- Email: [email protected]
Mass transfer mechanisms occurring in osmotic dehydration of guava
Available online at www.sciencedirect.com
Journal of Food Engineering 87 (2008) 386–390 www.elsevier.com/locate/jfoodeng
Mass transfer mechanisms occurring in osmotic dehydration of guava Gloria Panades a,*, Deborah Castro a, Amparo Chiralt b, Pedro Fito b, Margarita Nun˜ez a, Ramiro Jimenez a b
a Instituto de Investigaciones para la Industria Alimenticia, Carr. Guatao km 3.5, Lisa, C. Habana 19200, Cuba Departamento de Tecnologı´a de Alimentos, Universidad Politecnica de Valencia, Camino de Vera 14, Valencia 46022, Spain
Received 9 July 2007; received in revised form 19 December 2007; accepted 21 December 2007 Available online 8 January 2008
Abstract Two osmotic dehydration modes were applied to guava segments immersed in a 65 °Brix sucrose solution at 30, 40 and 50 °C: under constant atmospheric pressure and using a pulsed vacuum (5 min under vacuum, then at atmospheric pressure). The effective diffusivity in the liquid phase, De and the kinetic constants of net mass transfer, K and K0, were determined by fitting the experimental data to mathematical models. The highest effective diffusivities were obtained with pulsed vacuum at 40 and 50 °C on account of the hydrodynamic mechanism, with solids diffusion overcoming dehydration at the beginning of the process, at 30 and 40 °C. The effect of temperature on mass transfer kinetics, predictable by the Arrhenius equation, is more relevant at atmospheric pressure, where the pseudo-diffusion mechanism exerts the controlling role. Ó 2008 Elsevier Ltd. All rights reserved. Keywords: Osmotic dehydration; Kinetics; Effective diffusivity; Guava
1. Introduction In osmotic drying, water diffusion through the cellular membranes is the main transport mechanism, although there is an overlapping of diffusion and capillary phenomena in the tissue’s intercellular spaces (pores). Capillary phenomena occur at low pressure (Fito, 1994), but with the high compression ratios associated with the pulsed vacuum process (low pressure at the beginning of the treatment and atmospheric pressure later on) the entrance of the external liquid phase in the intercellular spaces through the hydrodynamic mechanism (HDM) can play an important role in mass transfer. Consequently, in osmotic dehydration (OD) several mechanisms intervene in different degrees, depending on process conditions. These mechanisms can be divided in two groups (Fito, 1994; Fito et al., 1994):
*
Corresponding author. Tel.: +53 7 2020919. E-mail address: [email protected] (G. Panades).
0260-8774/$ - see front matter Ó 2008 Elsevier Ltd. All rights reserved. doi:10.1016/j.jfoodeng.2007.12.021
– A group of mechanisms that depend on concentration gradients, generically labeled as pseudo-diffusional and usually modeled applying the second Fick’s law to a non stationary and unidirectional flow. – A mechanism that depends on pressure gradients, called the hydrodynamic mechanism (HDM) that acts at the beginning of the osmotic treatment. In previous papers a macroscopic model of the OD process integrating the pseudo-diffusional and hydrodynamic mechanisms has been studied (Barat et al., 1997, 2001; Fito and Chiralt, 1996). It involves the kinetics from two viewpoints: compositional changes of the food’s liquid phase (FLP) and changes in the product’s total mass. In the first case the model allows good predictions of the final composition of the product, in terms of a corrected coefficient of effective diffusion with the contribution of the HDM. This parameter can offer valuable information, since it takes into account the compositional changes of the liquid phase of the fruit due to the mass transfer processes that take place under different treatments, determining the
G. Panades et al. / Journal of Food Engineering 87 (2008) 386–390
387
Nomenclature Mw Ms M M0 Mt Xw0 Xwt Xs0 Xst YS Y HDM S Zst Zs0 Zse Z HDM s
water losses (%) solids gain (%) weight loss (%) initial weight (g) weight at time ‘‘t” (g) initial moisture (g water/g sample) moisture at time ‘‘t” (g water/g sample) initial solutes concentration (g solutes/g sample) solutes concentration at time ‘‘t” (g solutes/g sample) reduced driving force in the LP of the fruit reduced driving force considering the effect of the HDM solute concentration in the LP of the fruit at time t (g solutes/g liquid fraction) solute concentration in the LP in the initial moment (g solute/g liquid fraction) concentration of the LP in equilibrium with the osmotic solution, considered similar to that of the solution (g solute/g of liquid fraction) solute concentration in the LP of the sample resulting from the action of the HDM (g solute/g of liquid fraction)
quality and final condition of the product. It can thus become a basis for the design of products and processes. In the second case the model predicts the changes in total mass through kinetic constants for net mass transfer, which has an important effect on the productivity and profitability of the process. The reviewed literature includes studies on the kinetics of osmotic dehydration (OD) of guava under vacuum or atmospheric pressure that have yielded advances in process modeling and in controlling the variables that regulate it (Panades et al., 1996, 2003b, 2006). Other studies report on the influence of osmotic drying on product quality (Panades et al., 2003a; Pereira et al., 2004). However, few references deal with the mass transfer mechanisms occurring in the liquid fraction of the product during treatment at different pressure regimens. The objective of this study was to determine the effective diffusivity in the liquid phase of osmotically dehydrated guava and the kinetic constants of net mass transfer in the process variants at atmospheric pressure and under pulsed vacuum.
m mLP mi mHDM i yso Ks0
Ks K K0 t De l D0 Ea R T
sample mass in the initial instant (g) mass of the LP (g) impregnated mass (g) impregnated mass resulting from the effect of the HDM (g) solute concentration of the osmotic solution (g solute/g of liquid fraction) kinetic constant of solute transport occurring at very short treatment times in the pulsed vacuum regimen kinetic constant of solute transport kinetic constant of the combined kinetics of the pseudo-diffusional mechanisms kinetic constant of the net mass loss after a very short treatment time process time (s) effective diffusivity half thickness of the sample (0.00334 m) Arrhenius factor (m2/s) activation energy (kJ/mol) universal gas constant absolute temperature (K)
conditions established in the Cuban Standard (NC 77-52, 1986) and with a 53–59 mm diameter, to ensure the homogeneous size of samples. The fruits were peeled, cut in halves, cored and cut in eighths. 2.2. Osmotic dehydration treatment Guava slices were weighed in 110 g fractions (about 12 slices) and put in a 1 L glass flask containing 880 g of a sucrose solution of 65 °Brix, for a fruit: solution ratio of 1:8. The flask was then immersed in a thermostatic water bath, connected to a vacuum rotary evaporator with a rotation speed of 100 rpm and subjected to different pressure treatments for different times. Three temperatures, 30, 40 and 50 °C, six total times, 30, 60, 90, 120, 150 and 180 min and two pressure modes: atmospheric pressure and pulsed vacuum, were tested. In the pulsed vacuum regimen, a vacuum time of 5 min. was used. Absolute pressures of the system were those of the syrup vapor pressure, corresponding to every temperature studied: 30 °C – 4.3 kPa; 40 °C – 5.2 kPa; 50 °C – 10.7 kPa. Each experiment was carried out in triplicate.
2. Materials and methods 2.3. Analyses 2.1. Sample preparation For the study, hard ripened guavas (Psidium guava L.), Enana Roja variety, from the Estacion Nacional de Frutales, in Havana, were selected according to the maturity
After every treatment, samples were removed from the solution, drained and rinsed with distilled water to remove the syrup adhered to the surface, then gently blotted with tissue paper.
388
G. Panades et al. / Journal of Food Engineering 87 (2008) 386–390
In every experience moisture content was determined gravimetrically using a vacuum oven for drying to constant weight at 60 °C (AOAC, 1997). The soluble solids content was determined in a refractometer (ABBE, ATAGO Model 3 – T, Japan). All analyses were performed in triplicate.
The diffusivity coefficient in the fruit’s LP was determined from the integrated solutions of Fick’s equations for semi-infinite slabs and short times, considering a single term of the series (Crank, 1975): 0:5 De t ð12Þ 1 Ys ¼ 2 pl2
2.4. Mass balance
The effective diffusivity coefficient (De) was calculated from the slope of the linear fitting of the experimental data in the representation of 1 Ys versus t0.5.
The relationships among the component concentrations at a given time were defined through the Fito and Chiralt equations (1996), with the signs convention set considering the mass flows into the product as positive: ð1Þ ð2Þ
M ¼ Kt0:5 þ K 0 ð3Þ
ð5Þ
In the calculation of the reduced driving force in the pulsed vacuum mode the value of Zs0 has been corrected, assuming that in the product’s liquid phase a quick compositional change occurs at the very beginning of the osmotic process due to the contribution of the HDM, in agreement with the modifications brought about by Fito and Chiralt (1996): Z st Z se Z HDM Z se s m Z LP s0 þ mi y so Z HDM ¼ s mLP þ mi mLP ¼ mðxw0 þ xs0 Þ
Y HDM ¼ S
mi ¼
mHDM m i
mHDM i
K s0 1 ¼ 100 y so
ð6Þ
In Fig. 1 are shown all the values of (Mw + Ms) versus M with the objective of checking the mass balances. A good fit of the experimental results (R2 = 0.9107) was observed. 3.1. Changes in the food’s liquid phase composition (FLP) The predictive equations corresponding to the fitting of 1 Ys and 1 Y HDM versus t0.5, along with the effective S diffusivities and respective confidence intervals calculated for each treatment, are shown in Table 1. The De values obtained varied between 0.69 1010 and 1.47 1010 m2/s in the interval reported by other authors (Escriche et al., 2000). In both pressure modes, for a temperature increase from 30 to 50 °C, the coefficients tend to rise, coinciding with the results of other studies (Barat et al., 2001). In general, the highest values appear at 40 and 50 °C in the pulsed vacuum regimen, which is explained by the larger net gain of solutes that occur in that regimen in osmotically dehydrated guava, as a consequence of the HDM. This is in line with the findings of a previous study (Panades et al., 2006). At 50 °C diffusivity is the same in both treatments,
ð7Þ ð8Þ ð9Þ ð10Þ
-50
-45
-40
-35
-30
-25
-20
-15
-10 -10 -20 -30
y= 0.9074x - 2.1256
-40
2
R = 0.9107
Ks0 was determined according to the pattern developed by Fito and Chiralt (1996) and Barat et al. (1997): M s ¼ K s t0:5 þ K s0
The kinetic constants were obtained from the linear fitting of the experimental data to Eq. (13). 3. Results and discussion
For calculating the effective diffusivity (De) in the liquid phase of the product (water + soluble solids), an equation derived from Fick’s second law was used (Crank, 1975). Considering the guava segment as a slab of thickness h in the atmospheric pressure mode, the reduced driving force (Y = YS = Yw) was determined as a function of the liquid phase composition (LP) of the fruit (Fito and Chiralt, 1996): Z st Z se Z s0 Z se
ð13Þ
ð4Þ
2.5. Compositional changes in the liquid phase and effective diffusivity
YS ¼
The kinetic constants of mass transfer (K, K0) were determined according to the model developed by Fito and Chiralt (1996) and Barat et al. (1997):
Mw +M s (%)
M ¼ Mw þ Ms M t X wt M 0 X w0 Mw ¼ 100 M0 M t X st M 0 X s0 Ms ¼ 100 M0 Mt M0 M¼ 100 M0
2.6. Kinetic constants of net mass transfer
ð11Þ
-50
M (%) Fig. 1. Relationship between the values of Mw + Ms versus M in osmotically dehydrated guava.
G. Panades et al. / Journal of Food Engineering 87 (2008) 386–390
389
Table 1 Effective diffusivity (De) with confidence intervals and predictive equations in osmotically dehydrated guava processed at atmospheric pressure (APOD) and under pulsed vacuum (PVOD) Pressure mode
APOD
Temperature (°C)
Predictive equations 0.5
30 40 50
PVOD
30 40 50
Upper limit
0.55
0.83
0.95
0.83
1.07
1.40
1.33
1.47
¼ 0:0030t0:5 1 Y HDM S 2 R = 0.8916 1 Y HDM ¼ 0:0041t0:5 S 2 R = 0.8595 ¼ 0:0040t0:5 1 Y HDM S 2 R = 0.8601
0.79
0.71
0.87
1.47
1.08
1.86
1.40
1.03
1.77
0.00310 0.00315 0.00320 0.00325 0.00330 0.00335 -22.0
LnDe
Lower limit 0.69
In Fig. 2 the linear fitting of ln De versus 1/T for calculating the activation energy is shown. Smaller slopes than those reported by other authors in apple for the same range of experimental conditions (Barat et al., 2001) were obtained, suggesting that the effect of temperature on effective diffusivity is smaller in guava than in this fruit. This is corroborated by the activation energy values (Table 2), somewhat lower than those for apples (ranging between 41 and 43 kJ/ mole). However, it is worth commenting that similarly to other experiences, the highest value corresponded to the atmospheric pressure method, indicating that the effect of
y= -2780.1x -13.889 R² = 0.7036
-23.0 -23.5
95% confidence interval for De 1010 (m2/s)
1 Ys = 0.0028t R2 = 0.8604 1 Ys = 0.0033t0.5 R2 = 0.9024 1 Ys = 0.0040t0.5 R2 = 0.9013
probably due to the predominant action of diffusional mechanisms (further reinforced at the higher temperature), while the HDM could be inhibited by a softening of the porous structure and possible collapse of the pores. The temperature dependence on the effective diffusivity (De) is determined by the activation energy (Ea) through the Arrhenius equation. Ea De ¼ D0 exp ð14Þ RT
-22.5
De 1010 (m2/s)
y= -3391.5x -12.107 R2 = 0.9945
-24.0
1/T ( 1/K) APOD PVOD Linear (APOD) Linear (PVOD)
Fig. 2. Variation of ln De values versus 1/T in osmotically dehydrated guava processed at atmospheric pressure (APOD) and under pulsed vacuum (PVOD).
Table 2 Values of the activation energy (Ea) for the effective diffusivity and slopes (ln De versus 1/T), with confidence intervals, in osmotically dehydrated guava processed at atmospheric pressure (APOD) and under pulsed vacuum (PVOD) Pressure mode
Slope (ln De versus 1/T)
APOD PVOD
3391.5 2780.1
95% confidence interval for slope Lower limit
Upper limit
3532.7 3231.0
3250.3 2329.2
Ea (kJ/mol)
28.2 23.1
temperature is more important in that mode, where pseudo-diffusional mechanisms are controlling, and is less influential where the hydrodynamic mechanism acts, as in the pulsed vacuum processes (Escriche et al., 2000). 3.2. The net mass transfer Table 3 presents the kinetic constants with confidence intervals for the net mass transfer obtained from the adjusted experimental data (Eq. (13)). The parameters K and K0 represent the effect of the pseudo-diffusional and hydrodynamic mechanisms on the total mass changes, respectively. It is observed that at 30 and 40 °C the highest K values are achieved with pulsed vacuum. These results are logical if one keeps in mind that, with pulsed vacuum, HDM and the capillary forces accelerate water transport, and enhance the diffusional mechanism when the exchange surface between the fruit and the osmotic solution increases (Fito and Chiralt, 1995; Fito et al., 1992). At 50 °C, the pressure effect decreases, with values of K in both pressure modes closer together. This is due to the effect of the increased temperature on the exit velocity of water prevailing on the hydrodynamic and capillary mechanisms, not so markedly affected by temperature (Escriche et al., 2000). On the other hand, the positive values of K0 at 30 and 40 °C in the pulsed vacuum mode clearly reflect the
390
G. Panades et al. / Journal of Food Engineering 87 (2008) 386–390
Table 3 Kinetic parameters with confidence intervals for total mass changes in osmotically dehydrated guava processed at atmospheric pressure (APOD) and under pulsed vacuum (PVOD) Pressure mode
Temperature (°C)
K
95% confidence interval for K Lower limit
Upper limit
K0
95% confidence interval for K0 Lower limit
Upper limit
R2
APOD
30 40 50
0.1196 0.1308 0.3498
0.2076 0.2138 0.4338
0.0316 0.0478 0.2658
11.86 14.50 1.90
14.67 16.89 3.31
9.05 12.14 0.49
0.7407 0.8268 0.9702
PVOD
30 40 50
0.3202 0.3272 0.3059
0.4214 0.3792 0.4113
0.2190 0.2752 0.2005
1.61 0.45 4.83
0.23 0.04 7.84
2.99 0.86 1.82
0.9411 0.9866 0.9803
contribution of the HDM to the total mass changes of the sample; so, contrary to the other treatments used, a weight gain takes place at the beginning of the process. 4. Conclusions The effective diffusivities varied between 0.69 1010 and 1.47 1010 m2/s. The highest coefficients corresponded to the pulsed vacuum mode at 40 and 50 °C, due to the action of the hydrodynamic mechanism. The values of K0 obtained for the net mass loss at very short treatment times show that at the very beginning of the osmotic process using pulsed vacuum, at 30 and 40 °C, solids diffusion prevails on dehydration. On the other hand, the temperature effect is more important in the process performed at atmospheric pressure, where the pseudo-diffusional mechanism has the controlling function. References AOAC, 1997. Method 934.06. Moisture in dried fruits. In: Official Methods of Analysis of the Association of Official Analytical Chemists International, 16th ed. Adobe Software and E-DOC/CJS, Maryland. Barat, J.M., Alvarruiz, A., Chiralt, A., Fito, P., 1997. A mass transfer model in osmotic dehydration. P: G:81-84. In: Jowitt, R. (Ed.), Engineering and Food at ICEF 7. Academic Press Ltd., Sheffield, UK, pp. 77–80. Barat, J.M., Chiralt, A., Fito, P., 2001. Effect of osmotic solution concentration, temperature and vacuum impregnation pretreatment on osmotic dehydration kinetics of apple slices. Food Science and Technology International 7 (5), 451–456. Crank, J., 1975. The Mathematics of Diffusion. Oxford University Press, Oxford. Escriche, I., Garcı´a-Pinche, R., Andre´s, A., Fito, P., 2000. Osmotic dehydration of kiwifruit (Actinidia chinensis): fluxes and mass transfer kinetics. Journal of Food Process Engineering 23, 191–205.
Fito, P., 1994. Modeling of vacuum osmotic dehydration of food. Journal of Food Engineering 22, 313–328. Fito, P., Chiralt, A., 1995. An update on vacuum osmotic dehydration. In: Barbosa-Canovas, G.V., Welti-Chanes, J. (Eds.), Food Preservation by Moisture Control. Fundamentals and Applications. ISOPOW Practicum II. Technomic Publishing Company Inc., Lancaster, pp. 351–374. Fito, P., Chiralt, A., 1996. Osmotic dehydration: an approach to the modeling of solid food–liquid operations. In: Fito, P., Ortega, E., Barossa-Canovas, G.V. (Eds.), Food Engineering 2000. Chapman & Hall, New York, pp. 231–252. Fito, P., Shi, X.Q., Chiralt, A., Acosta, E., Andres, A., 1992. The influence of vacuum treatment on mass transfer during osmotic dehydration on some fruits. In: Fito, P., Mulet, A. (Eds.), Proceedings of ISOPOW-V: Water in Foods. Servicio de Publicaciones de la Universidad Politecnica de Valencia, Espan˜a. Fito, P., Andres, A., Pastor, R., Chiralt, A., 1994. Vacuum osmotic dehydration of fruits. In: Sing, R.P., Oliveira, F.A. (Eds.), Process Optimization and Minimal Processing of Foods. CRC Press, Boca Raton, Florida, pp. 107–121. NC 77-52, 1986. Frutas y vegetales naturales. Guayaba. Especificaciones de calidad. La Habana: Comite Estatal de Normalizacion. Panades, G., Treto, O., Fernandez, C., Castro, D., Nunez de Villavicencio, M., 1996. Pulse vacuum osmotic dehydration of guava. Food Science and Technology International 2 (5), 301–306. Panades, G., Chiralt, A., Fito, P., Rodriguez, I., Nunez, M., Albors, A., Jimenez, R., 2003a. Influence of operating conditions on sensory quality of minimally processed osmotically dehydrated guava. Journal of Food Quality 26, 91–103. Panades, G., Nunez, M., Acosta, V., 2003b. Deshidratacio´n osmo´tica de guayaba a diferentes condiciones de vacı´o pulsante. Alimentaria: Revista de Tecnologı´a e Higiene de los alimentos 40 (345), 67–70. Panades, G., Fito, P., Aguiar, Y., Nunez de Villavicencio, M., Acosta, V., 2006. Osmotic dehydration of guava: influence of operating parameters on process kinetics. Journal of Food Engineering 72, 383–389. Pereira, L.M., Rodrigues, A.C.C., Sarantopoulos, C.I.G.L., Junqueira, V.C., Cunha, R.L., Hubinger, M.D., 2004. Influence of modified atmosphere packaging and osmotic dehydration on the quality maintenance of minimally processed guavas. Journal of Food Science 69, 172–177.
Journal of Food Engineering 87 (2008) 386–390 www.elsevier.com/locate/jfoodeng
Mass transfer mechanisms occurring in osmotic dehydration of guava Gloria Panades a,*, Deborah Castro a, Amparo Chiralt b, Pedro Fito b, Margarita Nun˜ez a, Ramiro Jimenez a b
a Instituto de Investigaciones para la Industria Alimenticia, Carr. Guatao km 3.5, Lisa, C. Habana 19200, Cuba Departamento de Tecnologı´a de Alimentos, Universidad Politecnica de Valencia, Camino de Vera 14, Valencia 46022, Spain
Received 9 July 2007; received in revised form 19 December 2007; accepted 21 December 2007 Available online 8 January 2008
Abstract Two osmotic dehydration modes were applied to guava segments immersed in a 65 °Brix sucrose solution at 30, 40 and 50 °C: under constant atmospheric pressure and using a pulsed vacuum (5 min under vacuum, then at atmospheric pressure). The effective diffusivity in the liquid phase, De and the kinetic constants of net mass transfer, K and K0, were determined by fitting the experimental data to mathematical models. The highest effective diffusivities were obtained with pulsed vacuum at 40 and 50 °C on account of the hydrodynamic mechanism, with solids diffusion overcoming dehydration at the beginning of the process, at 30 and 40 °C. The effect of temperature on mass transfer kinetics, predictable by the Arrhenius equation, is more relevant at atmospheric pressure, where the pseudo-diffusion mechanism exerts the controlling role. Ó 2008 Elsevier Ltd. All rights reserved. Keywords: Osmotic dehydration; Kinetics; Effective diffusivity; Guava
1. Introduction In osmotic drying, water diffusion through the cellular membranes is the main transport mechanism, although there is an overlapping of diffusion and capillary phenomena in the tissue’s intercellular spaces (pores). Capillary phenomena occur at low pressure (Fito, 1994), but with the high compression ratios associated with the pulsed vacuum process (low pressure at the beginning of the treatment and atmospheric pressure later on) the entrance of the external liquid phase in the intercellular spaces through the hydrodynamic mechanism (HDM) can play an important role in mass transfer. Consequently, in osmotic dehydration (OD) several mechanisms intervene in different degrees, depending on process conditions. These mechanisms can be divided in two groups (Fito, 1994; Fito et al., 1994):
*
Corresponding author. Tel.: +53 7 2020919. E-mail address: [email protected] (G. Panades).
0260-8774/$ - see front matter Ó 2008 Elsevier Ltd. All rights reserved. doi:10.1016/j.jfoodeng.2007.12.021
– A group of mechanisms that depend on concentration gradients, generically labeled as pseudo-diffusional and usually modeled applying the second Fick’s law to a non stationary and unidirectional flow. – A mechanism that depends on pressure gradients, called the hydrodynamic mechanism (HDM) that acts at the beginning of the osmotic treatment. In previous papers a macroscopic model of the OD process integrating the pseudo-diffusional and hydrodynamic mechanisms has been studied (Barat et al., 1997, 2001; Fito and Chiralt, 1996). It involves the kinetics from two viewpoints: compositional changes of the food’s liquid phase (FLP) and changes in the product’s total mass. In the first case the model allows good predictions of the final composition of the product, in terms of a corrected coefficient of effective diffusion with the contribution of the HDM. This parameter can offer valuable information, since it takes into account the compositional changes of the liquid phase of the fruit due to the mass transfer processes that take place under different treatments, determining the
G. Panades et al. / Journal of Food Engineering 87 (2008) 386–390
387
Nomenclature Mw Ms M M0 Mt Xw0 Xwt Xs0 Xst YS Y HDM S Zst Zs0 Zse Z HDM s
water losses (%) solids gain (%) weight loss (%) initial weight (g) weight at time ‘‘t” (g) initial moisture (g water/g sample) moisture at time ‘‘t” (g water/g sample) initial solutes concentration (g solutes/g sample) solutes concentration at time ‘‘t” (g solutes/g sample) reduced driving force in the LP of the fruit reduced driving force considering the effect of the HDM solute concentration in the LP of the fruit at time t (g solutes/g liquid fraction) solute concentration in the LP in the initial moment (g solute/g liquid fraction) concentration of the LP in equilibrium with the osmotic solution, considered similar to that of the solution (g solute/g of liquid fraction) solute concentration in the LP of the sample resulting from the action of the HDM (g solute/g of liquid fraction)
quality and final condition of the product. It can thus become a basis for the design of products and processes. In the second case the model predicts the changes in total mass through kinetic constants for net mass transfer, which has an important effect on the productivity and profitability of the process. The reviewed literature includes studies on the kinetics of osmotic dehydration (OD) of guava under vacuum or atmospheric pressure that have yielded advances in process modeling and in controlling the variables that regulate it (Panades et al., 1996, 2003b, 2006). Other studies report on the influence of osmotic drying on product quality (Panades et al., 2003a; Pereira et al., 2004). However, few references deal with the mass transfer mechanisms occurring in the liquid fraction of the product during treatment at different pressure regimens. The objective of this study was to determine the effective diffusivity in the liquid phase of osmotically dehydrated guava and the kinetic constants of net mass transfer in the process variants at atmospheric pressure and under pulsed vacuum.
m mLP mi mHDM i yso Ks0
Ks K K0 t De l D0 Ea R T
sample mass in the initial instant (g) mass of the LP (g) impregnated mass (g) impregnated mass resulting from the effect of the HDM (g) solute concentration of the osmotic solution (g solute/g of liquid fraction) kinetic constant of solute transport occurring at very short treatment times in the pulsed vacuum regimen kinetic constant of solute transport kinetic constant of the combined kinetics of the pseudo-diffusional mechanisms kinetic constant of the net mass loss after a very short treatment time process time (s) effective diffusivity half thickness of the sample (0.00334 m) Arrhenius factor (m2/s) activation energy (kJ/mol) universal gas constant absolute temperature (K)
conditions established in the Cuban Standard (NC 77-52, 1986) and with a 53–59 mm diameter, to ensure the homogeneous size of samples. The fruits were peeled, cut in halves, cored and cut in eighths. 2.2. Osmotic dehydration treatment Guava slices were weighed in 110 g fractions (about 12 slices) and put in a 1 L glass flask containing 880 g of a sucrose solution of 65 °Brix, for a fruit: solution ratio of 1:8. The flask was then immersed in a thermostatic water bath, connected to a vacuum rotary evaporator with a rotation speed of 100 rpm and subjected to different pressure treatments for different times. Three temperatures, 30, 40 and 50 °C, six total times, 30, 60, 90, 120, 150 and 180 min and two pressure modes: atmospheric pressure and pulsed vacuum, were tested. In the pulsed vacuum regimen, a vacuum time of 5 min. was used. Absolute pressures of the system were those of the syrup vapor pressure, corresponding to every temperature studied: 30 °C – 4.3 kPa; 40 °C – 5.2 kPa; 50 °C – 10.7 kPa. Each experiment was carried out in triplicate.
2. Materials and methods 2.3. Analyses 2.1. Sample preparation For the study, hard ripened guavas (Psidium guava L.), Enana Roja variety, from the Estacion Nacional de Frutales, in Havana, were selected according to the maturity
After every treatment, samples were removed from the solution, drained and rinsed with distilled water to remove the syrup adhered to the surface, then gently blotted with tissue paper.
388
G. Panades et al. / Journal of Food Engineering 87 (2008) 386–390
In every experience moisture content was determined gravimetrically using a vacuum oven for drying to constant weight at 60 °C (AOAC, 1997). The soluble solids content was determined in a refractometer (ABBE, ATAGO Model 3 – T, Japan). All analyses were performed in triplicate.
The diffusivity coefficient in the fruit’s LP was determined from the integrated solutions of Fick’s equations for semi-infinite slabs and short times, considering a single term of the series (Crank, 1975): 0:5 De t ð12Þ 1 Ys ¼ 2 pl2
2.4. Mass balance
The effective diffusivity coefficient (De) was calculated from the slope of the linear fitting of the experimental data in the representation of 1 Ys versus t0.5.
The relationships among the component concentrations at a given time were defined through the Fito and Chiralt equations (1996), with the signs convention set considering the mass flows into the product as positive: ð1Þ ð2Þ
M ¼ Kt0:5 þ K 0 ð3Þ
ð5Þ
In the calculation of the reduced driving force in the pulsed vacuum mode the value of Zs0 has been corrected, assuming that in the product’s liquid phase a quick compositional change occurs at the very beginning of the osmotic process due to the contribution of the HDM, in agreement with the modifications brought about by Fito and Chiralt (1996): Z st Z se Z HDM Z se s m Z LP s0 þ mi y so Z HDM ¼ s mLP þ mi mLP ¼ mðxw0 þ xs0 Þ
Y HDM ¼ S
mi ¼
mHDM m i
mHDM i
K s0 1 ¼ 100 y so
ð6Þ
In Fig. 1 are shown all the values of (Mw + Ms) versus M with the objective of checking the mass balances. A good fit of the experimental results (R2 = 0.9107) was observed. 3.1. Changes in the food’s liquid phase composition (FLP) The predictive equations corresponding to the fitting of 1 Ys and 1 Y HDM versus t0.5, along with the effective S diffusivities and respective confidence intervals calculated for each treatment, are shown in Table 1. The De values obtained varied between 0.69 1010 and 1.47 1010 m2/s in the interval reported by other authors (Escriche et al., 2000). In both pressure modes, for a temperature increase from 30 to 50 °C, the coefficients tend to rise, coinciding with the results of other studies (Barat et al., 2001). In general, the highest values appear at 40 and 50 °C in the pulsed vacuum regimen, which is explained by the larger net gain of solutes that occur in that regimen in osmotically dehydrated guava, as a consequence of the HDM. This is in line with the findings of a previous study (Panades et al., 2006). At 50 °C diffusivity is the same in both treatments,
ð7Þ ð8Þ ð9Þ ð10Þ
-50
-45
-40
-35
-30
-25
-20
-15
-10 -10 -20 -30
y= 0.9074x - 2.1256
-40
2
R = 0.9107
Ks0 was determined according to the pattern developed by Fito and Chiralt (1996) and Barat et al. (1997): M s ¼ K s t0:5 þ K s0
The kinetic constants were obtained from the linear fitting of the experimental data to Eq. (13). 3. Results and discussion
For calculating the effective diffusivity (De) in the liquid phase of the product (water + soluble solids), an equation derived from Fick’s second law was used (Crank, 1975). Considering the guava segment as a slab of thickness h in the atmospheric pressure mode, the reduced driving force (Y = YS = Yw) was determined as a function of the liquid phase composition (LP) of the fruit (Fito and Chiralt, 1996): Z st Z se Z s0 Z se
ð13Þ
ð4Þ
2.5. Compositional changes in the liquid phase and effective diffusivity
YS ¼
The kinetic constants of mass transfer (K, K0) were determined according to the model developed by Fito and Chiralt (1996) and Barat et al. (1997):
Mw +M s (%)
M ¼ Mw þ Ms M t X wt M 0 X w0 Mw ¼ 100 M0 M t X st M 0 X s0 Ms ¼ 100 M0 Mt M0 M¼ 100 M0
2.6. Kinetic constants of net mass transfer
ð11Þ
-50
M (%) Fig. 1. Relationship between the values of Mw + Ms versus M in osmotically dehydrated guava.
G. Panades et al. / Journal of Food Engineering 87 (2008) 386–390
389
Table 1 Effective diffusivity (De) with confidence intervals and predictive equations in osmotically dehydrated guava processed at atmospheric pressure (APOD) and under pulsed vacuum (PVOD) Pressure mode
APOD
Temperature (°C)
Predictive equations 0.5
30 40 50
PVOD
30 40 50
Upper limit
0.55
0.83
0.95
0.83
1.07
1.40
1.33
1.47
¼ 0:0030t0:5 1 Y HDM S 2 R = 0.8916 1 Y HDM ¼ 0:0041t0:5 S 2 R = 0.8595 ¼ 0:0040t0:5 1 Y HDM S 2 R = 0.8601
0.79
0.71
0.87
1.47
1.08
1.86
1.40
1.03
1.77
0.00310 0.00315 0.00320 0.00325 0.00330 0.00335 -22.0
LnDe
Lower limit 0.69
In Fig. 2 the linear fitting of ln De versus 1/T for calculating the activation energy is shown. Smaller slopes than those reported by other authors in apple for the same range of experimental conditions (Barat et al., 2001) were obtained, suggesting that the effect of temperature on effective diffusivity is smaller in guava than in this fruit. This is corroborated by the activation energy values (Table 2), somewhat lower than those for apples (ranging between 41 and 43 kJ/ mole). However, it is worth commenting that similarly to other experiences, the highest value corresponded to the atmospheric pressure method, indicating that the effect of
y= -2780.1x -13.889 R² = 0.7036
-23.0 -23.5
95% confidence interval for De 1010 (m2/s)
1 Ys = 0.0028t R2 = 0.8604 1 Ys = 0.0033t0.5 R2 = 0.9024 1 Ys = 0.0040t0.5 R2 = 0.9013
probably due to the predominant action of diffusional mechanisms (further reinforced at the higher temperature), while the HDM could be inhibited by a softening of the porous structure and possible collapse of the pores. The temperature dependence on the effective diffusivity (De) is determined by the activation energy (Ea) through the Arrhenius equation. Ea De ¼ D0 exp ð14Þ RT
-22.5
De 1010 (m2/s)
y= -3391.5x -12.107 R2 = 0.9945
-24.0
1/T ( 1/K) APOD PVOD Linear (APOD) Linear (PVOD)
Fig. 2. Variation of ln De values versus 1/T in osmotically dehydrated guava processed at atmospheric pressure (APOD) and under pulsed vacuum (PVOD).
Table 2 Values of the activation energy (Ea) for the effective diffusivity and slopes (ln De versus 1/T), with confidence intervals, in osmotically dehydrated guava processed at atmospheric pressure (APOD) and under pulsed vacuum (PVOD) Pressure mode
Slope (ln De versus 1/T)
APOD PVOD
3391.5 2780.1
95% confidence interval for slope Lower limit
Upper limit
3532.7 3231.0
3250.3 2329.2
Ea (kJ/mol)
28.2 23.1
temperature is more important in that mode, where pseudo-diffusional mechanisms are controlling, and is less influential where the hydrodynamic mechanism acts, as in the pulsed vacuum processes (Escriche et al., 2000). 3.2. The net mass transfer Table 3 presents the kinetic constants with confidence intervals for the net mass transfer obtained from the adjusted experimental data (Eq. (13)). The parameters K and K0 represent the effect of the pseudo-diffusional and hydrodynamic mechanisms on the total mass changes, respectively. It is observed that at 30 and 40 °C the highest K values are achieved with pulsed vacuum. These results are logical if one keeps in mind that, with pulsed vacuum, HDM and the capillary forces accelerate water transport, and enhance the diffusional mechanism when the exchange surface between the fruit and the osmotic solution increases (Fito and Chiralt, 1995; Fito et al., 1992). At 50 °C, the pressure effect decreases, with values of K in both pressure modes closer together. This is due to the effect of the increased temperature on the exit velocity of water prevailing on the hydrodynamic and capillary mechanisms, not so markedly affected by temperature (Escriche et al., 2000). On the other hand, the positive values of K0 at 30 and 40 °C in the pulsed vacuum mode clearly reflect the
390
G. Panades et al. / Journal of Food Engineering 87 (2008) 386–390
Table 3 Kinetic parameters with confidence intervals for total mass changes in osmotically dehydrated guava processed at atmospheric pressure (APOD) and under pulsed vacuum (PVOD) Pressure mode
Temperature (°C)
K
95% confidence interval for K Lower limit
Upper limit
K0
95% confidence interval for K0 Lower limit
Upper limit
R2
APOD
30 40 50
0.1196 0.1308 0.3498
0.2076 0.2138 0.4338
0.0316 0.0478 0.2658
11.86 14.50 1.90
14.67 16.89 3.31
9.05 12.14 0.49
0.7407 0.8268 0.9702
PVOD
30 40 50
0.3202 0.3272 0.3059
0.4214 0.3792 0.4113
0.2190 0.2752 0.2005
1.61 0.45 4.83
0.23 0.04 7.84
2.99 0.86 1.82
0.9411 0.9866 0.9803
contribution of the HDM to the total mass changes of the sample; so, contrary to the other treatments used, a weight gain takes place at the beginning of the process. 4. Conclusions The effective diffusivities varied between 0.69 1010 and 1.47 1010 m2/s. The highest coefficients corresponded to the pulsed vacuum mode at 40 and 50 °C, due to the action of the hydrodynamic mechanism. The values of K0 obtained for the net mass loss at very short treatment times show that at the very beginning of the osmotic process using pulsed vacuum, at 30 and 40 °C, solids diffusion prevails on dehydration. On the other hand, the temperature effect is more important in the process performed at atmospheric pressure, where the pseudo-diffusional mechanism has the controlling function. References AOAC, 1997. Method 934.06. Moisture in dried fruits. In: Official Methods of Analysis of the Association of Official Analytical Chemists International, 16th ed. Adobe Software and E-DOC/CJS, Maryland. Barat, J.M., Alvarruiz, A., Chiralt, A., Fito, P., 1997. A mass transfer model in osmotic dehydration. P: G:81-84. In: Jowitt, R. (Ed.), Engineering and Food at ICEF 7. Academic Press Ltd., Sheffield, UK, pp. 77–80. Barat, J.M., Chiralt, A., Fito, P., 2001. Effect of osmotic solution concentration, temperature and vacuum impregnation pretreatment on osmotic dehydration kinetics of apple slices. Food Science and Technology International 7 (5), 451–456. Crank, J., 1975. The Mathematics of Diffusion. Oxford University Press, Oxford. Escriche, I., Garcı´a-Pinche, R., Andre´s, A., Fito, P., 2000. Osmotic dehydration of kiwifruit (Actinidia chinensis): fluxes and mass transfer kinetics. Journal of Food Process Engineering 23, 191–205.
Fito, P., 1994. Modeling of vacuum osmotic dehydration of food. Journal of Food Engineering 22, 313–328. Fito, P., Chiralt, A., 1995. An update on vacuum osmotic dehydration. In: Barbosa-Canovas, G.V., Welti-Chanes, J. (Eds.), Food Preservation by Moisture Control. Fundamentals and Applications. ISOPOW Practicum II. Technomic Publishing Company Inc., Lancaster, pp. 351–374. Fito, P., Chiralt, A., 1996. Osmotic dehydration: an approach to the modeling of solid food–liquid operations. In: Fito, P., Ortega, E., Barossa-Canovas, G.V. (Eds.), Food Engineering 2000. Chapman & Hall, New York, pp. 231–252. Fito, P., Shi, X.Q., Chiralt, A., Acosta, E., Andres, A., 1992. The influence of vacuum treatment on mass transfer during osmotic dehydration on some fruits. In: Fito, P., Mulet, A. (Eds.), Proceedings of ISOPOW-V: Water in Foods. Servicio de Publicaciones de la Universidad Politecnica de Valencia, Espan˜a. Fito, P., Andres, A., Pastor, R., Chiralt, A., 1994. Vacuum osmotic dehydration of fruits. In: Sing, R.P., Oliveira, F.A. (Eds.), Process Optimization and Minimal Processing of Foods. CRC Press, Boca Raton, Florida, pp. 107–121. NC 77-52, 1986. Frutas y vegetales naturales. Guayaba. Especificaciones de calidad. La Habana: Comite Estatal de Normalizacion. Panades, G., Treto, O., Fernandez, C., Castro, D., Nunez de Villavicencio, M., 1996. Pulse vacuum osmotic dehydration of guava. Food Science and Technology International 2 (5), 301–306. Panades, G., Chiralt, A., Fito, P., Rodriguez, I., Nunez, M., Albors, A., Jimenez, R., 2003a. Influence of operating conditions on sensory quality of minimally processed osmotically dehydrated guava. Journal of Food Quality 26, 91–103. Panades, G., Nunez, M., Acosta, V., 2003b. Deshidratacio´n osmo´tica de guayaba a diferentes condiciones de vacı´o pulsante. Alimentaria: Revista de Tecnologı´a e Higiene de los alimentos 40 (345), 67–70. Panades, G., Fito, P., Aguiar, Y., Nunez de Villavicencio, M., Acosta, V., 2006. Osmotic dehydration of guava: influence of operating parameters on process kinetics. Journal of Food Engineering 72, 383–389. Pereira, L.M., Rodrigues, A.C.C., Sarantopoulos, C.I.G.L., Junqueira, V.C., Cunha, R.L., Hubinger, M.D., 2004. Influence of modified atmosphere packaging and osmotic dehydration on the quality maintenance of minimally processed guavas. Journal of Food Science 69, 172–177.