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Application of the SAFES (systematic approach to food engineering systems) methodology to strawberry freezing process
Journal of Food Engineering 83 (2007) 238–249 www.elsevier.com/locate/jfoodeng
Application of the SAFES (systematic approach to food engineering systems) methodology to strawberry freezing process M.L. Castello´ *, P.J. Fito, A. Argu¨elles, P. Fito Institute of Food Engineering for Development, Food Technology Department, Valencia, Spain Available online 22 February 2007
Abstract SAFES methodology has been applied in strawberry freezing process using data from references. Three cases of freezing have been studied. All of them start from the refrigerated temperature (Tc) and there is a first stage of cooling until the initial freezing temperature (Tm) is reached. However, the changes of components depend on the temperature reached and the rate of freezing. Case 1 studies the decrease of temperature from Tm until the first layers of cells reach 18 °C, since this is the typical storage temperature in consumer’s freezer. In case 2, strawberries are frozen at the maximally cryoconcentrated temperature ðT 0m Þ of the matrix and then down to 100 °C. In case 3, a deep freezing process decreases the temperature of strawberries down to 196 °C. The last two cases are below the temperature of glass transition of strawberry (51.3 °C) and therefore they have higher stability than in case 1. By means of this methodology it is possible to follow and predict the critical points (appearance or disappearance of components or phases) of the process to prevent quality loss. Components, phases and aggregation systems can also be analysed. Moreover, transport phenomena, chemical reaction and transition can actually be described. It has been demonstrated that SAFES methodology can describe the behaviour of strawberry freezing by using composition data, state diagrams and thermodynamic parameters. Nevertheless, to get better results more information about kinetic data related to freezing process would be required. Ó 2007 Published by Elsevier Ltd. Keywords: Freezing; Strawberry; Cryoconcentration; SAFES
1. Introduction Among the conservative methods, freezing of fruits and vegetables is one of the most common ways to keep their quality. Nevertheless, this method of preservation is considerably complex. Nutritional and organoleptic characteristics of products will depend not only on the temperature, the freezing rate, storage time and maintenance of the cooling chain but also on the thawing conditions (Brown, 1991). As a process which induces changes in product states, it is important to consider the optimal conditions to avoid undesirable effects on their qualitative characteristics. Strawberries are extremely perishable fruits but they
*
Corresponding author. E-mail address: [email protected] (M.L. Castello´).
0260-8774/$ - see front matter Ó 2007 Published by Elsevier Ltd. doi:10.1016/j.jfoodeng.2007.02.035
are highly appreciated by the consumers and freezing can be applied as a suitable method to storage them. Removal of water during processing of many products often results in the formation of an amorphous state which is a non-equilibrium state with time dependent properties. The physical state of amorphous materials may change from a solid vitreous state to a liquid-like rubbery one when the glass transition temperature (Tg) is reached. As the Tg is dependent on the water content, a change from rubbery to a vitreous state can also occur as a consequence of a decrease in the product water content during its processing or storage (Moraga, Martı´nezNavarrete, & Chiralt, 2004). In products with crystallizing components, the determination of the critical water activity or critical water content at a given temperature to avoid crystallization will allow the product shelf-life to be extended (Moraga et al., 2004). State diagrams
M.L. Castello´ et al. / Journal of Food Engineering 83 (2007) 238–249
showing the relationships between product water content and its physical state as a function of temperature together with sorption isotherms are useful tools in process optimisation, food formulation, in establishing processing requirements and designing package/storage conditions. Freezing processes have been studied by means of state diagrams. Furthermore, the temperature of glass transition can be calculated following the model of Gordon and Taylor (1952) and Couchman and Karasz (1978). The state diagram allows us to know the physical state in which the watering phase would be as a function of moisture content and temperature. Depending on the freezing rate, the melting point could change with the freeze-concentration til eutectic point at low freezing rates or at high rates all the liquid phase change to subcooling liquid working as vitreous solid (Reid, Kerr, & Hsu, 1994). A more appropriate freezing process would allow to freeze all the available water until an amount of water in the aqueous phase would equal Wg’ (g water/g of solution maximally cryoconcentrated). In addition, this diagram lets us know the temperature at the beginning of glass transition of the maximally cryoconcentrated matrix ðT 0g Þ and the temperature when the fusion of ice which goes with this matrix is produced. They are not the same due to the fact that glass transition really happens in an interval of temperatures. The maximum formation of ice can only be obtained by keeping the system at a temperature between T 0g and T 0m for a specific length of time. By using this procedure it is possible to know how much product is in rubber or vitreous state. However, it is quite
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difficult to clarify what happens with the different phases involved in the process. As a consequence of all these changes that occurred in the frozen strawberry structure it is necessary to know the final use of this product to focus on the quality factor that the consumer is looking for. For instance, if the samples will be used in a freeze-drying process there is no need to keep the structure, since the process of sublimation will destroy it anyway. However, if the final objective is to use it in confectionery, the texture should remain as similar as possible to the fresh strawberry. Furthermore, it is essential to adjust the freezing-thawing process variables in order to better preserve and retain the quality of the product. Besides that, samples of strawberries which had undergone low ambient temperature or high air velocities present better structures preservation, due to the small size of ice crystals which were mainly intracellular (Delgado & Rubiolo, 2005). On the contrary, with a slow freezing rate, cells appear torn and irregular in shape and some loss of amorphous material and tissue distortion is observed (Delgado & Rubiolo, 2005). In recent studies, it has been specified that the most important nutritional changes in frozen foods are due to storage time (Sahari, Boostani, & Hamidi, 2004). On one hand, vitamin C has been used as a quality indicator (Erikson & Hung, 1997; Rosen & Kader, 1989; Ulrich, 1978). On the other hand, the maintenance of the red colour of strawberry is necessary for an appropriate commercialization. Temperature is one of the effective factors for anthocyanin resistance (Urbany & Horti, 1992; Withy, Nguyen, & Wrolstad, 1993).
Process of freezing M1
M0
Troom →Tm
M3
M2
Tm →Tstorage
T m →Tm Tg
Tm
isotherm 50
5 4.5
0
4
case 1 -50
3
T (˚C)
xw (kgw/kgms)
3.5
2.5
case 2
2
-100
1.5 -150
1 0.5
case 3
0
-200 1
0.8
0.6
0.4
0.2
0
aw
Fig. 1. Scheme of strawberry freezing process. Stage of changes explained on the strawberry isotherm and state diagram.
M.L. Castello´ et al. / Journal of Food Engineering 83 (2007) 238–249
240 Table 1 Strawberry composition xw
xss
0.91 ± 0.01
0.085 ± 0.007
0.907 ± 0.006 0.91 ± 0.01
0.08 ± 0.01 0.078 0.079
qa (g/cm3)
939 ± 7
qr (g/cm3)
1033
e
zs
0.06–0.07
0.086 ± 0.005
0.09
8±1
Considering all the previous comments, there are several parameters that should be taken into account in order to optimize this food industrial process. A powerful tool to control the process and the quality of the product would be the development of a systematic way to predict the characteristic of the final product. In this sense,
aw
References
0.992 ± 0.002 0.992 ± 0.002 0.99± 0.005
Talens, Escriche, Martı´nez-Navarrete, and Chiralt (2002) (var. Camarosa) Moraga et al. (2004) (var. Camarosa) Castello´, Fito, and Chiralt (2005) (var. Camarosa) Hammami and Rene´ (1997) (var. Pajaro)
SAFES (systematic approach to food engineering systems) is a new methodology that claims to solve or clarify food processes or systems by means of an integration of different models considering all the components, phases and stages of products (Fito, LeMaguer, Betoret, & Fito, in press).
Fig. 2. SAFES methodology application in the strawberry freezing process. See the above mentioned references for more details.
M.L. Castello´ et al. / Journal of Food Engineering 83 (2007) 238–249
In this study, SAFES methodology has been applied in strawberry freezing process using data from references in order to get the right approach to understand it better. 2. Material and methods 2.1. Material Traditional process of cooling and freezing fresh fruits consists basically in one single operation. The temperature of the products decreases until it reaches the initial freezing temperature and then the temperature continues to go down which causes a separation of frozen and unfrozen water. This fact causes a cryo-concentration of the liquid phase of the fruits and consequently, the more concentration liquid phase the lower the temperature required to freeze it. Therefore it is important to know what is happening in each stage of the freezing process according to the temperature and the freezing rate. Fig. 1 shows the same process but divided in stages which consider the changes in the matrix of fruits more exhaustively. Moraga et al. (2004) determined water sorption isotherms and glass transition as a function of moisture content of strawberries taking into account the whole or the homogenized fruit. GAB model was used to model the water plasticization effect. By knowing the composition of strawberries (Table 1) and the parameters of GAB (Moraga et al., 2004) and also Gordon and Taylor models it is possible to apply the SAFES methodology in order to know which changes have taken place in each component, phase and aggregation state. The melting temperature of strawberries can be obtained by means of an empirical equation (1) where a = 5.4 and b = 0.6. In this way the freezing curve predicted by this method can be obtained (Fig. 1) (Moraga et al., 2004). a Tm ¼ ð1Þ b 1 þ lnð2wÞ where Tm is the melting temperature; w is the water mass fraction in wet basis.
241
According to Moraga et al. (2004), the temperature of the maximally cryoconcentrated matrix T 0m of strawberry is 40.9 ± 1 °C, the value of the glass transition of maximally cryoconcentrated fruit liquid phase ðT 0g Þ of this fruit is 51.3 ± 0.7 °C and the amount of non-frozen water ðx0wg Þ is 0.221. All these data will be also used to develop the SAFES methodology in the strawberry freezing process. 2.2. Methods Three cases of freezing have been studied. All of them start from the refrigerated temperature and there is a first stage of cooling until the initial freezing temperature (Tm). However, the changes of components depend on the temperature reached and the rate of freezing. Case 1 studies the decrease of temperature from Tm to 18 °C, since this is the typical storage temperature in consumer’s freezer. In case 2, strawberries are frozen until the maximally freeze-concentrated glass temperature ðT 0g Þ and then down to 100 °C. In case 3, an deep freezing process decreases temperature of strawberries down to 196 °C, when the viscosity of the liquid phase rises rapidly working like a vitreous solid (see all the three cases in Fig. 1). SAFES methodology considers the product describing phases, components and aggregation states and their development during the studied process. In order to apply the SAFES methodology, it is important to analyze the critical points (i.e. stages of changes) of the process. The following step is to build the matrices of products, once the needed hypotheses are defined and all the required information is
Table 2 SAFES’s codes to strawberry freezing process ðX kij Þ Phases
j
Components
i
state
k
Solid matrix Liquid Soluble solids Frozen water Gas Whole food
1 2 3 4 5 0
Water Non soluble solids (native) Soluble solids (native)
1 2 3 4
Whole food
0
Gas (G) Liquid (L) Adsorbed (A) Rubber (R) Vitreous (V) Crystal (K)
0 1 2 3 4 5
Fig. 3. Scanning electron micrographs of cellular structure of fresh strawberry tissue (a); a sample frozen at 4.54 m/s and 30 °C (2.43 C/min) (b) and SEM of parenchyma tissue of a sample frozen at 0.82 °C/min (c). (Delgado & Rubiolo, 2005).
M.L. Castello´ et al. / Journal of Food Engineering 83 (2007) 238–249
242
M0,0 PHASES
COMPONENTS COMPONENT
STATE
SM
LPI
LPE
SS
FW
G (gas) A (adsorbed)
WF
0
0 0.821 0.089
0.821
L (liquid) WATER
GAS
0.089
0
R (rubber) V (vitreous)
0 0
K (crystal) TOTAL
0.089
0.821
0
0 0.910
0
L (liquid) A (adsorbed) NON SOLUBLE SOLIDS (NATIVE)
R (rubber) V (vitreous) K (crystal) TOTAL
0.01 0 0 0.01
0.009 0
0.081
L (liquid) A (adsorbed) SOLUBLE SOLIDS (NATIVE)
0 0.009 0.081
0
0
R (rubber) V (vitreous) K (crystal) TOTAL
0
0.081
0 0.000 1 0.097 4 1.00
GASES WHOLE FOOD MASS WHOLE FOOD VOLUME (L/kg)
W.F.TEMPERATURE (°C) W.F.PRESSURE (atm)
0.098 0.095 4 1.00
0.902 0.874 4 1.00
0 4
4 1.00
1.00
.081 0.000 .00 1.066 4 1.00
Fig. 4. Descriptive matrix of raw strawberry (M0,0) of the three cases. SM is solid matrix, LPI is liquid phase intracellular, LPE is liquid phase intracellular, SS is soluble solids, FW is frozen water phase, GAS is gas phase and WF is whole food.
M1,1 PHASES
COMPONENTS COMPONENT
STATE
SM
LPI
LPE
SS
FW
G (gas) A (adsorbed)
WF
0
0 0.828 0.082
0.828
L (liquid) WATER
GAS
0.082
0
R (rubber) V (vitreous) K (crystal) TOTAL
0.082
0.828
0
0 0
0
0 0.910
L (liquid) A (adsorbed) NON SOLUBLE SOLIDS (NATIVE)
R (rubber) V (vitreous) K (crystal) TOTAL
0.01 0 0 0.01
SOLUBLE SOLIDS (NATIVE)
0 0.009 0.081 0
0.081
L (liquid) A (adsorbed)
0.009 0
0
R (rubber) V (vitreous) K (crystal) TOTAL
0
0.081 0.000
GASES WHOLE FOOD MASS WHOLE FOOD VOLUME (L/Kg)
W.F.TEMPERATURE (°C) W.F.PRESSURE (atm)
0.091 0.0884 -0.906 1.00
0.909 0.881 -0.906 1.00
-0.906 1.00
-0.906 1.00
0.097 -0.906 1.00
0.081 0.000 1.00 1.066 -0.906 1.00
Fig. 5. Descriptive matrix of strawberry (M1,1) at the initial freezing temperature (Tm) for all cases.
M.L. Castello´ et al. / Journal of Food Engineering 83 (2007) 238–249
243
MC1,0 PHASES
COMPONENTS COMPONENT
STATE
SM
LPI
LPE
SS
FW
G (gas) A (adsorbed)
WF
0
0 0.007 -0.007
0.007
L (liquid) WATER
GAS
-0.007
0
R (rubber) V (vitreous)
0 0
K (crystal)
-0.007
TOTAL
0
0.007
0.000 0.000
0
L (liquid) A (adsorbed) NON SOLUBLE SOLIDS (NATIVE)
0.00 0 0 0.00
R (rubber) V (vitreous) K (crystal) TOTAL
0.000
L (liquid)
0
A (adsorbed) SOLUBLE SOLIDS (NATIVE)
0.000 0.000 0.000 0.000 0.000 0.000 0
R (rubber) V (vitreous) K (crystal)
0
TOTAL
0.000 0.000
GASES WHOLE FOOD MASS WHOLE FOOD VOLUME (kg/L)
W.F.TEMPERATURE (°C) W.F.PRESSURE (atm)
-0.007 -0.007 -4.906 0.00
0
0.007 0.007 -4.906 0.00
-4.906 0.00
0.000 -4.906 0.00
-4.906 0.00
0.000 0.000 0.000 0.000 -4.906 0.00
Fig. 6. Matrix of changes of strawberry in the stage from the refrigerated temperature until the first ice crystal appears (M1,0) for all cases.
available. Each of these matrices consists basically of a three dimensional space inserted in a plane surface as a matrix where columns represent the phases (j) and the main
rows represent the components (i). The information on the aggregation states of each component (k) is included amongst the main rows. Each cell of this space system is
M2,2 PHASES
COMPONENTS COMPONENT
STATE
SM
LPI
LPE
SS
FW
G (gas) A (adsorbed)
WF
0
0 0.331 0.082
0.331
L (liquid) WATER
GAS
0.082
0
R (rubber) V (vitreous) K (crystal) TOTAL
0.082
0.331
0.000
0.497 0.497
0.000
0.497 0.910
L (liquid) A (adsorbed) NON SOLUBLE SOLIDS (NATIVE)
R (rubber) V (vitreous) K (crystal) TOTAL
0.01 0 0 0.01 0.081
L (liquid) A (adsorbed) SOLUBLE SOLIDS (NATIVE)
0.009 0 0 0.009 0.081
0
0
R (rubber) V (vitreous) K (crystal) TOTAL
0
0.081
0.091 0.102 -18 1.00
0.413 0.381 -18 1.00
0 0
GASES WHOLE FOOD MASS WHOLE FOOD VOLUME (kg/L)
W.F.TEMPERATURE (°C) W.F.PRESSURE (atm)
-18 1.00
0.497 0.625 -18 1.00
0 0.000 0.112 -18 1.00
0.081 1.00 1.219 -18 1.00
Fig. 7. Descriptive matrix of strawberry freezing process until 18 °C, with low freezing rate. (M2,2) in case 1.
M.L. Castello´ et al. / Journal of Food Engineering 83 (2007) 238–249
244
MC2,1 PHASES
COMPONENTS COMPONENT
STATE
SM
LPI
LPE
SS
FATS
FATL
FW
GAS
WF
0
0 -0,497
G (gas)
-0,497
L (liquid)
0
A (adsorbed) WATER
0
0,000
R (rubber) V (vitreous) K (crystal)
0
TOTAL
-0,497
0
0
0
0,497 0,497
0
0,497 0,000
L (liquid) A (adsorbed) NON SOLUBLE SOLIDS (NATIVE)
0,00 0 0 0,00
R (rubber) V (vitreous) K (crystal) TOTAL
0 0,000
L (liquid)
0
0
0
0
0
A (adsorbed) SOLUBLE SOLIDS (NATIVE)
0
0,000 0 0 0 0 0
R (rubber)
0 0
V (vitreous) K (crystal)
0
TOTAL
0,000
0
0
L (liquid)
0
0
0
0
0,0 0
0
0
0 0 0
-17 0
0,497 0,625 -17 0
A (adsorbed)
0 0 0 0
R (rubber)
FATS
V (vitreous) K (crystal)
0
0
0,00 0,013 -17 0
-0,497 0,000 -17 0
TOTAL
0
0
0 0,000
GASES WHOLE FOOD MASS WHOLE FOOD VOLUME W.F.TEMPERATURE (°C) W.F.PRESSURE (atm)
-17 0
-17 0
-0,097 -17 0
0,0 0,541 -17 0
Fig. 8. Matrix of changes of freezing strawberry from Tm until temperature decreases to 18 °C (MC2,1) in case 1.
M2,2 PHASES
COMPONENTS COMPONENT
STATE
SM
LPI
LPE
SS
FW
G (gas) A (adsorbed)
WF
0
0 0.219 0.082
0.219
L (liquid) WATER
GAS
0.082
0
R (rubber) V (vitreous)
0.609 0.609
K (crystal) TOTAL
0.082
0.219
0.000
0.000
0.609 0.910
L (liquid) A (adsorbed) NON SOLUBLE SOLIDS (NATIVE)
R (rubber) V (vitreous) K (crystal) TOTAL
0.01 0 0 0.01
L (liquid) A (adsorbed) SOLUBLE SOLIDS (NATIVE)
0.010 0 0 0.081
0
0
0
0
0 0.010 0.081 0
R (rubber)
0 0
V (vitreous) K (crystal) TOTAL
0
0.081
0.092 0.119 -40.9 1.00
0.300 0.269 -40.9 1.00
0
0
-40.9 1.00
0.609 0.888 -40.9 1.00
GASES WHOLE FOOD MASS WHOLE FOOD VOLUME (Kg/L)
W.F.TEMPERATURE (°C) W.F.PRESSURE (atm)
0 0.091 0.129 -40.9 1.00
0.081 1.00 1.405 -40.9 1.00
Fig. 9. Descriptive matrix of strawberry freezing process until 40.9 °C with low freezing rate in case 2.
M.L. Castello´ et al. / Journal of Food Engineering 83 (2007) 238–249
245
filled by a number which is identified as xki;j (Fig. 2). Furthermore, the last three rows of the matrices refer to the volume, temperature and pressure for each phase (Fito et al., in press). There are three kinds of matrices:
In this paper, only the descriptive matrices and the matrices of change have been included.
The descriptive matrices show the composition of products expressed as mass fractions and consequently: XXX xki;j ¼ 1 ð2Þ
The target of this work is to understand the freezing process of strawberry through the SAFES approach. Previously is necessary to define the different phases in the strawberry matrix using microscopy of fresh and frozen tissue (see Fig. 3). This figure shows cellular tissue (parenchyma) fresh and frozen at different freezing rates. The definition of the phases, components and aggregation states of raw material will be the following (codes are shown in Table 2):
i
j
3. Results and discussion
k
The transformed matrices, where xi,jk concerns the shared out of mass in the system and usually: XXX xki;j 6¼ 1 ð3Þ i
j
k
– Components: Water, non soluble solids and soluble solids – States: gas, liquid, adsorbed, rubber, vitreous and crystal – Phases: Solid matrix (Insoluble solids), liquid, soluble solids, gas and frozen water.
One transformed matrix is calculated by multiplying the corresponding descriptive matrix by the ratio of mass variation. The Matrices of changes are worked out by subtracting two matrices referred to the same basis of calculus.
MC2,1 PHASES
COMPONENTS COMPONENT
STATE
SM
LPI
LPE
SS
FATS
FATL
FW
G (gas)
WATER
WF
0
0,00 -0,61
-0,609
L (liquid) A (adsorbed)
GAS
0
0
0,00
R (rubber) V (vitreous)
0,609 0,61
K (crystal) TOTAL
0
-0,609
0
0
0,61 0,00
L (liquid) NON SOLUBLE SOLIDS (NATIVE)
A (adsorbed) R (rubber) V (vitreous) K (crystal) TOTAL
0,00 0,00 0,00 0,00 0,000
L (liquid) A (adsorbed) SOLUBLE SOLIDS (NATIVE)
0,00 0,00 0,00 0,00 0,00
0
0,00
R (rubber) V (vitreous) K (crystal) TOTAL
0
0
0 0 0,000
0,00
L (liquid)
0
0,00
0
0,00 0,00 0,00 0,00
A (adsorbed) FATS
0 0 0 0
R (rubber) V (vitreous) K (crystal) TOTAL
GASES WHOLE FOOD MASS WHOLE FOOD VOLUME W.F.TEMPERATURE (°C) W.F.PRESSURE (atm)
0,001 0,031 -40,0 0,0
-0,609 -0,509 -40,0 0,00
0,000 0,000 -40,0 0,00
-40,0 0,00
-40,0 0,00
0,000 0,609 0,00 0,888 0,033 0,442 -40,0 -40,0 -40,0 0,00 0,00 0,00
Fig. 10. Matrix of changes of freezing strawberry from Tm until temperature decreases to the eutectical point (MC2,1) in case 2.
M.L. Castello´ et al. / Journal of Food Engineering 83 (2007) 238–249
246
M3,3 COMPONENTS COMPONENT
PHASES STATE
SM
LPI
LPE
SS
FATS
FATL
FW
G (gas)
GAS
WF
0
0 0
L (liquid) A (adsorbed) WATER
0,082
0
0,082
R (rubber)
0,219
V (vitreous)
0,609 0,609
K (crystal) TOTAL
0,082
0,219
0
0,219 0,609 0,91
0
L (liquid) A (adsorbed)
NON SOLUBLE SOLIDS (NATIVE)
R (rubber) V (vitreous) K (crystal) TOTAL
0 0,01 0 0,01
0 0,01 0 0,01 0
0
0
L (liquid) A (adsorbed) SOLUBLE SOLIDS (NATIVE)
R (rubber)
0,081
V (vitreous)
0 0 0,000
K (crystal) TOTAL
0
0,081
0,081 0 0,081
0
0
L (liquid) A (adsorbed) R (rubber)
FATS
V (vitreous) K (crystal) TOTAL
0
0
0
0
0 0 0 0
0 0 0 0
0
0 0,091
GASES WHOLE FOOD MASS WHOLE FOOD VOLUME W.F.TEMPERATURE (°C) W.F.PRESSURE (atm)
0,092 0,119 -100,0 1,00
0,300 0,105 -100,000 1,00
0
0,000 0,609 1,00 0,0000 0,888 0,129 1,1366 -100,000 -100,000 -100,000 -100,000 -100,000 -100,000 1,00 1,00 1,00 1,00 1,00 1,00
Fig. 11. Descriptive matrix of strawberry freezing process from 40.9 °C until 100 °C with low freezing rate in case 2.
MC3,2 PHASES
COMPONENTS COMPONENT
STATE
SM
LPI
LPE
SS
FATS
FATL
FW
G (gas) A (adsorbed)
WF
0
0 -0,219
-0,219
L (liquid) WATER
GAS
0
0
0
R (rubber)
0,219
V (vitreous)
0,000 0,000
K (crystal) TOTAL
0
0,000
0
0,000
0,219 0,000 0,00
L (liquid) NON SOLUBLE SOLIDS (NATIVE)
A (adsorbed) R (rubber) V (vitreous) K (crystal) TOTAL
-0,0 0,01 0,00 0,00 -0,081
L (liquid) A (adsorbed) SOLUBLE SOLIDS (NATIVE)
-0,01 0,01 0 0 -0,081
0
0
R (rubber)
0,081
V (vitreous) K (crystal) TOTAL
0
0,000
0 0 0 ,000
0,081 0 0
0 0
L (liquid)
0
0
0 0
A (adsorbed) FATS
0 0 0 0
R (rubber) V (vitreous) K (crystal) TOTAL
GASES WHOLE FOOD MASS WHOLE FOOD VOLUME W.F.TEMPERATURE (°C) W.F.PRESSURE (atm)
0,000 0,000 -59,1 0,0
0,000 0,000 -59,100 0,00
0 0 0 0
0,000 0,000 0,000 0,00 0,000 0,000 0,000 0,0000 -59,100 -59,100 -59,100 -59,100 -59,100 -59,100 0,00 0,00 0,00 0,00 0,00 0,00
Fig. 12. Matrix of changes of strawberry from the eutectical point until temperature decreases to 100 °C (MC3,2) in case 2.
M.L. Castello´ et al. / Journal of Food Engineering 83 (2007) 238–249
Fig. 4 shows the matrix of the fresh strawberries (M0,0). By means of the information given in the previous tables, some cells of this matrix can be filled following the steps of Fig. 2. For instance, the absorbed water is calculated by changing the monolayer moisture content from dry basis to wet basis, getting the value of 0.089 kg water/kg whole material. Therefore, the amount of liquid water will be obtained by subtracting from the moisture content the absorbed water. Nevertheless, there is not enough information to specify if it is extracellular or intracellular water. The cell of solid matrix is worked out by adding to the mass fraction of water the mass fraction of solids, assuming that the difference until one will give the amount of insoluble solids of the product. Besides, these will be in rubber state since the glass transition temperature has not been reached. The following equation has been used in order to calculate the density of liquid phase of strawberry (Lewis, 1987). qLP ¼ 462:17zs þ 991:05
ð4Þ
where zs is the solid mass fraction in liquid phase and qLP is the density of liquid phase. Initially the value of density of the liquid phase is 1028 kgm3. Considering in the empirical equation (1) the mass fraction of water, the initial temperature for the appearance of the first ice in the strawberry would be 0.9056 °C, this descriptive matrix is shown in Fig. 5. Fig. 6 shows the change matrix of the first stage of changes in all cases. No changes in the distribution of components have been considered in the matrix of product, although the amount
247
of absorbed water of solid matrix has been slightly reduced since the energetic levels are lower. Case 1 works at low freezing rate until 18 °C removing water from the liquid phase and from the absorbed water in the solid matrix (water absorption capacity of matrix is reduced with the temperature) to the new frozen water phase. In this stage, internal and latent heat changes take place while strawberries decrease in temperature and at the same time the water of matrix becomes frozen water, producing a concentration of liquid phase. By replacing 18 °C again in Eq. (1), the amount of non frozen water would be 0.413 g water/g sample (Fig. 7). Then the absorbed water should be deducted from the previous stage in order to get the mass fraction of liquid water. In this case it will be considered the same as in matrix M0,0. The rest of the water, up to 0.91 g water/ g samples of the initial value, is now in the cell corresponding to the water forming ice. Besides, all solids would be in rubbery state given that the temperature has not decreased to the glass transition temperature (Fig. 8). Descriptive matrices of case 2 are shown in Figs. 9 and 11. Figs. 8, 10 and 12 describes all changes of case 2, freezing strawberry down to 100 °C with low freezing rate crossing the eutectic point (40.9 °C). In this case, the rubbery matrix changes to vitreous state. In cases 1 and 2 the freezing rate is slower, then up to the eutectical point is forming ice crystals concentrating the liquid phase. These ices formed were estimated with the Tm curve (Eq. (1)). In addition, the final product arrives to the maximum solids concentration
M2,2 PHASES
COMPONENTS COMPONENT
STATE
SM
LPI
LPE
SS
FW
G (gas) A (adsorbed)
WF
0
0 0.000 0.082
0.000
L (liquid) WATER
GAS
0.082
0
R (rubber)
0.828
V (vitreous)
0.000 0.000
K (crystal) TOTAL
0.082
0.828
0.000
0.000
0.000 0.910
L (liquid) A (adsorbed) NON SOLUBLE SOLIDS (NATIVE)
R (rubber) V (vitreous) K (crystal) TOTAL
0.00 0.0089826 0 0.01
L (liquid) A (adsorbed) SOLUBLE SOLIDS (NATIVE)
0 0.000
0
0
0
0
0
0 0.091
-196
0.000 0.000 -196
0
0.000 0.0089826 0 0.009 0.000 0
R (rubber)
0.081
V (vitreous)
0 0
K (crystal) TOTAL
0
0.081
0.091 0.088 -196
0.909 0.907 -196
GASES WHOLE FOOD MASS WHOLE FOOD VOLUME (L/kg)
W.F.TEMPERATURE (°C)
0.097 -196
0.081 1.00 1.092 -196
Fig. 13. Descriptive matrix of strawberry freezing process until 196 °C with high freezing rate in case 3.
248
M.L. Castello´ et al. / Journal of Food Engineering 83 (2007) 238–249
MC2,1 COMPONENTS COMPONENT STATE G (gas) L (liquid) A (adsorbed) WATER R (rubber) V (vitreous) K (crystal) TOTAL L (liquid) A (adsorbed) NON R (rubber) SOLUBLE SOLIDS V (vitreous) (NATIVE) K (crystal) TOTAL L (liquid) A (adsorbed) SOLUBLE R (rubber) SOLIDS V (vitreous) (NATIVE) K (crystal) TOTAL L (liquid) A (adsorbed) R (rubber) FATS V (vitreous) K (crystal) TOTAL GASES WHOLE FOOD MASS WHOLE FOOD VOLUME W.F.TEMPERATURE (°C) W.F.PRESSURE (atm)
SM
LPI LPE
SS
PHASES FATS FATL
FW
GAS 0
-0,828 0
0 0,828
0
0,000
0,000 0,000
0
-0,01 0,01 0 0,00 -0,081
0
0,000
0 0 0
0,0810
0 0 0 0 0,00 0,000 -195,1 0,00
0,000 0,000 -195,1 0,00
0,828 0,000 0,000
-0,01 0,01 0 0,000 0 0
0 0,081
0
WF 0 -0,828 0,000
0
0,0000 0
0
0 0 0 0
0,000 0,000 0,000 0,000 0,000 0,000 -195,1 -195,1 -195,1 -195,1 -195,1 -195,1 0,00 0,00 0,00 0,00 0,00 0,00
Fig. 14. Matrix of changes of ultra-freezing process of strawberry until 196 °C with high freezing rate (case 3).
obtaining a subcooling liquid phase (Reid et al., 1994) and a new frozen water phase appears. The last case consists of a fast freezing rate process with liquid nitrogen arriving to 196 °C with freeze-concentration and again the appearance of a frozen phase (this case is described of Figs. 13 and 14). In this particular case, all the initial liquid phase (with high viscosity) behaves as vitreous solid (subcooling liquid with high viscosity working as a solid). All of these behaviours of these cases are shown in the matrix of changes (Figs. 6, 8, 10, 12 and 14). In Figs. 8 and 10 is possible to observe a new frozen water phase from the liquid phase and the transition of the matrix, initial rubbery changing to the vitreous aggregation state. Figs. 12 and 14 shows the matrices of change where appears a subcooling liquid phase with high viscosity working like a vitreous solid (Reid et al., 1994). According to these results, using SAFES methodology it is possible to follow and predict the critical point (appearance or disappearance of components or phases) of the freezing process of strawberries to prevent quality loses. Components, phases and aggregation systems also can be analysed. Moreover, transport phenomena, chemical reaction and transition can also be described.
4. Conclusions SAFES methodology may describe the behaviour of strawberry freezing using composition data, state diagrams and thermodynamic parameters. Nevertheless, to get better results it would be required more information about composition of frozen strawberry at different freezing rate levels. Water distribution is described in three different phases improving the knowledge of the process, and this permit to follow better the liquid phase transitions. Porosity variation along the freezing process is shown by means of the volume phases changes, this is relevant to understand the final textural properties. Analyzing the concentrations of liquid phase is possible to predict damage in unfrozen strawberry. Therefore, this methodology allows to know the structural changes at different freezing rates. These changes could be important to predict the final quality of the unfrozen product. Acknowledgements The authors would like to acknowledge the MEC (Ministerio de Educacio´n y Ciencia), CAPA (Consellerı´a de
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Agricultura Pesca y Alimentacio´n), CEUyC (Consellerı´a de Empresa, Universidad y Ciencia) and UPV (Universidad Polite´cnica de Valencia) for financial support. References Brown, M. H. (1991). Microbiological aspect of frozen foods. In W. B. Bald (Ed.), Food freezing: Today and tomorrow (pp. 15–25). London: Springer. Castello´, M. L., Fito, P. J., & Chiralt, A. (2005). Effect of osmotic dehydration on respiration rate of strawberries. LWT, Food Science and Technology, 39, 1171–1179. Castello´, M. L., Fito, P. J., Carvalho, C., Chiralt, A., & Fito, P. (2002). Effect of impregnation on respiration rate of fruits CESIA. Couchman, P. R., & Karasz, F. E. (1978). A classical thermodynamic discussion of the effect of composition on glass-transition temperatures. Macromolecules, 11, 117–125. Delgado, A. E., & Rubiolo, A. C. (2005). Microstructural changes in strawberry after freezing and thawing processes. LWT, Food Science and Technology, 38, 135–142. Erikson, M. C., & Hung, Y. (1997). Quality in frozen food (1st ed.). New York, USA: Chapman and Hall. Fito, P., LeMaguer, M., Betoret, N., & Fito, P. J. (in press). An advanced food process engineering to design real foods and processes: The SAFES methodology. Journal Food Engineering. doi:10.1016/ j.jfoodeng.2007.02.017. Gordon, M., & Taylor, J. S. (1952). Ideal copolymers and the secondorder transitions of synthetic rubbers. I. Non-crystalline copolymers. Journal of Applied Chemistry, 2, 493–500.
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Hammami, C., & Rene´, F. (1997). Determination of Freeze-drying process variables for strawberries. Journal of Food Engineering, 32, 133–154. Lewis, M. J. (1987). Chapter 2. Physical properties of foods and food processing systems. Chichester, England: E.H. Ltd. Moraga, G., Martı´nez-Navarrete, N., & Chiralt, A. (2004). Water sorption isotherms and glass transition in strawberries: influence of pre-treatment. Journal of Food Engineering, 62, 315–321. Perry, R. H., & Green, D. W. (1992). Chemical engineers’ handbook. NY, USA: McGraw Hill. Reid, D. S., Kerr, W., & Hsu, J. (1994). The glass transition in the freezing process. Journal of Food Engineering, 22, 483–494. Rosen, J. C., & Kader, A. A. (1989). Post-harvest physiology and quality maintenance of sliced pear and strawberry fruits. Journal of Food Science, 45, 656–659. Sahari, M. A., Boostani, F. M., & Hamidi, E. Z. (2004). Effect of low temperature on the ascorbic acid content and quality characteristics of frozen strawberry. Food Chemistry, 86, 357–363. Talens, P., Escriche, I., Martı´nez-Navarrete, N., & Chiralt, A. (2002). Study of the influence of osmotic dehydration and freezing on the volatile profile of strawberries. Food Chemistry and Toxicology, 67(5), 1648–1653. Ulrich, R. (1978). Very low temperature (quick freezing) and pseudostabilization of the chemical composition of vegetable foods. Annuales de la Nutrition et de l’Alimentation, 32, 523–532. Urbany, G. Y., & Horti, K. (1992). Changes of surface colour of the fruit and of the anthocyanin content of sour cherries during frozen storage. Acta Alimentaria, 21, 3–4. Withy, L. M., Nguyen, T. T., & Wrolstad, R. F. (1993). Storage changes in anthocyanin concentrate of red raspberry juice content. Journal of Food Science, 1, 190–192.
Application of the SAFES (systematic approach to food engineering systems) methodology to strawberry freezing process M.L. Castello´ *, P.J. Fito, A. Argu¨elles, P. Fito Institute of Food Engineering for Development, Food Technology Department, Valencia, Spain Available online 22 February 2007
Abstract SAFES methodology has been applied in strawberry freezing process using data from references. Three cases of freezing have been studied. All of them start from the refrigerated temperature (Tc) and there is a first stage of cooling until the initial freezing temperature (Tm) is reached. However, the changes of components depend on the temperature reached and the rate of freezing. Case 1 studies the decrease of temperature from Tm until the first layers of cells reach 18 °C, since this is the typical storage temperature in consumer’s freezer. In case 2, strawberries are frozen at the maximally cryoconcentrated temperature ðT 0m Þ of the matrix and then down to 100 °C. In case 3, a deep freezing process decreases the temperature of strawberries down to 196 °C. The last two cases are below the temperature of glass transition of strawberry (51.3 °C) and therefore they have higher stability than in case 1. By means of this methodology it is possible to follow and predict the critical points (appearance or disappearance of components or phases) of the process to prevent quality loss. Components, phases and aggregation systems can also be analysed. Moreover, transport phenomena, chemical reaction and transition can actually be described. It has been demonstrated that SAFES methodology can describe the behaviour of strawberry freezing by using composition data, state diagrams and thermodynamic parameters. Nevertheless, to get better results more information about kinetic data related to freezing process would be required. Ó 2007 Published by Elsevier Ltd. Keywords: Freezing; Strawberry; Cryoconcentration; SAFES
1. Introduction Among the conservative methods, freezing of fruits and vegetables is one of the most common ways to keep their quality. Nevertheless, this method of preservation is considerably complex. Nutritional and organoleptic characteristics of products will depend not only on the temperature, the freezing rate, storage time and maintenance of the cooling chain but also on the thawing conditions (Brown, 1991). As a process which induces changes in product states, it is important to consider the optimal conditions to avoid undesirable effects on their qualitative characteristics. Strawberries are extremely perishable fruits but they
*
Corresponding author. E-mail address: [email protected] (M.L. Castello´).
0260-8774/$ - see front matter Ó 2007 Published by Elsevier Ltd. doi:10.1016/j.jfoodeng.2007.02.035
are highly appreciated by the consumers and freezing can be applied as a suitable method to storage them. Removal of water during processing of many products often results in the formation of an amorphous state which is a non-equilibrium state with time dependent properties. The physical state of amorphous materials may change from a solid vitreous state to a liquid-like rubbery one when the glass transition temperature (Tg) is reached. As the Tg is dependent on the water content, a change from rubbery to a vitreous state can also occur as a consequence of a decrease in the product water content during its processing or storage (Moraga, Martı´nezNavarrete, & Chiralt, 2004). In products with crystallizing components, the determination of the critical water activity or critical water content at a given temperature to avoid crystallization will allow the product shelf-life to be extended (Moraga et al., 2004). State diagrams
M.L. Castello´ et al. / Journal of Food Engineering 83 (2007) 238–249
showing the relationships between product water content and its physical state as a function of temperature together with sorption isotherms are useful tools in process optimisation, food formulation, in establishing processing requirements and designing package/storage conditions. Freezing processes have been studied by means of state diagrams. Furthermore, the temperature of glass transition can be calculated following the model of Gordon and Taylor (1952) and Couchman and Karasz (1978). The state diagram allows us to know the physical state in which the watering phase would be as a function of moisture content and temperature. Depending on the freezing rate, the melting point could change with the freeze-concentration til eutectic point at low freezing rates or at high rates all the liquid phase change to subcooling liquid working as vitreous solid (Reid, Kerr, & Hsu, 1994). A more appropriate freezing process would allow to freeze all the available water until an amount of water in the aqueous phase would equal Wg’ (g water/g of solution maximally cryoconcentrated). In addition, this diagram lets us know the temperature at the beginning of glass transition of the maximally cryoconcentrated matrix ðT 0g Þ and the temperature when the fusion of ice which goes with this matrix is produced. They are not the same due to the fact that glass transition really happens in an interval of temperatures. The maximum formation of ice can only be obtained by keeping the system at a temperature between T 0g and T 0m for a specific length of time. By using this procedure it is possible to know how much product is in rubber or vitreous state. However, it is quite
239
difficult to clarify what happens with the different phases involved in the process. As a consequence of all these changes that occurred in the frozen strawberry structure it is necessary to know the final use of this product to focus on the quality factor that the consumer is looking for. For instance, if the samples will be used in a freeze-drying process there is no need to keep the structure, since the process of sublimation will destroy it anyway. However, if the final objective is to use it in confectionery, the texture should remain as similar as possible to the fresh strawberry. Furthermore, it is essential to adjust the freezing-thawing process variables in order to better preserve and retain the quality of the product. Besides that, samples of strawberries which had undergone low ambient temperature or high air velocities present better structures preservation, due to the small size of ice crystals which were mainly intracellular (Delgado & Rubiolo, 2005). On the contrary, with a slow freezing rate, cells appear torn and irregular in shape and some loss of amorphous material and tissue distortion is observed (Delgado & Rubiolo, 2005). In recent studies, it has been specified that the most important nutritional changes in frozen foods are due to storage time (Sahari, Boostani, & Hamidi, 2004). On one hand, vitamin C has been used as a quality indicator (Erikson & Hung, 1997; Rosen & Kader, 1989; Ulrich, 1978). On the other hand, the maintenance of the red colour of strawberry is necessary for an appropriate commercialization. Temperature is one of the effective factors for anthocyanin resistance (Urbany & Horti, 1992; Withy, Nguyen, & Wrolstad, 1993).
Process of freezing M1
M0
Troom →Tm
M3
M2
Tm →Tstorage
T m →Tm Tg
Tm
isotherm 50
5 4.5
0
4
case 1 -50
3
T (˚C)
xw (kgw/kgms)
3.5
2.5
case 2
2
-100
1.5 -150
1 0.5
case 3
0
-200 1
0.8
0.6
0.4
0.2
0
aw
Fig. 1. Scheme of strawberry freezing process. Stage of changes explained on the strawberry isotherm and state diagram.
M.L. Castello´ et al. / Journal of Food Engineering 83 (2007) 238–249
240 Table 1 Strawberry composition xw
xss
0.91 ± 0.01
0.085 ± 0.007
0.907 ± 0.006 0.91 ± 0.01
0.08 ± 0.01 0.078 0.079
qa (g/cm3)
939 ± 7
qr (g/cm3)
1033
e
zs
0.06–0.07
0.086 ± 0.005
0.09
8±1
Considering all the previous comments, there are several parameters that should be taken into account in order to optimize this food industrial process. A powerful tool to control the process and the quality of the product would be the development of a systematic way to predict the characteristic of the final product. In this sense,
aw
References
0.992 ± 0.002 0.992 ± 0.002 0.99± 0.005
Talens, Escriche, Martı´nez-Navarrete, and Chiralt (2002) (var. Camarosa) Moraga et al. (2004) (var. Camarosa) Castello´, Fito, and Chiralt (2005) (var. Camarosa) Hammami and Rene´ (1997) (var. Pajaro)
SAFES (systematic approach to food engineering systems) is a new methodology that claims to solve or clarify food processes or systems by means of an integration of different models considering all the components, phases and stages of products (Fito, LeMaguer, Betoret, & Fito, in press).
Fig. 2. SAFES methodology application in the strawberry freezing process. See the above mentioned references for more details.
M.L. Castello´ et al. / Journal of Food Engineering 83 (2007) 238–249
In this study, SAFES methodology has been applied in strawberry freezing process using data from references in order to get the right approach to understand it better. 2. Material and methods 2.1. Material Traditional process of cooling and freezing fresh fruits consists basically in one single operation. The temperature of the products decreases until it reaches the initial freezing temperature and then the temperature continues to go down which causes a separation of frozen and unfrozen water. This fact causes a cryo-concentration of the liquid phase of the fruits and consequently, the more concentration liquid phase the lower the temperature required to freeze it. Therefore it is important to know what is happening in each stage of the freezing process according to the temperature and the freezing rate. Fig. 1 shows the same process but divided in stages which consider the changes in the matrix of fruits more exhaustively. Moraga et al. (2004) determined water sorption isotherms and glass transition as a function of moisture content of strawberries taking into account the whole or the homogenized fruit. GAB model was used to model the water plasticization effect. By knowing the composition of strawberries (Table 1) and the parameters of GAB (Moraga et al., 2004) and also Gordon and Taylor models it is possible to apply the SAFES methodology in order to know which changes have taken place in each component, phase and aggregation state. The melting temperature of strawberries can be obtained by means of an empirical equation (1) where a = 5.4 and b = 0.6. In this way the freezing curve predicted by this method can be obtained (Fig. 1) (Moraga et al., 2004). a Tm ¼ ð1Þ b 1 þ lnð2wÞ where Tm is the melting temperature; w is the water mass fraction in wet basis.
241
According to Moraga et al. (2004), the temperature of the maximally cryoconcentrated matrix T 0m of strawberry is 40.9 ± 1 °C, the value of the glass transition of maximally cryoconcentrated fruit liquid phase ðT 0g Þ of this fruit is 51.3 ± 0.7 °C and the amount of non-frozen water ðx0wg Þ is 0.221. All these data will be also used to develop the SAFES methodology in the strawberry freezing process. 2.2. Methods Three cases of freezing have been studied. All of them start from the refrigerated temperature and there is a first stage of cooling until the initial freezing temperature (Tm). However, the changes of components depend on the temperature reached and the rate of freezing. Case 1 studies the decrease of temperature from Tm to 18 °C, since this is the typical storage temperature in consumer’s freezer. In case 2, strawberries are frozen until the maximally freeze-concentrated glass temperature ðT 0g Þ and then down to 100 °C. In case 3, an deep freezing process decreases temperature of strawberries down to 196 °C, when the viscosity of the liquid phase rises rapidly working like a vitreous solid (see all the three cases in Fig. 1). SAFES methodology considers the product describing phases, components and aggregation states and their development during the studied process. In order to apply the SAFES methodology, it is important to analyze the critical points (i.e. stages of changes) of the process. The following step is to build the matrices of products, once the needed hypotheses are defined and all the required information is
Table 2 SAFES’s codes to strawberry freezing process ðX kij Þ Phases
j
Components
i
state
k
Solid matrix Liquid Soluble solids Frozen water Gas Whole food
1 2 3 4 5 0
Water Non soluble solids (native) Soluble solids (native)
1 2 3 4
Whole food
0
Gas (G) Liquid (L) Adsorbed (A) Rubber (R) Vitreous (V) Crystal (K)
0 1 2 3 4 5
Fig. 3. Scanning electron micrographs of cellular structure of fresh strawberry tissue (a); a sample frozen at 4.54 m/s and 30 °C (2.43 C/min) (b) and SEM of parenchyma tissue of a sample frozen at 0.82 °C/min (c). (Delgado & Rubiolo, 2005).
M.L. Castello´ et al. / Journal of Food Engineering 83 (2007) 238–249
242
M0,0 PHASES
COMPONENTS COMPONENT
STATE
SM
LPI
LPE
SS
FW
G (gas) A (adsorbed)
WF
0
0 0.821 0.089
0.821
L (liquid) WATER
GAS
0.089
0
R (rubber) V (vitreous)
0 0
K (crystal) TOTAL
0.089
0.821
0
0 0.910
0
L (liquid) A (adsorbed) NON SOLUBLE SOLIDS (NATIVE)
R (rubber) V (vitreous) K (crystal) TOTAL
0.01 0 0 0.01
0.009 0
0.081
L (liquid) A (adsorbed) SOLUBLE SOLIDS (NATIVE)
0 0.009 0.081
0
0
R (rubber) V (vitreous) K (crystal) TOTAL
0
0.081
0 0.000 1 0.097 4 1.00
GASES WHOLE FOOD MASS WHOLE FOOD VOLUME (L/kg)
W.F.TEMPERATURE (°C) W.F.PRESSURE (atm)
0.098 0.095 4 1.00
0.902 0.874 4 1.00
0 4
4 1.00
1.00
.081 0.000 .00 1.066 4 1.00
Fig. 4. Descriptive matrix of raw strawberry (M0,0) of the three cases. SM is solid matrix, LPI is liquid phase intracellular, LPE is liquid phase intracellular, SS is soluble solids, FW is frozen water phase, GAS is gas phase and WF is whole food.
M1,1 PHASES
COMPONENTS COMPONENT
STATE
SM
LPI
LPE
SS
FW
G (gas) A (adsorbed)
WF
0
0 0.828 0.082
0.828
L (liquid) WATER
GAS
0.082
0
R (rubber) V (vitreous) K (crystal) TOTAL
0.082
0.828
0
0 0
0
0 0.910
L (liquid) A (adsorbed) NON SOLUBLE SOLIDS (NATIVE)
R (rubber) V (vitreous) K (crystal) TOTAL
0.01 0 0 0.01
SOLUBLE SOLIDS (NATIVE)
0 0.009 0.081 0
0.081
L (liquid) A (adsorbed)
0.009 0
0
R (rubber) V (vitreous) K (crystal) TOTAL
0
0.081 0.000
GASES WHOLE FOOD MASS WHOLE FOOD VOLUME (L/Kg)
W.F.TEMPERATURE (°C) W.F.PRESSURE (atm)
0.091 0.0884 -0.906 1.00
0.909 0.881 -0.906 1.00
-0.906 1.00
-0.906 1.00
0.097 -0.906 1.00
0.081 0.000 1.00 1.066 -0.906 1.00
Fig. 5. Descriptive matrix of strawberry (M1,1) at the initial freezing temperature (Tm) for all cases.
M.L. Castello´ et al. / Journal of Food Engineering 83 (2007) 238–249
243
MC1,0 PHASES
COMPONENTS COMPONENT
STATE
SM
LPI
LPE
SS
FW
G (gas) A (adsorbed)
WF
0
0 0.007 -0.007
0.007
L (liquid) WATER
GAS
-0.007
0
R (rubber) V (vitreous)
0 0
K (crystal)
-0.007
TOTAL
0
0.007
0.000 0.000
0
L (liquid) A (adsorbed) NON SOLUBLE SOLIDS (NATIVE)
0.00 0 0 0.00
R (rubber) V (vitreous) K (crystal) TOTAL
0.000
L (liquid)
0
A (adsorbed) SOLUBLE SOLIDS (NATIVE)
0.000 0.000 0.000 0.000 0.000 0.000 0
R (rubber) V (vitreous) K (crystal)
0
TOTAL
0.000 0.000
GASES WHOLE FOOD MASS WHOLE FOOD VOLUME (kg/L)
W.F.TEMPERATURE (°C) W.F.PRESSURE (atm)
-0.007 -0.007 -4.906 0.00
0
0.007 0.007 -4.906 0.00
-4.906 0.00
0.000 -4.906 0.00
-4.906 0.00
0.000 0.000 0.000 0.000 -4.906 0.00
Fig. 6. Matrix of changes of strawberry in the stage from the refrigerated temperature until the first ice crystal appears (M1,0) for all cases.
available. Each of these matrices consists basically of a three dimensional space inserted in a plane surface as a matrix where columns represent the phases (j) and the main
rows represent the components (i). The information on the aggregation states of each component (k) is included amongst the main rows. Each cell of this space system is
M2,2 PHASES
COMPONENTS COMPONENT
STATE
SM
LPI
LPE
SS
FW
G (gas) A (adsorbed)
WF
0
0 0.331 0.082
0.331
L (liquid) WATER
GAS
0.082
0
R (rubber) V (vitreous) K (crystal) TOTAL
0.082
0.331
0.000
0.497 0.497
0.000
0.497 0.910
L (liquid) A (adsorbed) NON SOLUBLE SOLIDS (NATIVE)
R (rubber) V (vitreous) K (crystal) TOTAL
0.01 0 0 0.01 0.081
L (liquid) A (adsorbed) SOLUBLE SOLIDS (NATIVE)
0.009 0 0 0.009 0.081
0
0
R (rubber) V (vitreous) K (crystal) TOTAL
0
0.081
0.091 0.102 -18 1.00
0.413 0.381 -18 1.00
0 0
GASES WHOLE FOOD MASS WHOLE FOOD VOLUME (kg/L)
W.F.TEMPERATURE (°C) W.F.PRESSURE (atm)
-18 1.00
0.497 0.625 -18 1.00
0 0.000 0.112 -18 1.00
0.081 1.00 1.219 -18 1.00
Fig. 7. Descriptive matrix of strawberry freezing process until 18 °C, with low freezing rate. (M2,2) in case 1.
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244
MC2,1 PHASES
COMPONENTS COMPONENT
STATE
SM
LPI
LPE
SS
FATS
FATL
FW
GAS
WF
0
0 -0,497
G (gas)
-0,497
L (liquid)
0
A (adsorbed) WATER
0
0,000
R (rubber) V (vitreous) K (crystal)
0
TOTAL
-0,497
0
0
0
0,497 0,497
0
0,497 0,000
L (liquid) A (adsorbed) NON SOLUBLE SOLIDS (NATIVE)
0,00 0 0 0,00
R (rubber) V (vitreous) K (crystal) TOTAL
0 0,000
L (liquid)
0
0
0
0
0
A (adsorbed) SOLUBLE SOLIDS (NATIVE)
0
0,000 0 0 0 0 0
R (rubber)
0 0
V (vitreous) K (crystal)
0
TOTAL
0,000
0
0
L (liquid)
0
0
0
0
0,0 0
0
0
0 0 0
-17 0
0,497 0,625 -17 0
A (adsorbed)
0 0 0 0
R (rubber)
FATS
V (vitreous) K (crystal)
0
0
0,00 0,013 -17 0
-0,497 0,000 -17 0
TOTAL
0
0
0 0,000
GASES WHOLE FOOD MASS WHOLE FOOD VOLUME W.F.TEMPERATURE (°C) W.F.PRESSURE (atm)
-17 0
-17 0
-0,097 -17 0
0,0 0,541 -17 0
Fig. 8. Matrix of changes of freezing strawberry from Tm until temperature decreases to 18 °C (MC2,1) in case 1.
M2,2 PHASES
COMPONENTS COMPONENT
STATE
SM
LPI
LPE
SS
FW
G (gas) A (adsorbed)
WF
0
0 0.219 0.082
0.219
L (liquid) WATER
GAS
0.082
0
R (rubber) V (vitreous)
0.609 0.609
K (crystal) TOTAL
0.082
0.219
0.000
0.000
0.609 0.910
L (liquid) A (adsorbed) NON SOLUBLE SOLIDS (NATIVE)
R (rubber) V (vitreous) K (crystal) TOTAL
0.01 0 0 0.01
L (liquid) A (adsorbed) SOLUBLE SOLIDS (NATIVE)
0.010 0 0 0.081
0
0
0
0
0 0.010 0.081 0
R (rubber)
0 0
V (vitreous) K (crystal) TOTAL
0
0.081
0.092 0.119 -40.9 1.00
0.300 0.269 -40.9 1.00
0
0
-40.9 1.00
0.609 0.888 -40.9 1.00
GASES WHOLE FOOD MASS WHOLE FOOD VOLUME (Kg/L)
W.F.TEMPERATURE (°C) W.F.PRESSURE (atm)
0 0.091 0.129 -40.9 1.00
0.081 1.00 1.405 -40.9 1.00
Fig. 9. Descriptive matrix of strawberry freezing process until 40.9 °C with low freezing rate in case 2.
M.L. Castello´ et al. / Journal of Food Engineering 83 (2007) 238–249
245
filled by a number which is identified as xki;j (Fig. 2). Furthermore, the last three rows of the matrices refer to the volume, temperature and pressure for each phase (Fito et al., in press). There are three kinds of matrices:
In this paper, only the descriptive matrices and the matrices of change have been included.
The descriptive matrices show the composition of products expressed as mass fractions and consequently: XXX xki;j ¼ 1 ð2Þ
The target of this work is to understand the freezing process of strawberry through the SAFES approach. Previously is necessary to define the different phases in the strawberry matrix using microscopy of fresh and frozen tissue (see Fig. 3). This figure shows cellular tissue (parenchyma) fresh and frozen at different freezing rates. The definition of the phases, components and aggregation states of raw material will be the following (codes are shown in Table 2):
i
j
3. Results and discussion
k
The transformed matrices, where xi,jk concerns the shared out of mass in the system and usually: XXX xki;j 6¼ 1 ð3Þ i
j
k
– Components: Water, non soluble solids and soluble solids – States: gas, liquid, adsorbed, rubber, vitreous and crystal – Phases: Solid matrix (Insoluble solids), liquid, soluble solids, gas and frozen water.
One transformed matrix is calculated by multiplying the corresponding descriptive matrix by the ratio of mass variation. The Matrices of changes are worked out by subtracting two matrices referred to the same basis of calculus.
MC2,1 PHASES
COMPONENTS COMPONENT
STATE
SM
LPI
LPE
SS
FATS
FATL
FW
G (gas)
WATER
WF
0
0,00 -0,61
-0,609
L (liquid) A (adsorbed)
GAS
0
0
0,00
R (rubber) V (vitreous)
0,609 0,61
K (crystal) TOTAL
0
-0,609
0
0
0,61 0,00
L (liquid) NON SOLUBLE SOLIDS (NATIVE)
A (adsorbed) R (rubber) V (vitreous) K (crystal) TOTAL
0,00 0,00 0,00 0,00 0,000
L (liquid) A (adsorbed) SOLUBLE SOLIDS (NATIVE)
0,00 0,00 0,00 0,00 0,00
0
0,00
R (rubber) V (vitreous) K (crystal) TOTAL
0
0
0 0 0,000
0,00
L (liquid)
0
0,00
0
0,00 0,00 0,00 0,00
A (adsorbed) FATS
0 0 0 0
R (rubber) V (vitreous) K (crystal) TOTAL
GASES WHOLE FOOD MASS WHOLE FOOD VOLUME W.F.TEMPERATURE (°C) W.F.PRESSURE (atm)
0,001 0,031 -40,0 0,0
-0,609 -0,509 -40,0 0,00
0,000 0,000 -40,0 0,00
-40,0 0,00
-40,0 0,00
0,000 0,609 0,00 0,888 0,033 0,442 -40,0 -40,0 -40,0 0,00 0,00 0,00
Fig. 10. Matrix of changes of freezing strawberry from Tm until temperature decreases to the eutectical point (MC2,1) in case 2.
M.L. Castello´ et al. / Journal of Food Engineering 83 (2007) 238–249
246
M3,3 COMPONENTS COMPONENT
PHASES STATE
SM
LPI
LPE
SS
FATS
FATL
FW
G (gas)
GAS
WF
0
0 0
L (liquid) A (adsorbed) WATER
0,082
0
0,082
R (rubber)
0,219
V (vitreous)
0,609 0,609
K (crystal) TOTAL
0,082
0,219
0
0,219 0,609 0,91
0
L (liquid) A (adsorbed)
NON SOLUBLE SOLIDS (NATIVE)
R (rubber) V (vitreous) K (crystal) TOTAL
0 0,01 0 0,01
0 0,01 0 0,01 0
0
0
L (liquid) A (adsorbed) SOLUBLE SOLIDS (NATIVE)
R (rubber)
0,081
V (vitreous)
0 0 0,000
K (crystal) TOTAL
0
0,081
0,081 0 0,081
0
0
L (liquid) A (adsorbed) R (rubber)
FATS
V (vitreous) K (crystal) TOTAL
0
0
0
0
0 0 0 0
0 0 0 0
0
0 0,091
GASES WHOLE FOOD MASS WHOLE FOOD VOLUME W.F.TEMPERATURE (°C) W.F.PRESSURE (atm)
0,092 0,119 -100,0 1,00
0,300 0,105 -100,000 1,00
0
0,000 0,609 1,00 0,0000 0,888 0,129 1,1366 -100,000 -100,000 -100,000 -100,000 -100,000 -100,000 1,00 1,00 1,00 1,00 1,00 1,00
Fig. 11. Descriptive matrix of strawberry freezing process from 40.9 °C until 100 °C with low freezing rate in case 2.
MC3,2 PHASES
COMPONENTS COMPONENT
STATE
SM
LPI
LPE
SS
FATS
FATL
FW
G (gas) A (adsorbed)
WF
0
0 -0,219
-0,219
L (liquid) WATER
GAS
0
0
0
R (rubber)
0,219
V (vitreous)
0,000 0,000
K (crystal) TOTAL
0
0,000
0
0,000
0,219 0,000 0,00
L (liquid) NON SOLUBLE SOLIDS (NATIVE)
A (adsorbed) R (rubber) V (vitreous) K (crystal) TOTAL
-0,0 0,01 0,00 0,00 -0,081
L (liquid) A (adsorbed) SOLUBLE SOLIDS (NATIVE)
-0,01 0,01 0 0 -0,081
0
0
R (rubber)
0,081
V (vitreous) K (crystal) TOTAL
0
0,000
0 0 0 ,000
0,081 0 0
0 0
L (liquid)
0
0
0 0
A (adsorbed) FATS
0 0 0 0
R (rubber) V (vitreous) K (crystal) TOTAL
GASES WHOLE FOOD MASS WHOLE FOOD VOLUME W.F.TEMPERATURE (°C) W.F.PRESSURE (atm)
0,000 0,000 -59,1 0,0
0,000 0,000 -59,100 0,00
0 0 0 0
0,000 0,000 0,000 0,00 0,000 0,000 0,000 0,0000 -59,100 -59,100 -59,100 -59,100 -59,100 -59,100 0,00 0,00 0,00 0,00 0,00 0,00
Fig. 12. Matrix of changes of strawberry from the eutectical point until temperature decreases to 100 °C (MC3,2) in case 2.
M.L. Castello´ et al. / Journal of Food Engineering 83 (2007) 238–249
Fig. 4 shows the matrix of the fresh strawberries (M0,0). By means of the information given in the previous tables, some cells of this matrix can be filled following the steps of Fig. 2. For instance, the absorbed water is calculated by changing the monolayer moisture content from dry basis to wet basis, getting the value of 0.089 kg water/kg whole material. Therefore, the amount of liquid water will be obtained by subtracting from the moisture content the absorbed water. Nevertheless, there is not enough information to specify if it is extracellular or intracellular water. The cell of solid matrix is worked out by adding to the mass fraction of water the mass fraction of solids, assuming that the difference until one will give the amount of insoluble solids of the product. Besides, these will be in rubber state since the glass transition temperature has not been reached. The following equation has been used in order to calculate the density of liquid phase of strawberry (Lewis, 1987). qLP ¼ 462:17zs þ 991:05
ð4Þ
where zs is the solid mass fraction in liquid phase and qLP is the density of liquid phase. Initially the value of density of the liquid phase is 1028 kgm3. Considering in the empirical equation (1) the mass fraction of water, the initial temperature for the appearance of the first ice in the strawberry would be 0.9056 °C, this descriptive matrix is shown in Fig. 5. Fig. 6 shows the change matrix of the first stage of changes in all cases. No changes in the distribution of components have been considered in the matrix of product, although the amount
247
of absorbed water of solid matrix has been slightly reduced since the energetic levels are lower. Case 1 works at low freezing rate until 18 °C removing water from the liquid phase and from the absorbed water in the solid matrix (water absorption capacity of matrix is reduced with the temperature) to the new frozen water phase. In this stage, internal and latent heat changes take place while strawberries decrease in temperature and at the same time the water of matrix becomes frozen water, producing a concentration of liquid phase. By replacing 18 °C again in Eq. (1), the amount of non frozen water would be 0.413 g water/g sample (Fig. 7). Then the absorbed water should be deducted from the previous stage in order to get the mass fraction of liquid water. In this case it will be considered the same as in matrix M0,0. The rest of the water, up to 0.91 g water/ g samples of the initial value, is now in the cell corresponding to the water forming ice. Besides, all solids would be in rubbery state given that the temperature has not decreased to the glass transition temperature (Fig. 8). Descriptive matrices of case 2 are shown in Figs. 9 and 11. Figs. 8, 10 and 12 describes all changes of case 2, freezing strawberry down to 100 °C with low freezing rate crossing the eutectic point (40.9 °C). In this case, the rubbery matrix changes to vitreous state. In cases 1 and 2 the freezing rate is slower, then up to the eutectical point is forming ice crystals concentrating the liquid phase. These ices formed were estimated with the Tm curve (Eq. (1)). In addition, the final product arrives to the maximum solids concentration
M2,2 PHASES
COMPONENTS COMPONENT
STATE
SM
LPI
LPE
SS
FW
G (gas) A (adsorbed)
WF
0
0 0.000 0.082
0.000
L (liquid) WATER
GAS
0.082
0
R (rubber)
0.828
V (vitreous)
0.000 0.000
K (crystal) TOTAL
0.082
0.828
0.000
0.000
0.000 0.910
L (liquid) A (adsorbed) NON SOLUBLE SOLIDS (NATIVE)
R (rubber) V (vitreous) K (crystal) TOTAL
0.00 0.0089826 0 0.01
L (liquid) A (adsorbed) SOLUBLE SOLIDS (NATIVE)
0 0.000
0
0
0
0
0
0 0.091
-196
0.000 0.000 -196
0
0.000 0.0089826 0 0.009 0.000 0
R (rubber)
0.081
V (vitreous)
0 0
K (crystal) TOTAL
0
0.081
0.091 0.088 -196
0.909 0.907 -196
GASES WHOLE FOOD MASS WHOLE FOOD VOLUME (L/kg)
W.F.TEMPERATURE (°C)
0.097 -196
0.081 1.00 1.092 -196
Fig. 13. Descriptive matrix of strawberry freezing process until 196 °C with high freezing rate in case 3.
248
M.L. Castello´ et al. / Journal of Food Engineering 83 (2007) 238–249
MC2,1 COMPONENTS COMPONENT STATE G (gas) L (liquid) A (adsorbed) WATER R (rubber) V (vitreous) K (crystal) TOTAL L (liquid) A (adsorbed) NON R (rubber) SOLUBLE SOLIDS V (vitreous) (NATIVE) K (crystal) TOTAL L (liquid) A (adsorbed) SOLUBLE R (rubber) SOLIDS V (vitreous) (NATIVE) K (crystal) TOTAL L (liquid) A (adsorbed) R (rubber) FATS V (vitreous) K (crystal) TOTAL GASES WHOLE FOOD MASS WHOLE FOOD VOLUME W.F.TEMPERATURE (°C) W.F.PRESSURE (atm)
SM
LPI LPE
SS
PHASES FATS FATL
FW
GAS 0
-0,828 0
0 0,828
0
0,000
0,000 0,000
0
-0,01 0,01 0 0,00 -0,081
0
0,000
0 0 0
0,0810
0 0 0 0 0,00 0,000 -195,1 0,00
0,000 0,000 -195,1 0,00
0,828 0,000 0,000
-0,01 0,01 0 0,000 0 0
0 0,081
0
WF 0 -0,828 0,000
0
0,0000 0
0
0 0 0 0
0,000 0,000 0,000 0,000 0,000 0,000 -195,1 -195,1 -195,1 -195,1 -195,1 -195,1 0,00 0,00 0,00 0,00 0,00 0,00
Fig. 14. Matrix of changes of ultra-freezing process of strawberry until 196 °C with high freezing rate (case 3).
obtaining a subcooling liquid phase (Reid et al., 1994) and a new frozen water phase appears. The last case consists of a fast freezing rate process with liquid nitrogen arriving to 196 °C with freeze-concentration and again the appearance of a frozen phase (this case is described of Figs. 13 and 14). In this particular case, all the initial liquid phase (with high viscosity) behaves as vitreous solid (subcooling liquid with high viscosity working as a solid). All of these behaviours of these cases are shown in the matrix of changes (Figs. 6, 8, 10, 12 and 14). In Figs. 8 and 10 is possible to observe a new frozen water phase from the liquid phase and the transition of the matrix, initial rubbery changing to the vitreous aggregation state. Figs. 12 and 14 shows the matrices of change where appears a subcooling liquid phase with high viscosity working like a vitreous solid (Reid et al., 1994). According to these results, using SAFES methodology it is possible to follow and predict the critical point (appearance or disappearance of components or phases) of the freezing process of strawberries to prevent quality loses. Components, phases and aggregation systems also can be analysed. Moreover, transport phenomena, chemical reaction and transition can also be described.
4. Conclusions SAFES methodology may describe the behaviour of strawberry freezing using composition data, state diagrams and thermodynamic parameters. Nevertheless, to get better results it would be required more information about composition of frozen strawberry at different freezing rate levels. Water distribution is described in three different phases improving the knowledge of the process, and this permit to follow better the liquid phase transitions. Porosity variation along the freezing process is shown by means of the volume phases changes, this is relevant to understand the final textural properties. Analyzing the concentrations of liquid phase is possible to predict damage in unfrozen strawberry. Therefore, this methodology allows to know the structural changes at different freezing rates. These changes could be important to predict the final quality of the unfrozen product. Acknowledgements The authors would like to acknowledge the MEC (Ministerio de Educacio´n y Ciencia), CAPA (Consellerı´a de
M.L. Castello´ et al. / Journal of Food Engineering 83 (2007) 238–249
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