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Non-isotropic shrinkage and interfaces during convective drying of potato slabs within the frame of the systematic approach to food engineering systems (SAFES) methodology
Journal of Food Engineering 83 (2007) 285–292 www.elsevier.com/locate/jfoodeng
Non-isotropic shrinkage and interfaces during convective drying of potato slabs within the frame of the systematic approach to food engineering systems (SAFES) methodology R. Campos-Mendiola a, H. Herna´ndez-Sa´nchez a, J.J. Chanona-Pe´rez a, L. Alamilla-Beltra´n a, A. Jime´nez-Aparicio b, P. Fito c, G.F. Gutie´rrez-Lo´pez a,* a
Departamento de Graduados e Investigacio´n en Alimentos, Escuela Nacional de Ciencias Biolo´gicas, Instituto Polite´cnico Nacional, Carpio y Plan de Ayala S/N, CP 11340, Me´xico DF, Mexico b Centro de Desarrollo de Productos Bio´ticos del IPN, Carretera Jojutla km 8.5, Col. San Isidro, C.P. 62731, Yautepec, Morelos, Mexico c Instituto Universitario de Ingenierı´a en Alimentos para el Desarrollo, Universidad Polite´cnica de Valencia, Camino de Vera 46022 s/n Valencia, Spain Available online 21 February 2007
Abstract Non-isotropic shrinkage of potato slabs was studied within the frame of the systematic approach to food engineering systems (SAFES) methodology. Digital images of potato slabs were taken and lateral projected areas (Alat) of material during drying were recorded. Two characteristics peaks in graphs Alat vs. time were detected. Also, cellular surface area of potato cells was recorded and related to moisture content by means of an empirical equation with in conjunction with SAFES methodology and Alat values at the two afore mentioned peaks, allowed to evaluate intra- and extracellular moisture contents. Fractal dimension (Df) of solid–air interfaces during drying were also calculated. Graphs of Df vs. time also showed two peaks which appeared at approximately the same drying times than those for Alat which may indicate that inner structures composed of solid–air matrixes are projected towards the surface in the form of fractal solid–air interfaces. Ó 2007 Elsevier Ltd. All rights reserved. Keywords: SAFES; Convective drying; Shrinkage; Fractal interfaces; Image analysis
1. Introduction Traditional food processing considers the food as a homogeneous and do not provide enough information regarding internal and external transport and physical properties including microstructure. Recently, the systematic approach to food engineering systems (SAFES) methodology was developed and applied to several food processes (Chenoll, Heredia, Seguı´, & Fito, 2005). This approach considers different phases, components and aggregation states present in the food and takes into account structure and interactions among components. In this context, the inclusion of dynamic and complex inter*
Corresponding author. Tel.: +55 57296300. E-mail address: [email protected] (G.F. Gutie´rrez-Lo´pez).
0260-8774/$ - see front matter Ó 2007 Elsevier Ltd. All rights reserved. doi:10.1016/j.jfoodeng.2007.02.027
faces, both internal and external may be of interest to further explain the complex transfer mechanisms and interactions of components during processing. Dehydrated foodstuffs often present problems related to their structural characteristics, which affect rehydration, aroma retention, sensory attributes (colour, texture), as well as heat and mass transport phenomena during processing (Aguilera, 2003). Foodstuffs are considered complex structural systems, formed by different tissues responsible for their composition and structural characteristics. Vegetables undergo structural changes during drying, such as volume reduction, density and porosity increase, and texture alterations, which affect the characteristics of the final product (Ramos, Brandao, & Silva, 2003). Also, upon drying structures and, consequently interfaces are generated and destroyed. Reduction of volume or shrinkage has been studied on
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Nomenclature Alat Ac D D Df Gw L k
lateral projected area cell relative cellular area Acell t =A0 diameter fractal exponent fractal dimension water vapour fraction thickness of potato slab thickness of potato slab (Gekas & Lamberg, 1991) M i,j descriptive matrix MC i,j matrix of changes Mds mass of dry solid Mp mass of potato slab Mw mass of water
several vegetables (Karathanos, Kanellopoulos, & Belessiotis, 1996; Lozano, Rotstein, & Urbicain, 1980; Zogzas, Maroulis, & Marinos-Kouris, 1994). Since shrinkage affects moisture transfer along dehydration, changing geometry of the food during drying makes understanding of moisture transfer mechanisms complex (Gekas & Lamberg, 1991). Also, Yang, Sakai, and Watanabe (2001) described potato shrinkage as non-isotropic or irregular. These authors proposed a predictive model for the deformation of finite potato cylinders, where the centre shrinks more than the surface. At microstructural level, Perre´ and May (2001) modelled the cell configuration of parenchyma, and reported that cells move and rotate producing a global deformation of the material. Tools such as image analysis have been recently used to study structural changes of foodstuffs such as shrinkage. Image analysis requires the capture of an image while microscopes, among other instruments, are used to study microstructure. Images are converted into a number of matrixes with the help of computer software, that determine geometrical parameters allowing such matrixes to be contrasted, darkened, clarified, etc. (Aguilera, 2003). One way for characterizing a digital image of foods during drying is by means of the fractal dimension of the distribution of surface temperatures of the surface of the sample undertaking drying (Gutie´rrez Lo´pez et al., 2002). Also, fractal geometry may be useful for studying interfaces and their roles as transfer-controlling barriers. Non-isotropic shrinkage of products has not been extensively studied. The aim of the present work is to obtain information on the non-isotropic shrinkage of potato slabs and cells during convective dehydration and to evaluate profiles of solid–gas interfaces generated by means of image analysis and fractal geometry. The information was useful for obtaining data on intra- and extracellular water contents; results were processed within the frame of SAFES methodology.
RH T u Vi, Vf xic xw X Zds Zec Zic
relative moisture content of air temperature air velocity initial and final volume intracellular water fraction water fraction moisture content (kg water/kg dry solids) mass fraction of dry solids extracellular solids fraction intracellular solids fraction
Subscripts t time (0, 15, 40 min) 0 initial
2. Materials and methods Potato (Solanum tuberosum var. Alpha) was cut into circular slabs, 40 mm diameter. Slabs were submerged into a 0.05% solution of sodium meta-bisulphite (Sigma 768157-4) for 2 min to control browning. Two slices were simultaneously dehydrated in an experimental air drier (Fig. 1). A 43 experimental design was applied using MINITAB software (MINITAB Release 13.1, USA), including three
6
4
LATERAL VIEW 1 2
airflow
5 3
6
8
7
5
FRONT VIEW Fig. 1. Diagram of the experimental drier coupled to the image recording system: (1) drier tunnel, (2) fan and heater, (3) airflow temperature control, (4) airflow control, (5) testing section and sample, (6) upper digital camera, (7) side digital camera and (8) windows for image capturing.
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factors (temperature, drying air rate and thickness of the sample), four levels and five repetitions in the central point. Accordingly, four drying air temperatures (40, 50, 60 and 70 °C), four air velocities (1, 1.5, 2.0 and 2.5 m/s) and four thicknesses of sample (1, 2, 3 and 4 mm) were tested. One of the slices was used to record the shrinkage/deformation process by capturing, digital images of the lateral and top view of samples during drying was carried out using two digital cameras (DC290 zoom, Kodak, USA). Both cameras were connected to a serial port of a generic PC (AMD-K6, 450 MHz, 312 MB RAM, 40 GB hard disk) equipped with a video recording card (ATI, All in Wonder Rage-128pro, USA) and image recording software (ATI version 6.2, Multimedia Center). The other slab was used to evaluate weight loss and moisture of sample along drying. Weights of samples were taken in an analytical balance (OAHUS, Analytical plus, USA). Initial moisture of slabs was determined according to the AOAC 32.1.03 method (AOAC, 1995). A fluorescent light ring (Universal driver model 13 plus, USA) was placed around the lenses of the cameras to illuminate objects. Images obtained from the side and upper views of the slabs were stored as colour images (640X480 pixels) in a bit map format. ImageJ software 1.34 NIH (National Institutes of Health, Bethesda, MD, USA) was used to analyze recorded images of slabs as well as to measure the area of the cell (Acel) during drying. The analysis included transformation into a grey scale of captured images, followed by segmentation of the lateral boundary in order to obtain the projected shape of solid–air interface of slabs. Dimensionless values of lateral projected area of potato slabs (Alat t/Alat 0) were taken as indicators of non-isotropic shrinkage/deformation in conjunction with values of area of potato cells obtained during drying to determine a correlation with moisture removal of sample. Cellular shrinkage was evaluated from the images captured during drying by coupling a stereoscopic microscope (Nikon SMZ1500) fitted with a digital CCD camera (Nikon, Coolpix4500) to the experimental drier. Five cells were photographed from the central field of the microscope and for each experiment, three replicates were carried out. Another experiment was performed to evaluate structural changes in the solid–gas interface. Images of such interfaces were taken during drying by means of the same microscope-camera image capturing system as described above. Five images for each drying zone (centre and border) were obtained. Also, fractal dimension of images of profiles of solid–gas interfaces generated along drying were obtained and their fractal dimension were calculated using the box counting method as recommended by Alamilla-Beltra´n, ChanonaPe´rez, Jime´nez-Aparicio, and Gutie´rrez-Lo´pez (2005). Fractal Count 1.42 plugin of ImageJ was used to evaluated the fractal dimension of the profiles of the solid–gas interfaces.
287
2.1. SAFES Matrixes including phases, components and aggregation states were defined after applying experimental and reported values of physical properties. A flow chart was constructed and hypotheses were formulated to establish the state and change matrixes, following the SAFES methodology proposed by Chenoll et al. (2005). Also, geometric patterns of the non-isotropic shrinkage and interfaces of potato slabs were recorded to relate them to values of intra- and extracellular water in the SAFES matrixes. For the purposes of this work, no contrast matrixes were calculated since useful data for characterization and systematization of the drying process, including shrinkage were established within descriptive and changes matrixes. 2.1.1. Definition of phases, components and aggregation states Phases considered in this experiment were (1) (2) (3) (4) (5)
Solid intracellular phase. Solid extracellular phase. Intracellular liquid phase. Extracellular liquid phase. Gas phase. Air–water vapour mix into sample due to porosity.
The components are (a) Water. Mostly in the liquid state. (b) Solids. All the components described in both, intraand extracellular solid phases. (c) Gaseous. Air–water vapour mix.
2.1.2. Flow chart of the drying process Descriptive and changing matrixes for the evaluation of water motion were evaluated according to flow chart depicted in Fig. 2. Initial total solids: 20.6% (wet basis). 3. Results and discussion 3.1. Non-isotropic shrinkage of potato slabs Fig. 3 depicts images of initial projected lateral area of sample, showing an elongated rectangular shape which
Fresh potato M 0,0
1st deformation stage M 1,1
MC 1,0 = M 1,1 - M 0,0
2nd deformation stage M 2,2
MC 2,1 = M 2,2 – M 1,1
Fig. 2. Flow chart for evaluation of matrixes (M is descriptive matrix and MC is matrix of change).
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Fig. 5. Alat/Alat 0 of fresh and rehydrated potato slabs as a function time (T = 55 °C, u = 1.7 m/s, L = 2.5 mm).
Fig. 3. Side image of a potato slabs at different drying times (T = 55 °C, u = 1.7 m/s, L = 2.5 mm).
1.05
1.8
1.00
1.6
0.95
/ A0
cell
2.0
cell
1.4
0.90
At
Alat/Alat,0
tends to bend, thus producing higher values of projected lateral area (Alat) as compared to initial sample (Alat 0). Kinetics of Alat t/Alat 0 vs. time in Fig. 4 indicates that drying gives place to non-isotropic shrinkage/deformation. When looking to Fig. 5, it is possible to observe that when drying fresh material, two peaks were evident while when drying rehydrated samples (to the initial moisture content of fresh material), only the first peak was found. This may be due to the fact that when processing the rehydrated materials, mainly extracellular water is removed. These findings are in agreement with works by Krokida and Maourulis (2001), who stated that drying of extracellular water is followed by removal of intracellular liquid and
that rehydration of intracellular spaces is a slow and difficult process. The onset of first peak may be related to the dehydration of pores and capillaries, according to Krokida and Maourulis (2001). Therefore, the second deformation peak may be caused by other factors, such as the collapse of the cell wall (Prothon, Ahrne´, & Sjo¨holm, 2003). (Ac) changes with moisture content is shown in Fig. 6. To find out extra and intra moisture contents, the change of area of the cell was considered proportional to volume changes and consequently to moisture removal. Fig. 7 shows solid-drying air interfaces during process. It is possible to observe that increments and decrements of roughness are evident. Fractal dimension and Alat kinetics followed similar patterns. It is noticeable that fractal dimension patterns in central zone sections and product border followed the same general trend which may indicate that deformation is due to similar phenomena in both locations as shown in Figs. 8 and 9.
1.2
0.85
1.0
0.80
0.8
0.75
0
20
40
60
80
100
120
140
time (min) Fig. 4. Alat/Alat 0 of potato slabs as a function time (T = 55 °C, u = 1.7 m/ s, L = 2.5 mm).
0
1
2
3
4
5
kg water/kg ds cell Fig. 6. Acell as a function moisture content during drying of potato t =A0 slabs (T = 55 °C, u = 1.75 m/s, L = 2.5 mm).
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289
Fig. 7. Image of solid–air interfaces during drying of potato slabs showing Df variations during dehydration.
1.18
1.18
1.16
1.16 1.14
1.14
1.12
Df
Df
1.12 1.10
1.10 1.08
1.08
1.06
1.06
1.04 1.02
1.04 0
20
40
60
80
100
120
140
160
0
20
time (min)
40
60
80
100
120
140
160
time (min)
Fig. 8. Df of solid–air interfaces of central zone sections during dehydration of potatoes slabs.
Fig. 9. Df of surfaces of external border of potato slabs during dehydration.
3.2. SAFES
Z ic0 ¼ 0:1998 Extracellular solids
For fresh potato M(0,0) Experimental data and values xwt ðmoisture fraction for time tÞ ¼ M wt =M p ds Z ds t ðsolid fraction for time tÞ ¼ M t =M p For 0 min: xw0 ¼ 0:794 Z ds 0 ¼ 0:206 Intracellular solids Hypotheses 1. In the interior of the cell, starch is associated with proteins and ions, forming a matrix that retains water and solids in amorphous state (Gidley, 2001).
Hypotheses 2. It was considered that in the exterior of the cell, exist the rigid vascular matrixes and cell walls, which are fibrous structures (Aguilera & Stanley, 1999), and the extracellular liquid contains a small amount of low-molecular weight components (Kumar, Singh, & Kumar, 2004). 3 Z ec 0 ¼ 4:985 10
Intracellular liquid Unknown ðxic Þ Extracellular liquid xw0 xic
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Gaseous Phase Porosity = 0.6 (Zogzas et al., 1994) the total void volume is 62.8 mm3. This volume can hold an equal amount of air at approximately 90% RH for 80% initial moisture content; sorption data from Iglesias and Chirife (1982).
3.2.1. Experimental data Descriptive matrix for 15 min (M 1,1)
Gw0 ¼ 1:45 105
The matrix of changes (MC 1,0) shows the water fraction lost from 0 to 15 min (Table 2 and 3):
xw15 ¼ 0:559 Z ds 15 ¼ 0:206
The matrix descriptive for minute 0, M 0,0 is shown in Table 1. Df is the fractal dimension for solid–air interfaces obtained by image analysis (Fig. 7), which may be changing during dehydration. Descriptive matrix for material after 15 min of drying (1st deformation, Fig. 4), M 1,1: to obtain value of xic
MC 1; 0 ¼ M 0; 0 M 1; 1 Dxic0–15 ¼ Initialwaterfraction Waterfractionat 15 min ¼ xic0 xic15 The water fraction for intracellular phase may be calculated using an empirical equation obtained from change of volume data applying image analysis, where DAcell is prot portional to DV cell (Gekas & Lamberg, 1991). t d Vi ki ¼ Vf kf
Hypothesis 3. Water removed correlated to first shrinkage peak (0–15 min, Fig. 4) corresponds to intra- and extracellular water.
Table 1 Descriptive matrix for minute 0 (M 0,0) Component
State
Water
Liquid Gas Total
Soluble solids
Rubbery Total
Solid nonsoluble
Rubbery Total
Whole food
Intracellular solids
Extracellular solids
Intracellular liquid
Extracellular liquid
Extracellular gas phase
Whole food
xic
0.794 xic
xic
0.794 xic
1.44 105 1.44 105
0.794
xic
0.794 xic
1.44 105
1
0.199 0.199 4.98 103 4.98 103 4.98 103
0.199
1.0677
Df
Table 2 Descriptive matrix for minute 15 (M 1,1) Component Water Soluble solid
Solid non-soluble
State
Intracellular solids
Extracellular solid
Intracellular liquid xic15 xic15
Liquid Total Rubbery Crystal Total
Extracellular liquid 0:559 0:559
xic15 xic15
Whole food 0.559
0.199 0.199
0.199 3
4.98 10 4.98 103
Rubbery Total
Whole food
4.98 103
4.98 103
0.199
0.559
0.765
Table 3 Matrix of changes for minute 0 to 15 (MC 1,0) Component Water Whole food Df
State
Intracellular solids
Extracellular solids
Intracellular liquid ic
Liquid Total
Dx Dxic 0
0
Extracellular liquid
Whole Food
ic
0.235 Dx 0.235 Dxic
0.235
0.235
0.235 1.0036
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291
Table 4 Descriptive matrix for minute 40 (M 2,2) Component
State
Water
Liquid Total
Soluble solids
Rubbery total
Solid non-soluble
Rubbery Total
Intracellular solid
Extracellular solid
Intracellular liquid
Extracellular liquid
Whole food
0.320 0.320
0 0
0.320
0.199 0.199
Whole food
0.199 4.98 103 4.98 103 4.98 103
0.199
0.320
0
4.98 103 0.526
Table 5 Matrix of changes for minute 15 to 40 (MC 2,1) Component
State
Water
Liquid Total
Intracellular solid
Whole food
0
Intracellular solid
0
Intracellular liquid
Intracellular liquid
Whole Food
0.239 0.239
0 0
0.239
0.239
0.239
Df
1.0710
Table 6 Alat and Df values and corresponding intra- and extracellular moisture fractions during drying Time (min)
Intracellular fraction water
Extracellular water fraction
Alat/Alat 0
Df interfaces
0 10 15 30 40 100 140
0.794 0.638 0.559 0.405 0.321 0.102 0.089
0.794 0.638
1 1.743 1.814 1.652 1.728 1.666 1.646
1.067 1.076 1.071 1.050 1.143 1.101 1.097
where d is a fractal exponent which changes little during drying. For calculation purposes, its numerical value is equal to 1, so it can be considered that Vi/Vf Ai/Af. For obtaining Dxic for 0–15 min interval, an empirical correlation Act vs. X was obtained from Fig. 6: cell 3 2 Act ¼ Acell ;t =A;0 ¼ 0:011X t 0:099X t þ 0:308X þ 0:647
and Dxic0–15 ¼ Dxic15–40 DAc0–15 =DAc15–40
For knowing Dx15–40 it is necessary to calculate MC 2,1 as follows: MC 2; 1 ¼ M 1; 1 M 2; 2 M 2,2 for minute 40 is presented next (Table 4). Matrix of changes 2,1 for 15–40 min is as follows (Table 5): For evaluating Act : Ac0 ¼ 1, and using the values of moisture at 15 (2.7 kg of water/kg solid dry) and 40 min (1.6 kg of water/kg dry solids) Ac15 ¼ 0:9794 Ac40 ¼ 0:9298
DAc0–15 ¼ 0:0206 DAc15–40 ¼ 0:0496 Using matrix MC 2,1: Dxic15–40 ¼ 0:239 and Dxic0–15 ¼ 0:099 and fraction of extracelullarwaterphase ¼ 0:235 Dxic0–15 ¼ 0:1358 This completes MC 1,0 as expected. In Table 6, Alat/Alat 0 and Df values and corresponding intra- and extracellular moisture fractions are shown during drying, showing the same general two-peak tendency mentioned above. 4. Conclusions Intra- and extracellular water fractions may be evaluated using data from non-isotropic shrinkage. In particular, intracellular water fraction was determined with the aid of SAFES methodology. Solid–air interfaces showed a profile which may be characterized with the aid of fractal geometry. These interfaces can be considered as another phase within SAFES. Fractal dimension of these interfaces evaluated during drying showed a similar tendency to the
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one found for Alat. This may indicate that inner structures composed of solid–air matrixes are projected towards the surface in the form of fractal solid–air interfaces. SAFES proved to be a very useful methodology for systematization knowledge-base on transport along solids subjected to convective drying. Acknowledgements Financial support from: CONACYT-Mexico Project SEP-04-co1-48061, CGEPI-IPN Projects 20050121 and 20060114. Author R. Campos thanks CONACYT-Mexico for study grant. References Aguilera, J. M. (2003). Drying and dried products under the microscope. Food Science and Technology International, 9(3), 137–143. Aguilera, J. M., & Stanley, D. W. (1999). Simultaneous heat and mass transfer: Dehydration. In Microstructural principles of food processing and engineering (2nd ed.). London: Elsevier Applied Science Publisher. Alamilla-Beltra´n, L., Chanona-Pe´rez, J. J., Jime´nez-Aparicio, A. R., & Gutie´rrez-Lo´pez, G. F. (2005). Description of morphological changes of particles along spray drying. Journal of Food Engineering, 67, 179–184. AOAC (1995). Official methods of analysis (16th ed.). Arlington, Virginia: Association of Official Analytical Chemists International. Chenoll, C., Heredia, A., Seguı´, L., & Fito, P. (2005). Quality and safety modeling of tasajo processing: SAFES methodology. In: Proceedings of V Iberoamerican congress of food engineering (CIBIA V), Puerto Vallarta, Mexico. Gekas, V., & Lamberg, I. (1991). Determination of diffusion coefficients in volume changing systems—application in the case of potato drying. Journal of Food Engineering, 14(4), 317–326.
Gidley, M. J. (2001). Starch structure/function relationships achievements and challenges. In T. L. Barsby (Ed.), Starch advances in structure and function. Bodmin, Cornwell, UK: MOG Books Ltd. Gutie´rrez Lo´pez, G. F., Chanona-Pe´rez, J., Alamilla-Beltra´n, L., Herna´ndez-Parada, A., Jime´nez-Aparicio, A., Farrera-Rebollo, R., et al. (2002). A proposal of analysis of the drying phenomena by means of fractal theory. In J. Welti-Cahanes, G. V. Barbosa-Ca´novas, & J. M. Aguilera (Eds.), Engineering and food for the 21st century. CRC Press. Iglesias, H. A., & Chirife, J. (1982). Handbook of food isotherms: Water sorption parameters for food components. New York: Academic Press. Karathanos, V., Kanellopoulos, N. K., & Belessiotis, V. G. (1996). Development of porous structure during air drying of agricultural plant products. Journal of Food Engineering, 29, 167–183. Krokida, M. K., & Maourulis, Z. B. (2001). Structural properties of dehydrated products during rehydration. International Journal of Food Science and Technology, 36, 529–538. Kumar, D., Singh, B. P., & Kumar, P. (2004). On overview of the factors affecting sugar content of potatoes. Annals of Applied Biology, 145, 247–256. Lozano, J. E., Rotstein, E., & Urbicain, M. J. (1980). Total porosity and open-pore porosity in the drying of fruit. Journal of Food Science, 45, 1403–1407. Perre´, P., & May, B. K. (2001). A numerical drying model that accounts for the coupling between transfers and solid mechanics. Case of highly deformable products. Drying Technology, 19(8), 1629–1643. Prothon, F., Ahrne´, L., & Sjo¨holm, I. (2003). Mechanisms and prevention of plant tissue collapse during dehydration: A critical review. Critical Reviews in Food Science and Nutrition, 43(4), 447–479. Ramos, I. N., Brandao, T. R. S., & Silva, C. L. M. (2003). Structural changes during air drying of fruits and vegetables. Food Science and Technology International, 9(3), 201–206. Yang, H., Sakai, N., & Watanabe, M. (2001). Drying model with nonisotropic shrinkage deformation undergoing simultaneous heat and mass transfer. Drying Technology, 19(7), 1441–1460. Zogzas, N. P., Maroulis, Z. B., & Marinos-Kouris, D. (1994). Densities, shrinkage and porosity of some vegetables during air drying. Drying Technology, 12(7), 1653–1666.
Non-isotropic shrinkage and interfaces during convective drying of potato slabs within the frame of the systematic approach to food engineering systems (SAFES) methodology R. Campos-Mendiola a, H. Herna´ndez-Sa´nchez a, J.J. Chanona-Pe´rez a, L. Alamilla-Beltra´n a, A. Jime´nez-Aparicio b, P. Fito c, G.F. Gutie´rrez-Lo´pez a,* a
Departamento de Graduados e Investigacio´n en Alimentos, Escuela Nacional de Ciencias Biolo´gicas, Instituto Polite´cnico Nacional, Carpio y Plan de Ayala S/N, CP 11340, Me´xico DF, Mexico b Centro de Desarrollo de Productos Bio´ticos del IPN, Carretera Jojutla km 8.5, Col. San Isidro, C.P. 62731, Yautepec, Morelos, Mexico c Instituto Universitario de Ingenierı´a en Alimentos para el Desarrollo, Universidad Polite´cnica de Valencia, Camino de Vera 46022 s/n Valencia, Spain Available online 21 February 2007
Abstract Non-isotropic shrinkage of potato slabs was studied within the frame of the systematic approach to food engineering systems (SAFES) methodology. Digital images of potato slabs were taken and lateral projected areas (Alat) of material during drying were recorded. Two characteristics peaks in graphs Alat vs. time were detected. Also, cellular surface area of potato cells was recorded and related to moisture content by means of an empirical equation with in conjunction with SAFES methodology and Alat values at the two afore mentioned peaks, allowed to evaluate intra- and extracellular moisture contents. Fractal dimension (Df) of solid–air interfaces during drying were also calculated. Graphs of Df vs. time also showed two peaks which appeared at approximately the same drying times than those for Alat which may indicate that inner structures composed of solid–air matrixes are projected towards the surface in the form of fractal solid–air interfaces. Ó 2007 Elsevier Ltd. All rights reserved. Keywords: SAFES; Convective drying; Shrinkage; Fractal interfaces; Image analysis
1. Introduction Traditional food processing considers the food as a homogeneous and do not provide enough information regarding internal and external transport and physical properties including microstructure. Recently, the systematic approach to food engineering systems (SAFES) methodology was developed and applied to several food processes (Chenoll, Heredia, Seguı´, & Fito, 2005). This approach considers different phases, components and aggregation states present in the food and takes into account structure and interactions among components. In this context, the inclusion of dynamic and complex inter*
Corresponding author. Tel.: +55 57296300. E-mail address: [email protected] (G.F. Gutie´rrez-Lo´pez).
0260-8774/$ - see front matter Ó 2007 Elsevier Ltd. All rights reserved. doi:10.1016/j.jfoodeng.2007.02.027
faces, both internal and external may be of interest to further explain the complex transfer mechanisms and interactions of components during processing. Dehydrated foodstuffs often present problems related to their structural characteristics, which affect rehydration, aroma retention, sensory attributes (colour, texture), as well as heat and mass transport phenomena during processing (Aguilera, 2003). Foodstuffs are considered complex structural systems, formed by different tissues responsible for their composition and structural characteristics. Vegetables undergo structural changes during drying, such as volume reduction, density and porosity increase, and texture alterations, which affect the characteristics of the final product (Ramos, Brandao, & Silva, 2003). Also, upon drying structures and, consequently interfaces are generated and destroyed. Reduction of volume or shrinkage has been studied on
286
R. Campos-Mendiola et al. / Journal of Food Engineering 83 (2007) 285–292
Nomenclature Alat Ac D D Df Gw L k
lateral projected area cell relative cellular area Acell t =A0 diameter fractal exponent fractal dimension water vapour fraction thickness of potato slab thickness of potato slab (Gekas & Lamberg, 1991) M i,j descriptive matrix MC i,j matrix of changes Mds mass of dry solid Mp mass of potato slab Mw mass of water
several vegetables (Karathanos, Kanellopoulos, & Belessiotis, 1996; Lozano, Rotstein, & Urbicain, 1980; Zogzas, Maroulis, & Marinos-Kouris, 1994). Since shrinkage affects moisture transfer along dehydration, changing geometry of the food during drying makes understanding of moisture transfer mechanisms complex (Gekas & Lamberg, 1991). Also, Yang, Sakai, and Watanabe (2001) described potato shrinkage as non-isotropic or irregular. These authors proposed a predictive model for the deformation of finite potato cylinders, where the centre shrinks more than the surface. At microstructural level, Perre´ and May (2001) modelled the cell configuration of parenchyma, and reported that cells move and rotate producing a global deformation of the material. Tools such as image analysis have been recently used to study structural changes of foodstuffs such as shrinkage. Image analysis requires the capture of an image while microscopes, among other instruments, are used to study microstructure. Images are converted into a number of matrixes with the help of computer software, that determine geometrical parameters allowing such matrixes to be contrasted, darkened, clarified, etc. (Aguilera, 2003). One way for characterizing a digital image of foods during drying is by means of the fractal dimension of the distribution of surface temperatures of the surface of the sample undertaking drying (Gutie´rrez Lo´pez et al., 2002). Also, fractal geometry may be useful for studying interfaces and their roles as transfer-controlling barriers. Non-isotropic shrinkage of products has not been extensively studied. The aim of the present work is to obtain information on the non-isotropic shrinkage of potato slabs and cells during convective dehydration and to evaluate profiles of solid–gas interfaces generated by means of image analysis and fractal geometry. The information was useful for obtaining data on intra- and extracellular water contents; results were processed within the frame of SAFES methodology.
RH T u Vi, Vf xic xw X Zds Zec Zic
relative moisture content of air temperature air velocity initial and final volume intracellular water fraction water fraction moisture content (kg water/kg dry solids) mass fraction of dry solids extracellular solids fraction intracellular solids fraction
Subscripts t time (0, 15, 40 min) 0 initial
2. Materials and methods Potato (Solanum tuberosum var. Alpha) was cut into circular slabs, 40 mm diameter. Slabs were submerged into a 0.05% solution of sodium meta-bisulphite (Sigma 768157-4) for 2 min to control browning. Two slices were simultaneously dehydrated in an experimental air drier (Fig. 1). A 43 experimental design was applied using MINITAB software (MINITAB Release 13.1, USA), including three
6
4
LATERAL VIEW 1 2
airflow
5 3
6
8
7
5
FRONT VIEW Fig. 1. Diagram of the experimental drier coupled to the image recording system: (1) drier tunnel, (2) fan and heater, (3) airflow temperature control, (4) airflow control, (5) testing section and sample, (6) upper digital camera, (7) side digital camera and (8) windows for image capturing.
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factors (temperature, drying air rate and thickness of the sample), four levels and five repetitions in the central point. Accordingly, four drying air temperatures (40, 50, 60 and 70 °C), four air velocities (1, 1.5, 2.0 and 2.5 m/s) and four thicknesses of sample (1, 2, 3 and 4 mm) were tested. One of the slices was used to record the shrinkage/deformation process by capturing, digital images of the lateral and top view of samples during drying was carried out using two digital cameras (DC290 zoom, Kodak, USA). Both cameras were connected to a serial port of a generic PC (AMD-K6, 450 MHz, 312 MB RAM, 40 GB hard disk) equipped with a video recording card (ATI, All in Wonder Rage-128pro, USA) and image recording software (ATI version 6.2, Multimedia Center). The other slab was used to evaluate weight loss and moisture of sample along drying. Weights of samples were taken in an analytical balance (OAHUS, Analytical plus, USA). Initial moisture of slabs was determined according to the AOAC 32.1.03 method (AOAC, 1995). A fluorescent light ring (Universal driver model 13 plus, USA) was placed around the lenses of the cameras to illuminate objects. Images obtained from the side and upper views of the slabs were stored as colour images (640X480 pixels) in a bit map format. ImageJ software 1.34 NIH (National Institutes of Health, Bethesda, MD, USA) was used to analyze recorded images of slabs as well as to measure the area of the cell (Acel) during drying. The analysis included transformation into a grey scale of captured images, followed by segmentation of the lateral boundary in order to obtain the projected shape of solid–air interface of slabs. Dimensionless values of lateral projected area of potato slabs (Alat t/Alat 0) were taken as indicators of non-isotropic shrinkage/deformation in conjunction with values of area of potato cells obtained during drying to determine a correlation with moisture removal of sample. Cellular shrinkage was evaluated from the images captured during drying by coupling a stereoscopic microscope (Nikon SMZ1500) fitted with a digital CCD camera (Nikon, Coolpix4500) to the experimental drier. Five cells were photographed from the central field of the microscope and for each experiment, three replicates were carried out. Another experiment was performed to evaluate structural changes in the solid–gas interface. Images of such interfaces were taken during drying by means of the same microscope-camera image capturing system as described above. Five images for each drying zone (centre and border) were obtained. Also, fractal dimension of images of profiles of solid–gas interfaces generated along drying were obtained and their fractal dimension were calculated using the box counting method as recommended by Alamilla-Beltra´n, ChanonaPe´rez, Jime´nez-Aparicio, and Gutie´rrez-Lo´pez (2005). Fractal Count 1.42 plugin of ImageJ was used to evaluated the fractal dimension of the profiles of the solid–gas interfaces.
287
2.1. SAFES Matrixes including phases, components and aggregation states were defined after applying experimental and reported values of physical properties. A flow chart was constructed and hypotheses were formulated to establish the state and change matrixes, following the SAFES methodology proposed by Chenoll et al. (2005). Also, geometric patterns of the non-isotropic shrinkage and interfaces of potato slabs were recorded to relate them to values of intra- and extracellular water in the SAFES matrixes. For the purposes of this work, no contrast matrixes were calculated since useful data for characterization and systematization of the drying process, including shrinkage were established within descriptive and changes matrixes. 2.1.1. Definition of phases, components and aggregation states Phases considered in this experiment were (1) (2) (3) (4) (5)
Solid intracellular phase. Solid extracellular phase. Intracellular liquid phase. Extracellular liquid phase. Gas phase. Air–water vapour mix into sample due to porosity.
The components are (a) Water. Mostly in the liquid state. (b) Solids. All the components described in both, intraand extracellular solid phases. (c) Gaseous. Air–water vapour mix.
2.1.2. Flow chart of the drying process Descriptive and changing matrixes for the evaluation of water motion were evaluated according to flow chart depicted in Fig. 2. Initial total solids: 20.6% (wet basis). 3. Results and discussion 3.1. Non-isotropic shrinkage of potato slabs Fig. 3 depicts images of initial projected lateral area of sample, showing an elongated rectangular shape which
Fresh potato M 0,0
1st deformation stage M 1,1
MC 1,0 = M 1,1 - M 0,0
2nd deformation stage M 2,2
MC 2,1 = M 2,2 – M 1,1
Fig. 2. Flow chart for evaluation of matrixes (M is descriptive matrix and MC is matrix of change).
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Fig. 5. Alat/Alat 0 of fresh and rehydrated potato slabs as a function time (T = 55 °C, u = 1.7 m/s, L = 2.5 mm).
Fig. 3. Side image of a potato slabs at different drying times (T = 55 °C, u = 1.7 m/s, L = 2.5 mm).
1.05
1.8
1.00
1.6
0.95
/ A0
cell
2.0
cell
1.4
0.90
At
Alat/Alat,0
tends to bend, thus producing higher values of projected lateral area (Alat) as compared to initial sample (Alat 0). Kinetics of Alat t/Alat 0 vs. time in Fig. 4 indicates that drying gives place to non-isotropic shrinkage/deformation. When looking to Fig. 5, it is possible to observe that when drying fresh material, two peaks were evident while when drying rehydrated samples (to the initial moisture content of fresh material), only the first peak was found. This may be due to the fact that when processing the rehydrated materials, mainly extracellular water is removed. These findings are in agreement with works by Krokida and Maourulis (2001), who stated that drying of extracellular water is followed by removal of intracellular liquid and
that rehydration of intracellular spaces is a slow and difficult process. The onset of first peak may be related to the dehydration of pores and capillaries, according to Krokida and Maourulis (2001). Therefore, the second deformation peak may be caused by other factors, such as the collapse of the cell wall (Prothon, Ahrne´, & Sjo¨holm, 2003). (Ac) changes with moisture content is shown in Fig. 6. To find out extra and intra moisture contents, the change of area of the cell was considered proportional to volume changes and consequently to moisture removal. Fig. 7 shows solid-drying air interfaces during process. It is possible to observe that increments and decrements of roughness are evident. Fractal dimension and Alat kinetics followed similar patterns. It is noticeable that fractal dimension patterns in central zone sections and product border followed the same general trend which may indicate that deformation is due to similar phenomena in both locations as shown in Figs. 8 and 9.
1.2
0.85
1.0
0.80
0.8
0.75
0
20
40
60
80
100
120
140
time (min) Fig. 4. Alat/Alat 0 of potato slabs as a function time (T = 55 °C, u = 1.7 m/ s, L = 2.5 mm).
0
1
2
3
4
5
kg water/kg ds cell Fig. 6. Acell as a function moisture content during drying of potato t =A0 slabs (T = 55 °C, u = 1.75 m/s, L = 2.5 mm).
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Fig. 7. Image of solid–air interfaces during drying of potato slabs showing Df variations during dehydration.
1.18
1.18
1.16
1.16 1.14
1.14
1.12
Df
Df
1.12 1.10
1.10 1.08
1.08
1.06
1.06
1.04 1.02
1.04 0
20
40
60
80
100
120
140
160
0
20
time (min)
40
60
80
100
120
140
160
time (min)
Fig. 8. Df of solid–air interfaces of central zone sections during dehydration of potatoes slabs.
Fig. 9. Df of surfaces of external border of potato slabs during dehydration.
3.2. SAFES
Z ic0 ¼ 0:1998 Extracellular solids
For fresh potato M(0,0) Experimental data and values xwt ðmoisture fraction for time tÞ ¼ M wt =M p ds Z ds t ðsolid fraction for time tÞ ¼ M t =M p For 0 min: xw0 ¼ 0:794 Z ds 0 ¼ 0:206 Intracellular solids Hypotheses 1. In the interior of the cell, starch is associated with proteins and ions, forming a matrix that retains water and solids in amorphous state (Gidley, 2001).
Hypotheses 2. It was considered that in the exterior of the cell, exist the rigid vascular matrixes and cell walls, which are fibrous structures (Aguilera & Stanley, 1999), and the extracellular liquid contains a small amount of low-molecular weight components (Kumar, Singh, & Kumar, 2004). 3 Z ec 0 ¼ 4:985 10
Intracellular liquid Unknown ðxic Þ Extracellular liquid xw0 xic
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Gaseous Phase Porosity = 0.6 (Zogzas et al., 1994) the total void volume is 62.8 mm3. This volume can hold an equal amount of air at approximately 90% RH for 80% initial moisture content; sorption data from Iglesias and Chirife (1982).
3.2.1. Experimental data Descriptive matrix for 15 min (M 1,1)
Gw0 ¼ 1:45 105
The matrix of changes (MC 1,0) shows the water fraction lost from 0 to 15 min (Table 2 and 3):
xw15 ¼ 0:559 Z ds 15 ¼ 0:206
The matrix descriptive for minute 0, M 0,0 is shown in Table 1. Df is the fractal dimension for solid–air interfaces obtained by image analysis (Fig. 7), which may be changing during dehydration. Descriptive matrix for material after 15 min of drying (1st deformation, Fig. 4), M 1,1: to obtain value of xic
MC 1; 0 ¼ M 0; 0 M 1; 1 Dxic0–15 ¼ Initialwaterfraction Waterfractionat 15 min ¼ xic0 xic15 The water fraction for intracellular phase may be calculated using an empirical equation obtained from change of volume data applying image analysis, where DAcell is prot portional to DV cell (Gekas & Lamberg, 1991). t d Vi ki ¼ Vf kf
Hypothesis 3. Water removed correlated to first shrinkage peak (0–15 min, Fig. 4) corresponds to intra- and extracellular water.
Table 1 Descriptive matrix for minute 0 (M 0,0) Component
State
Water
Liquid Gas Total
Soluble solids
Rubbery Total
Solid nonsoluble
Rubbery Total
Whole food
Intracellular solids
Extracellular solids
Intracellular liquid
Extracellular liquid
Extracellular gas phase
Whole food
xic
0.794 xic
xic
0.794 xic
1.44 105 1.44 105
0.794
xic
0.794 xic
1.44 105
1
0.199 0.199 4.98 103 4.98 103 4.98 103
0.199
1.0677
Df
Table 2 Descriptive matrix for minute 15 (M 1,1) Component Water Soluble solid
Solid non-soluble
State
Intracellular solids
Extracellular solid
Intracellular liquid xic15 xic15
Liquid Total Rubbery Crystal Total
Extracellular liquid 0:559 0:559
xic15 xic15
Whole food 0.559
0.199 0.199
0.199 3
4.98 10 4.98 103
Rubbery Total
Whole food
4.98 103
4.98 103
0.199
0.559
0.765
Table 3 Matrix of changes for minute 0 to 15 (MC 1,0) Component Water Whole food Df
State
Intracellular solids
Extracellular solids
Intracellular liquid ic
Liquid Total
Dx Dxic 0
0
Extracellular liquid
Whole Food
ic
0.235 Dx 0.235 Dxic
0.235
0.235
0.235 1.0036
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Table 4 Descriptive matrix for minute 40 (M 2,2) Component
State
Water
Liquid Total
Soluble solids
Rubbery total
Solid non-soluble
Rubbery Total
Intracellular solid
Extracellular solid
Intracellular liquid
Extracellular liquid
Whole food
0.320 0.320
0 0
0.320
0.199 0.199
Whole food
0.199 4.98 103 4.98 103 4.98 103
0.199
0.320
0
4.98 103 0.526
Table 5 Matrix of changes for minute 15 to 40 (MC 2,1) Component
State
Water
Liquid Total
Intracellular solid
Whole food
0
Intracellular solid
0
Intracellular liquid
Intracellular liquid
Whole Food
0.239 0.239
0 0
0.239
0.239
0.239
Df
1.0710
Table 6 Alat and Df values and corresponding intra- and extracellular moisture fractions during drying Time (min)
Intracellular fraction water
Extracellular water fraction
Alat/Alat 0
Df interfaces
0 10 15 30 40 100 140
0.794 0.638 0.559 0.405 0.321 0.102 0.089
0.794 0.638
1 1.743 1.814 1.652 1.728 1.666 1.646
1.067 1.076 1.071 1.050 1.143 1.101 1.097
where d is a fractal exponent which changes little during drying. For calculation purposes, its numerical value is equal to 1, so it can be considered that Vi/Vf Ai/Af. For obtaining Dxic for 0–15 min interval, an empirical correlation Act vs. X was obtained from Fig. 6: cell 3 2 Act ¼ Acell ;t =A;0 ¼ 0:011X t 0:099X t þ 0:308X þ 0:647
and Dxic0–15 ¼ Dxic15–40 DAc0–15 =DAc15–40
For knowing Dx15–40 it is necessary to calculate MC 2,1 as follows: MC 2; 1 ¼ M 1; 1 M 2; 2 M 2,2 for minute 40 is presented next (Table 4). Matrix of changes 2,1 for 15–40 min is as follows (Table 5): For evaluating Act : Ac0 ¼ 1, and using the values of moisture at 15 (2.7 kg of water/kg solid dry) and 40 min (1.6 kg of water/kg dry solids) Ac15 ¼ 0:9794 Ac40 ¼ 0:9298
DAc0–15 ¼ 0:0206 DAc15–40 ¼ 0:0496 Using matrix MC 2,1: Dxic15–40 ¼ 0:239 and Dxic0–15 ¼ 0:099 and fraction of extracelullarwaterphase ¼ 0:235 Dxic0–15 ¼ 0:1358 This completes MC 1,0 as expected. In Table 6, Alat/Alat 0 and Df values and corresponding intra- and extracellular moisture fractions are shown during drying, showing the same general two-peak tendency mentioned above. 4. Conclusions Intra- and extracellular water fractions may be evaluated using data from non-isotropic shrinkage. In particular, intracellular water fraction was determined with the aid of SAFES methodology. Solid–air interfaces showed a profile which may be characterized with the aid of fractal geometry. These interfaces can be considered as another phase within SAFES. Fractal dimension of these interfaces evaluated during drying showed a similar tendency to the
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one found for Alat. This may indicate that inner structures composed of solid–air matrixes are projected towards the surface in the form of fractal solid–air interfaces. SAFES proved to be a very useful methodology for systematization knowledge-base on transport along solids subjected to convective drying. Acknowledgements Financial support from: CONACYT-Mexico Project SEP-04-co1-48061, CGEPI-IPN Projects 20050121 and 20060114. Author R. Campos thanks CONACYT-Mexico for study grant. References Aguilera, J. M. (2003). Drying and dried products under the microscope. Food Science and Technology International, 9(3), 137–143. Aguilera, J. M., & Stanley, D. W. (1999). Simultaneous heat and mass transfer: Dehydration. In Microstructural principles of food processing and engineering (2nd ed.). London: Elsevier Applied Science Publisher. Alamilla-Beltra´n, L., Chanona-Pe´rez, J. J., Jime´nez-Aparicio, A. R., & Gutie´rrez-Lo´pez, G. F. (2005). Description of morphological changes of particles along spray drying. Journal of Food Engineering, 67, 179–184. AOAC (1995). Official methods of analysis (16th ed.). Arlington, Virginia: Association of Official Analytical Chemists International. Chenoll, C., Heredia, A., Seguı´, L., & Fito, P. (2005). Quality and safety modeling of tasajo processing: SAFES methodology. In: Proceedings of V Iberoamerican congress of food engineering (CIBIA V), Puerto Vallarta, Mexico. Gekas, V., & Lamberg, I. (1991). Determination of diffusion coefficients in volume changing systems—application in the case of potato drying. Journal of Food Engineering, 14(4), 317–326.
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