ltd. All rights reserved.
1. Introduction As bulk product, skim milk powder is used in a wide range of food industries. Several foods such as soups, sauces, confectionery and bakery products beneﬁt from the functionality of skim milk powder. Further processing of skim milk powder commonly includes various transport, storage and dose processes up to the ﬁnal customer. Thus, the powders have to exhibit good handling properties, even after long storage periods, to ensure trouble-free processing. However, since skim milk powder contains lactose in its amorphous state (Kelly, 2009), stickiness and caking may occur when stored under unfavourable temperature and humidity conditions. Stickiness and caking reduce signiﬁcantly the utilisation value of milk powders, and result in product losses, poor quality classiﬁcation as well as customer complaints. Stickiness of amorphous food powders develops above the glass transition temperature (Tg) as a result of a decrease in surface viscosity and plasticisation, which allows the material to adhere to another particle or surface (Aguilera, Levi, & Karel, 1993; Chuy & Labuza, 1994; Downton, Flores-Luna, & King, 1982; Wallack & King, 1988). The transition from the non-sticky region to the sticky state (sticky point) occurs a few degrees above Tg and is often referred to the difference between powder temperature and glass
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(F. Schulnies). https://doi.org/10.1016/j.idairyj.2018.05.005 0958-6946/© 2018 Elsevier Ltd. All rights reserved.
transition temperature [T-Tg] (Hogan & O'Callaghan, 2010). For skim milk powder, sticky points of 23.3 K (Hennigs, Kockel, & Langrish, 2001), 14e22 K (Ozmen & Langrish, 2003), 38 K (Paterson, Bronlund, Zuo, & Chatterjee, 2007), 33.6 K (Murti, Paterson, Pearce, & Bronlund, 2009) and 29 K (Hogan & O'Callaghan, 2010) have been measured. Knowledge of [T-Tg] where the powder becomes sticky is very important for spray drying to reduce wall depositions, cyclone blockages as well as ﬁre and explosion hazards (Hennigs et al., 2001; Kudra, 2003). However, during storage contact time and contact pressure between particles are much higher in comparison with spray drying and therefore sticky points obtained by stickiness measurements may not always be useful to predict susceptibility to lumping when powders are stored in stacked bags or big bags. Caking of amorphous substances can be regarded as a process by which a free ﬂowing powder is transformed into lumps due to bridging and agglomeration of sticky particles (Aguilera, del Valle, & Karel, 1995). Since stickiness and caking are time-dependent phenomena (Downton et al., 1982; Paterson, Brooks, Bronlund, & Foster, 2005), bridging and compaction will result in a solid block, if sufﬁcient time is available. Considering ﬂowability of skim milk powder, several authors have estimated an easy or free ﬂowing characteristic by using shear cell technique (Fitzpatrick, Barry, Delaneya, & Keogh, 2005; Fitzpatrick, Iqbal, Delaney, Twomey, & Keogh, 2004; Fitzpatrick et al., 2007a; Teunou & Fitzpatrick, 1999). Exposure of skim milk powder to 46% relative humidity for 18 h caused an cohesive ﬂow
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behaviour (Fitzpatrick et al., 2004). Moreover, caking of skim milk powder has been investigated by means of empirical methods. € Ozkan, Withy, and Chen (2003) used an Instron machine to investigate caking of SMP in the temperature range from 50 C to 70 C. Moisture content and [T-Tg] values were not addressed and could have varied during experiments. Furthermore, Fitzpatrick et al. (2007b) and Fitzpatrick, O'Callaghan, and O'Flynn (2008) used an empirical force-displacement caking test to measure caking of skim milk powder at 76% and 100% relative humidity. No signiﬁcant caking was observed at [T-Tg] < 10 K. However, powder was not consolidated before testing. To eliminate the inﬂuence of stress history (e.g., ﬁlling, preceding deformation) preshearing until steady-state ﬂow is recommended prior to measurement of powder or cake strength (Schulze, 2008). Penetration tests, such as introduced by Knight and Johnson (1988), were found to have big scatter from results of identical tests and time consolidation tendencies could hardly be detected (Schwedes, 2003). Because shear cell measurements include a deﬁned consolidation procedure, less scatter in test results can be expected and one obtains the greatest strength at a given consolidation stress (Schulze, 2008). Thus, powder strength is not underestimated and susceptibility to caking can be determined on the safe side. Since most previous work has focused on stickiness and caking measurement using empirical tests, the aim of this work was to measure time consolidation kinetic of commercial skim milk powder under industrial relevant consolidation stresses using a ring shear tester. Time consolidation was investigated at low [T-Tg] (<10 K) to determine caking times in the near region of the glass transition. Two consolidation stresses were used to simulate storage pressures in the lower and upper part of a pallet of stacked bags or in ﬂexible bulk containers. Information of caking kinetics will be helpful to assess powder state at different storage conditions. 2. Material and methods 2.1. Skim milk powder Commercial spray dried skim milk powder (SMP) was kindly donated by Prolcatal (Prolactal GmbH, Hartberg, Austria). The powder had a median particle size (d50) of 87 mm and a span (width of size distribution) of 1.44, as measured by dynamic image analysis (Microtrac SIA, Microtrac GmbH, Krefeld, Germany). The moisture, protein, lactose and fat contents of the powder were 4.2, 36, 59, and 1.1% (dry basis), respectively, and the loose bulk density was 518 kg m1. The SMP was stored in a sealed 25 kg bag until use. 2.2. Moisture sorption isotherm The SMP (initial moisture content 4.2% on dry basis (db); water activity, aw, 0.22) was dried over P2O5 overnight at 50 C prior to isotherm measurement. Four grammes of dried SMP samples were then equilibrated at 23 C in desiccators over saturated salt solutions generating relative humidities (RH) of 11% (LiCl), 22% (CH3COOHK), 33% (Mg(Cl)2), 43% (K2CO3), 53% (Mg(NO3)2) and 76% (NaCl). After 4 weeks of storage, powder samples were analysed for moisture content (oven drying method; IDF, 2004) and water activity (AquaLab 4TEV, Meter Group, Inc., Pullman, USA). BET model (1) was ﬁtted to experimental moisture sorption data:
Mdb Caw ¼ M0 ½ð1 aw Þð1 aw þ Caw Þ
where C is the BET constant, Mdb is the moisture content of the powder and Mo is the moisture content at monolayer coverage.
2.3. Time consolidation trials at 35% relative humidity Before time consolidation trials, SMP was stored at 30% RH and 20 C for two weeks in a climate chamber (Binder KMF 115, Binder GmbH, Tuttlingen, Germany) to minimise the effect of changing water activity and glass transition temperature during time consolidation trials at 35% RH. To avoid caking during powder equilibration, RH was kept below the critical water activity of SMP, which is in the range of 0.33e0.37 (Jouppila & Roos, 1994b; Roos, 1993; Vuataz, 2002). A ring shear tester (RST-XS, Dr. Ing. Dietmar Schulze Schüttgutmesstechnik, Wolfenbüttel, Germany) was used for ﬂowability and cake strength measurements. Two yield loci of pre-conditioned SMP were measured in duplicates at 1000 Pa and 4000 Pa preshear load to characterise initial ﬂowability at low and high consolidation pressures. Shear speed was automatically controlled in the range of 1 mm min1. From each yield locus the major consolidation stress, s1, and the unconﬁned yield strength, sc, were derived using Mohr circles. Flowability was characterised by the ratio ffc of major consolidation stress to unconﬁned yield strength (Jenike, 1964; Schulze, 1995). For time consolidation trials, pre-conditioned powder was presheared on the ring shear tester using the same normal loads as described above. After preshearing, the ring shear cell was transferred in the climate chamber, and loaded with weights using a consolidation stand. The mass of the weights was chosen according to the major consolidation stress determined from initial yield locus measurement. The relative humidity of the climate chamber was set to 35% in all experiments. Consolidation trials were carried out at 18.5 C, 22.5 C, 27.5 C, 32.5 C and 37.5 C. After different storage times, SMP was sheared on the shear tester at normal loads of 40% of the preshear load. Cake strength (sc) was estimated from the approximated time yield locus by parallel translation of the linearised yield locus through the measured shear point (Schulze, 2008; Schwedes, 2003). After shearing, small powder samples were taken from the bottom side of the annular lid for analyses of water activity and glass transition temperature. 2.4. Glass transition temperature Tg Glass transition temperature (Tg) was measured using differ€tebau GmbH, ential scanning calorimetry (DSC 204 F1, Netzsch Gera Selb, Germany). Ten milligrammes of SMP was weighed into aluminium pans, and then hermetically sealed. The measurement procedure included a ﬁrst heating scan from 20 C to 60 C, followed by rapid cooling (20 K min1) to 0 C, and a subsequent second heating scan to 80 C at 5 K min1. Glass transition temperature was estimated from the glass transition occurring during the second heating scan as onset temperature (Descamps, Palzer, Roos, & Fitzpatrick, 2013; Vuataz, 2002). Tg was measured for fresh SMP, pre-conditioned SMP and for some SMP samples taken after time consolidation trials. 2.5. Sieving of time consolidated skim milk powder (caking index) To relate the extent of caking to the unconﬁned yield strength, cylindrical SMP compacts were generated using an uniaxial compression test (Evolution Powder Tester, PS Prozesstechnik GmbH, Basel, Switzerland), and then sieved. For this purpose, preconditioned SMP was ﬁlled in the cylindrical test cells, and loaded with a consolidation stress of 10 kPa. Storage of the cells was conducted at 30 C and 35% RH to induce caking of the SMP. After different storage times, three test cells were removed from the climate cabinet. One of the cells was used for conducting failure test on the uniaxial apparatus to determine the unconﬁned yield
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strength. From the other two cells, powder compacts were removed carefully on a sieve having a mesh size of 180 mm. Powder compacts were then sieved on a vibratory sieve shaker (Analysette 3, Fritsch GmbH, Idar-Oberstein, Germany) for 1 min at an amplitude of 1 mm. Caking index was deﬁned as weight fraction relative to the original powder mass retained by the sieve (Aguilera et al., 1995; Nijdam & Langrish, 2006). 3. Results and discussion 3.1. Moisture sorption isotherm and glass transition temperature Fig. 1 shows the measured sorption isotherm and glass transition temperatures as a function of SMP water activity. In the aw range from 0.1 to 0.3 moisture content increased linear with increasing water activity. Moisture sorption in this area is often related to adsorbed water (Reh, Bhat, & Berrut, 2004). At aw < 0.2, casein is supposed to be the main water absorber, whereby in the intermediate region water sorption is dominated by lactose (Schuck, Mejean, Dolivet, Jeantet, & Bhandari, 2007). For aw > 0.33, moisture contents decreased due to lactose crystallisation and loss of adsorbed water. Lactose crystallisation in SMP was found to occur within 200 he600 h when stored at 24e25 C and 40e54% RH (Jouppila & Roos, 1994b; Vuataz, 1988). From the ﬁtted BET equation, a monolayer water content, M0, of 5.3% db was obtained. The monolayer water content is in the range from 4.3% to 5.8% reported by other authors for SMP (Furmaniak, Terzyk, Gołembiewski, Gauden, & Czepirski, 2009; Jouppila & Roos, 1994a; Lomauro, Bakshi, & Labuza, 1985; Vuataz, 2002). It should be noted that only experimental data points up to 33% RH were included in the ﬁtting procedure because sorption parameters are not valid for conditions where phase transition and lactose crystallisation will occur (Bronlund & Paterson, 2004; Haque & Roos, 2004). Considering the measured glass transition temperatures in Fig. 1 it can be seen that Tg was lowered with increasing water activity and moisture content. This is a well-known phenomenon for amorphous food materials, since water acts as plasticiser and increases molecular mobility of the matrix (Roos & Karel, 1991; Roos, 1993; Slade & Levine, 1991). For the fresh SMP, (aw 0.22) Tg was 45 C. After 2 weeks of storage at 30% RH, water activity increased to 0.3 and Tg decreased to 34 C. During the ﬁrst 24 h of time consolidation at 35% RH, a water activity of 0.33 with a corresponding Tg of 27 C was reached in almost every consolidation
Fig. 1. Moisture content ( ) and glass transition temperature ( ) of SMP as a function of water activity. In the water activity range from 0.1 to 0.33 moisture sorption isotherm was ﬁtted using BET model (1) ( ). Glass transition line ( ) was calculated with eq. (2).
trial. Overall, the measured glass transition temperatures were in good agreement with the Tg (aw) line calculated with a third degree polynomial (2) suggested by Vuataz (2002) for estimating glass transition of milk powders as a function of their water activity at 25 C.
Tg ¼ 425a3w þ 545a2w 355aw þ 101
We used equation (2) to calculate Tg of SMP samples taken after each consolidation time by determining their water activity at 25 C. Thus, it was possible to estimate the difference between storage and glass transition temperature, [T-Tg], for each time step of consolidation. 3.2. Time consolidation kinetic In Table 1 initial yield loci results are presented. The ﬂowability of the pre-conditioned SMP prior to time consolidation was cohesive (ffc < 4) and easy ﬂowing (ffc > 4) at a consolidation stress of 1.8 kPa and 10 kPa, respectively. Although the unconﬁned yield strength increased with increasing consolidation stress, the SMP had a better ﬂowability at a higher consolidation stress. This can be explained by the fact that ﬂowability is the ratio of consolidation stress to unconﬁned yield strength, and this ratio increases with increasing consolidation stress for most powders (Schulze, 2008). When considering the pressure at the bottom of a ﬂexible intermediate bulk container or a pallet with stacked sacks, the two consolidation stresses used would represent a ﬁlling or stack height of approximately 0.37 m (s1 1.8 kPa) and 2 m (s1 10 kPa) when bulk density is 500 kg m3. This is given by the fact that ﬂexible walls cannot support the bulk. In this case, the hydrostatic pressure equation can be used to calculate the stress as a function of height (Schulze, 2008). We used the low and high consolidation stress for time consolidation tests to simulate the caking process in different heights. Fig. 2 shows an example of the measured yield loci and time yield loci of the SMP. From the measured points of incipient ﬂow, a yield locus was drawn from which a Mohr stress circle for the unconﬁned yield strength, sc, could be constructed. In the example in Fig. 2, the preshearing at 4000 Pa resulted in a major consolidation stress, s1, of around 10,000 Pa. The corresponding unconﬁned yield strength without time consolidation was 1800 Pa. After preshearing and storage at 18.5 C and 35% RH for 912 h, the measured shear stress at a normal stress of 1600 Pa (40% of the preshear load) increased from 1700 Pa to nearly 3000 Pa. From the estimated time yield locus a cake strength of 6300 Pa was obtained. The development of cake strength at different storage temperatures and 35% RH is shown in Fig. 3. Unconﬁned yield strength increased nearly linear with storage time. The SMP consolidated much faster at higher storage temperatures and consolidation pressures. For example, at 37.5 C and 1.8 kPa pressure load (Fig. 3 A), an unconﬁned yield strength of 50 kPa was reached after 20 h. In contrast, it took almost 120 h to obtain a powder strength of 10 kPa at 22.5 C. It can be seen in Fig. 3 B that an increase in the pressure load to 10 kPa resulted in a two to four fold higher cake strength than at 1.8 kPa. After 20 h of storage at 37.5 C, powder strength nearly doubled in comparison with the trial with 1.8 kPa consolidation stress, and reached 100 kPa. Fig. 4 shows that the SMP consolidated even at very low storage temperatures. After 38 days of storage at 18.5 C and at a consolidation stress of 10 kPa, a powder strength of 6 kPa was measured. Thus, the ﬂowability changed from an easy ﬂowing to a very cohesive (ffc < 2) characteristic. During time consolidation, powder structure became coarser with increasing cake strength. Fig. 5 presents pictures of SMP
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Table 1 Flowability characteristic of SMP prior to time consolidation.a Preshear normal load (Pa)
Consolidation stress (Pa)
Unconﬁned yield strength (Pa)
Bulk density (kg m3)
1812 ± 8 10456 ± 671
487 ± 1 1832 ± 99
3,7 ± 0.0 5,7 ± 0.3
593 ± 28 805 ± 69
Values are means of duplicate measurements.
Fig. 2. Yield locus of pre-conditioned SMP for a preshear normal stress of 4000 Pa ) ( , preshear point) and approximated time yield locus for a storage time of ( 912 h at 18.5 C and 35% RH ( ).
samples taken after emptying the shear cell. Signiﬁcant lump formation started at an unconﬁned yield strength of around 13 kPa (Fig. 5C). However, these lumps were fragile and easy to crush. Bigger lumps were noticed at a cake strength of around 30 kPa (Fig. 5 D), which were very hard and difﬁcult to break. It is known that viscosity of an amorphous matrix decreases during glass transition and viscous properties will more and more dominate the mechanical behavior (Palzer, 2005; Roos & Karel, 1991; Wallack & King, 1988). Viscous ﬂow of the material will then cause sinter bridge formation between adjacent particles and the powder will become a lot more cohesive (Aguilera et al., 1995, 1993; Descamps et al., 2013; Downton et al., 1982; Tsourouﬂis, Flink, & Karel, 1976). Because consolidation trials were carried out at 35% RH and the measured glass transition temperature was around 25 C (Mdb 6%) it is clear that consolidation of the tested SMP at temperatures above 25 C was caused by a decrease in surface viscosity and sinter bridge formation. Since higher temperatures above Tg lead to greater molecular mobility and an increasing rate of bridge development (Foster, Bronlund, & Paterson, 2006; Paterson et al., 2005), the unconﬁned yield
strength of the SMP increased faster at higher storage temperatures. However, the consolidation trials at 22.5 C and 18.5 C showed that cohesion increased also below Tg. Theoretically, the viscosity of an amorphous matrix is too high in the glassy state to cause viscous ﬂow and bridge formation. For amorphous lactose, the glass transition viscosity is assumed to be in the range of 1011e1014 Pa s (Murti, Paterson, Pearce, & Bronlund, 2010). However, the only measured value of viscosity of amorphous lactose at Tg is around 1014 Pa s (Paterson, Ripberger, & Bridges, 2015). In spite of the high viscosity, matrix relaxation, as the beginning of molecular mobility, is known to take place below Tg (Descamps, Palzer, & Zuercher, 2009; Liu, Bhandari, & Zhou, 2006). Relaxation was found to increase for various amorphous sugar glasses with increasing ageing time at ageing temperatures of 10e30 C below Tg (Kawai, Hagiwara, Takai, & Suzuki, 2005). Ageing phenomena below Tg may modify physical and mechanical properties of glassy materials (Enrione, Díaz, Matiacevich, & Hill, 2012; Haque, Kawai, & Suzuki, 2006; Shogren, 1992). Possibly this relaxation process contributed to the observed time consolidation below 25 C due to small changes in the contact area between particles. In addition, particles can rearrange under consolidation stress whereby contact area and adhesion forces could increase (Rumpf, Sommer, & Steier, 1976). As already mentioned, powder strength developed much faster at 10 kPa consolidation pressure. An explanation can be derived from the sinter equation given by Rumpf et al. (1976). Higher contact pressures between particles increase the diameter of the material bridge. Thus, the formed solid bridges had higher strength at the same consolidation time. 3.3. Caking index and caking time For estimating the caking time, a common question arises regarding the powder strength corresponding to a caked or lumped powder. Hartmann and Palzer (2011) and Palzer (2005) regarded a powder sample as caked when the unconﬁned yield strength was higher than 2000 Pa and 1000 Pa, respectively. Besides this,
Fig. 3. Development of unconﬁned yield strength of SMP with storage time at consolidation stresses of 1.8 kPa (A) and 10 kPa (B). Storage temperatures at 35% RH were: , 37.5 C; , 32.5 C; , 27.5 C; , 22.5 C.
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Fig. 6. Caking index of SMP as a function of unconﬁned yield strength. Fig. 4. Development of cake strength of SMP at 18.5 C and 35% RH. Applied consolidation stress was 10 kPa.
Descamps et al. (2013) considered powder caking if ffc < 1. € Furthermore, Ozkan et al. (2003) used an attrition test to relate the extend of powder caking to the measured penetration force. They deﬁned a weak cake formation when 10 wt. % of the SMP compacts remained intact after the attrition test. The corresponding penetration force was 1.4 N. In our study, we used a sieving method (caking index) to ﬁnd out the relationship between the extent of caking and the measured unconﬁned yield strength of the SMP. Fig. 6 shows the mass of intact SMP compacts after sieving as a function of cake strength. Up to a powder strength of about 15 kPa, SMP compacts were fragile and completely destroyed during sieving. This was in good agreement with our qualitative observations (Fig. 5), where lumps could easily be disturbed up to a powder strength of about 13 kPa. Above a cake strength of 20 kPa, the amount of SMP lumps retained by the sieve increased signiﬁcantly with powder strength. Hence, we considered SMP as caked when unconﬁned yield strength was 20 kPa.
Fig. 7 shows the caking times (storage time until an unconﬁned yield strength of 20 kPa was reached) as a function of the temperature difference [T-Tg]. Caking times were calculated from the linear slope of each time consolidation kinetic and setting a powder strength of 20 kPa. Glass transition temperature was estimated
Fig. 7. Dependence of caking time of SMP on difference between storage and glass transition temperature [T-Tg]. Consolidation stress 10 kPa ( ), consolidation stress 1.8 kPa ( ).
Fig. 5. Development of lump formation during time consolidation trials at 1.8 kPa consolidation stress: A, sc ¼ 0.5 kPa (initial sc); B, sc ¼ 4.8 kPa; C, sc ¼ 12.5 kPa; D, sc ¼ 29.4 kPa.
Fig. 8. Comparison of caking and crystallisation times for different food powders. Caking times of SMP (s1 10 kPa) determined in this study ( ), caking times SMP eq. (3) ( ), onset of undesired agglomeration calculated by Palzer (2005) ( ), WLF-Fit of lactose crystallisation in whole milk powder ( ) (data from Vuataz, 2002).
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Table 2 Model parameters used to calculate caking and crystallisation times for milk powders. Powder
g (mN m1)
SMP caking Tomato powder, dextrose syrup Crystallisation whole milk powder
2.3 17.4 8.9
10.0 51.6 14.4
This study Palzer (2005) Vuataz (2002)
from the measured water activity after each storage time using eq. (2). It can be seen in Fig. 7 that a slight increase in storage temperature around the Tg resulted in a drastic decrease of the storage stability. For example, when stored at a [T-Tg] of 2.5 K, caking time was 110 h at a consolidation stress of 10 kPa. In contrast, raising the storage temperature by 4 C, the caking time was reduced by 80% to only 18 h. At low storage pressures, caking times were greater because sinter velocity was probably lower. It seems like that the difference in caking times between low and high consolidation pressures increased a little bit with increasing [T-Tg]. This would mean that there was a bigger inﬂuence of storage pressure at higher [T-Tg]. The caking time increased markedly when the storage temperature was more than 3 C below the Tg of the SMP. Thus, for the prevention of a signiﬁcant lumping, the storage temperature should be at least 3 C below the glass transition temperature of the SMP. Foster et al. (2006) and Paterson et al. (2005) investigated cohesion development of amorphous sugars by a blow tester. They postulated that the level of stickiness is independent of the individual temperature and RH conditions and only a function of [T-Tg]. However, Chen (2007) showed that the rate of sticking can also depend on Tg (water content). But for small [T-Tg] the difference in the rate of stickiness development was marginal (Chen, 2007). Based on these results caking times shown in Fig. 7 should also be valid for other combinations of temperature and relative humidity. Fig. 7 could then be used to assess storage stability of SMP under different storage conditions.
Ft ¼ s1 a2
In Fig. 8 caking times and model results from eq. (3) are compared for different food powders. For comparative purpose, we also include the time scale until lactose will crystallise in whole milk powder (which may be adapted to SMP) calculated by Vuataz (2002) using WLF-equation. Model parameters are summarised in Table 2. Eq. (3) ﬁtted the caking time data for SMP consolidated at 10 kPa very well. However, caking times obtained at 1.8 kPa consolidation stress could not be ﬁtted. The best ﬁt x/a-value was found to be 0.014 which means that a sinter bridge diameter of approximately 1.2 mm caused the SMP to cake (sc ¼ 20 kPa) at 10 kPa consolidation stress. In comparison with the results of Palzer (2005), caking times of SMP investigated in this study were lower at [T-Tg] < 8 K. A reason might be the higher consolidation stress used in our experiments. Furthermore, Palzer (2005) used the universal WLF constants for viscosity prediction, which resulted in a steeper decrease and increase in caking times with changing [T-Tg]. However, the universal WLF constants may only be used to show a trend and are probably product speciﬁc (Peleg, 1992). It is obvious from Fig. 8 that the induction period of lactose crystallisation is extremely high in comparison with the caking process. Even at a [T-Tg] of 20 K it takes approximately 18 h until lactose will crystallise in milk powders. Crystallisation will take place in a few minutes when [T-Tg] is in the range of 30e40 K (Ibach & Kind, 2007; Langrish, 2008). At this material state the powder will already have formed a solid block. 4. Conclusions
3.4. Modelling caking time As already discussed in section 3.2, caking of amorphous substances is a result of viscous ﬂow and particle fusion occurring above Tg. Therefore, caking process is often described by sinter kinetic models (Palzer, 2005; Paterson et al., 2005). Palzer (2005) combined sinter kinetic proposed by Rumpf et al. (1976) with the WLF-equation (Williams, Landel, & Ferry, 1955) and obtained eq. (3) to calculate the onset of undesired agglomeration of amorphous particles.
5 a2 p 4 sa p þ 2 Ft
10 C2þðTTg Þ
In eq. (3) tcake is the caking time, a is the particle diameter, s is the surface tension, Ft is the contact force, hg is the viscosity at Tg (1012 Pa s), x/a is the relative sinter bridge diameter and C1 and C2 are the universal WLF constants, which describe the temperature dependence of the viscosity of the amorphous material. A signiﬁcant adhesion force between particles, e.g. a stable powder cake can be expected when x/a is in the range of 0.01 and 0.1 (Downton et al., 1982; Wallack & King, 1988). Palzer (2005) ﬁtted eq. (3) to caking and stickiness data of tomato powder, dextrose syrup and previous cited work using a x/a-value of 0.1 and the universal WLF constants (C1 ¼ 17.4, C2 ¼ 51.6 K). We also used eq. (3) to ﬁt caking time data shown in Fig. 7 by adjusting x/a, C1 and C2 using Excel-Solver. For calculation of contact force, Ft, between particles we used eq. (4) assuming an ideal cubic packaging of monodisperse spheres (Runge, 1994).
In this work, time consolidation of skim milk powder was investigated near the glass transition temperature ([T-Tg] < 10 K) using shear cell measurements. The powder strength increased linearly during storage at temperatures of 18.5 Ce37.5 C and 35% relative humidity. Higher storage pressures and temperatures resulted in a faster consolidation of the powder samples. The SMP formed hard lumps when the unconﬁned yield strength reached 20 kPa. Using a sinter kinetic model, a sinter bridge diameter of 1.2 mm was estimated to cause this cake strength. In the [T-Tg] range investigated, the caking times (time to reach 20 kPa strength) varied from 3 h to 180 h. Interestingly, the SMP consolidated even some degree below the Tg, possibly due to relaxation or rearrangement of the powder particles. However, when the storage temperature was more than 3 C below Tg, cohesion development was very slow. Thus, SMP should be stored at least 3 C below the onset of its glass transition to prevent caking during long-term storage under high consolidation pressures. From the results of the time consolidation trials, it is possible to assess storage stability of skim milk powders under consolidation stress at various material states characterised by [T-Tg]. Thereby, product and quality losses due to lumping can be avoided and the processability of the powders will be ensured. Acknowledgement This IGF Project AIF 16624 BR of the FEI was supported via AiF within the programme for promoting the Industrial Collective
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