Sorption isotherms and heat of sorption of pineapple

M.D. Hossain a,*, B.K. Bala a, M.A. Hossain b, M.R.A. Mondol a

a Department of Farm Power and Machinery, Bangladesh Agricultural University, Mymensingh 2202, Bangladeshb F.M.P. Engineering Division, Bangladesh Agricultural Research Institute, Gazipu 1701, Bangladesh

Received 5 April 2000; accepted 25 July 2000

Abstract

Sorption isotherms of pineapple were determined at 20°C, 30°C, 40°C and 50°C temperatures by using dynamic method. Six two-

parameter and one three-parameter isotherm models were selected to ®t the observed data, and the modi®ed BET model was found

to be the best-®tted model for pineapple. The heat of sorption of pineapple decreased with an increase in moisture content and the

heat of sorption was found to be a power function of moisture content. Ó 2001 Elsevier Science Ltd. All rights reserved.

Keywords: Dynamic method; Equilibrium moisture content; Heat of sorption; Isotherm model; Pineapple; Sorption isotherm

1. Introduction

Sorption isotherms of foodstu�s are essential for de-sign, modelling and optimisation of many processessuch as drying, aeration and storage (Labuza, 1968;Bala, 1991). Knowledge of sorption isotherms is alsoimportant for predicting stability and quality changesduring packaging and storage of dried foods. Manyresearchers have developed mathematical equations todescribe the sorption isotherms of food materials. Chi-rife and Iglesias (1978) reviewed 23 isotherm equations,both theoretical and experimental, and their use for®tting sorption isotherms of foods and food products.None of these equations described accurately the sorp-tion isotherm over the whole range of relative humidityand for di�erent types of food materials. Labuza (1975)noted that no sorption isotherms model could ®t dataover the entire range of relative humidity because wateris associated with the food matrix by di�erent mecha-nisms in di�erent activity regions. Lomauro, Bakshi,and Labuza (1985) evaluated two two-parameter equa-tions and one three-parameter equation for 163 foodmaterials including fruits, vegetables, spices and starchyfoods. They found that the three-parameter Guggen-heim, Anderson and den Boer (GAB) equation (Van denBerg, 1984) described the sorption isotherms for mostfoods better than two-parameter equations. The BETequation developed by Brunauer, Emmett, and Teller(1938) is the most popular due to its thermodynamic

base. But this equation is valid only from 10±50% rela-tive humidity (Labuza, 1968; Coulson & Richardson,1975). Many researchers modi®ed the BET equation andthe modi®ed equation gave a good ®t up to 90% relativehumidity (Dincer & Esin, 1996). The Smith equation(1947) is useful in describing the sorption isotherm ofbiological materials such as starch and cellulose. Hen-derson (1952) proposed a semi-empirical model for theequilibrium moisture content of cereal grains. Day andNelson (1965) modi®ed the Henderson equation to de-scribe wheat up to 70% relative humidity. The Chung andPfost (1967) equation ®ts grain equilibrium moisturecontent data well over the 20±90% relative humidity range.

Knowledge of the heat of sorption is important inunderstanding the mechanism of sorption. It is a valu-able tool in designing equipment for drying (Iglesias &Chirife, 1976, 1978; Balaban, Zurith, Singh, & Hayak-awa, 1987). Iglesias and Chirife (1976) calculated andconstructed heat curves from sorption isotherms ofseveral foods, including fruits, protein foods, vegetablesand spices. They found that, with a few exceptions, theheat curves showed a regular decrease with increasingmoisture content. So this study was undertaken to de-termine sorption isotherms to ®t the experimental datato the isotherm models, and to calculate the heat ofsorption of pineapple (Annas comosus L.).

2. Materials and method

The experiment was conducted at the Process Engi-neering Laboratory, in the Department of Farm Power

Journal of Food Engineering 48 (2001) 103±107

www.elsevier.com/locate/jfoodeng

* Corresponding author.

0260-8774/01/$ - see front matter Ó 2001 Elsevier Science Ltd. All rights reserved.

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and Machinery, Bangladesh Agricultural University,Mymensingh, Bangladesh, during the period of Janu-ary±June, 1999. The dynamic method (Hossain, Bala,Sarkar, & Sarkar, 1998) was used to measure theadsorption equilibrium moisture content of pineapple(A. comosus L.). Airtight cylindrical plastic containers,115-mm diameter and 135-mm height, containing satu-rated salt solutions were placed in an electric oven toprovide constant temperature and relative humidityenvironments. The digital temperature controller (modelXMTJ) provided the desired temperature (accuracy�1°C). A mini fan of 60-mm (3 V, 0.25 A) was ®ttedinside the plastic container to provide continuous stir-ring of the air inside the container. The values for rel-ative humidity of the saturated salt solutions wereobtained from the works of Wexler and Hasegawa(1954) and Young (1967) and these are listed in Table 1.About 10 g of dried sample from fully ripe pineapple(sugar content about 10.50%) was placed inside the cy-lindrical nylon box (50-mm diameter and 40-mm height)

and suspended over the saturated salt solutions in thecontainer and the container was made airtight with aplastic cover. The container was then placed in the ovenat a desired constant temperature and allowed toequilibrate with the environment inside the containers.The selected temperatures were 20°C, 30°C, 40°C and50°C with an accuracy of �1°C variation. The experi-ment was conducted in the months of December±Janu-ary when the ambient temperature was 9±18°C. Theweight of each sample was recorded at 6-h intervals bytaking out the sample from the container very fast andthen replacing the sample in the container. The weightrecording period was about 15±20 s. This procedure wascontinued until the weight was constant. About 1.5±5.0days were required for adsorption equilibrium of thepineapple with the environment maintained by saturatedsalt solutions. No visible mould growth was observedduring the experiments. The moisture content of eachsample was then determined by the oven-drying methodat 80°C for 24 h.

Notations

a, b, c parameters of isotherm equations

K constant

Me equilibrium moisture content, % (dry basis)

Mo observed moisture content, % (dry basis)

Mp predicted moisture content, % (dry basis)

Qst net isosteric heat of sorption, KJ/mole

rh relative humidity (decimal)

RMSE root mean square error

R universal gas constant (8.315 kJ/kg mol K)

T temperature, °C

Tab absolute temperature, K

Table 1

Percent relative humidity of the saturated salt solutions at various temperature

Salts Temperature (°C) Reference

20 30 40 50

Lithium chloride (LiCl) 11.4 11.2 11.2 11.1 Young (1967)

Magnesium chloride

(MgCl2 á 6H2O)

33.0 32.4 31.8 31.2 Wexler and Hasegawa (1954)

Sodium dichromate

(Na2Cr2O7 á 2H2O)

55.2 52.5 49.8 46.3 Wexler and Hasegawa (1954)

Sodium chloride (NaCl) 75.5 75.6 75.4 74.5 Wexler and Hasegawa (1954)

Potassium nitrate (KNO3) 93.2 90.7 87.9 85.0 Wexler and Hasegawa (1954)

Potassium sulphate (K2SO4) 97.2 96.6 96.2 95.8 Wexler and Hasegawa (1954)

Table 2

Selected isotherm equations for experimental data ®tting

Name of models Mathematical expression

1. Smith (1947) Me � aÿ b ln�1ÿ rh�2. Chung and Pfost (1967) ln�rh� � ÿa=�RTab�exp�ÿb Me�3. Henderson (1952) 1ÿ rh � exp�ÿa Tab Mb

e �4. Modi®ed BET (1996) Me � a=�1ÿ b rh�5. Iglesias and Chirife (1981) Me � a� b �rh=�1ÿ rh��6. Day and Nelson (1965) 1ÿ rh � exp�ÿa=Mb

e �7. GAB (Van den Berg, 1984) Me � a b c rh=�1ÿ c rh��1ÿ c rh� b c rh�

104 M.D. Hossain et al. / Journal of Food Engineering 48 (2001) 103±107

2.1. Model selection

Six two-parameter and one three-parameter (GAB)isotherm equations were selected for ®tting the experi-mental data for sorption isotherms for pineapple. Theselected equations are given in Table 2.

The parameters of the equations were estimated byregression analysis using Microsoft Excel 97 software.The value of root mean square error (RMSE) representsthe ®tting ability of a model in relation to the number ofdata points. The smaller the RMSE value, the better the®t of the model.

RMSE �����������������������������������������Xn

i�1

�Mp ÿMo�2n

!vuut : �1�

Heat of sorption phenomena can be explained by theClausius±Clayperon equation (Iglesias & Chirife, 1976;Okos, Narsimhan, Singh, & Weitmauuer, 1992) as fol-lows: T

ab

le3

Est

imate

dp

ara

met

ers

of

di�

eren

tm

od

els

for

the

sorp

tio

nis

oth

erm

of

pin

eap

ple

at

di�

eren

tte

mp

eratu

res

Mo

del

sA

BC

20°C

30°C

40°C

50°C

20°C

30°C

40°C

50°C

20°C

30°C

40°C

50°C

1.

Sm

ith

(19

47

)5

4.6

06

49.3

544.1

538.3

145.7

242.9

038.9

134.3

6

2.

Ch

un

ga

nd

Pfo

st(1

96

7)

30

31

3.7

52

30

83.4

920

701.5

017

666.1

00.1

015

0.1

033

0.1

101

0.1

20

3.

Hen

der

son

(19

52)

1.3

8E)

07

4.0

5E)

07

7.7

4E)

07

1.5

2E)

07

2.8

52.6

22.5

21.4

2

4.

Mo

di®

edB

ET

(19

96)

17

.27

14.4

812.4

810.3

90.7

30.7

56

0.7

80.7

9

5.

Igle

sia

sa

nd

Ch

irif

e(1

98

1)

27

.28

23.5

320.5

016.9

11.0

51.1

91.2

21.2

4

6.

Day

an

dN

elso

n(1

965)

116

504.8

18

456.8

6558.5

2316.6

3.6

63.2

34

3.0

32.8

4

7.

GA

B(V

an

den

Ber

g,

19

84)

40

87.8

47

5012.6

90

5026.9

11

4898.1

23

3.4

723

1.4

402

1.0

862

0.9

917

8.2

4E)

03

7.0

9E)

03

7.9

2E)

03

8.7

7E)

03

Fig. 1. ln(rh) vs 1/Tab graphs for calculating the heat of sorption of

pineapple.

Fig. 2. Experimental sorption isotherms of pineapple at di�erent

temperatures.

M.D. Hossain et al. / Journal of Food Engineering 48 (2001) 103±107 105

o ln�rh�oT

� Qst

RT 2: �2�

Integrating Eq. (2), assuming that the net isosteric heatof sorption (Qst) is temperature independent, gives thefollowing equation:

ln�rh� � ÿ Qst

R

� �1

Tab

� K: �3�

The value of Qst was calculated from the slope of theplot between the values of ln(rh) and 1/Tab at constantmoisture content as shown in Fig. 1. The relative hu-midities at di�erent temperatures and at constantmoisture content were obtained from the Fig. 2.

3. Results and discussion

Sorption isotherms of pineapple at temperatures of20°C, 30°C, 40°C and 50°C in the relative humidityrange of 11±97% are presented in Fig. 2. Higher equi-librium moisture contents were found at the lowertemperature at the same relative humidity. The reasonmay be that with the increase in temperature, watermolecules get activated due to their energy level, causingthem to become less stable and to break away from thewater-binding site of the food materials, thus decreasingthe mono-layer moisture content. Labuza (1968);Hossain et al. (1998) and Rahman and Labuza (1999)have presented similar results. Isotherm curves werefound to be sigmoid in shape and all curves followedsimilar patterns. Statistically computed parameters fordi�erent isotherm models and their coe�cients of deter-mination for sorption of pineapple are given in Tables 3and 4. For all the models, parameters a, b and c arefound to be temperature dependent. In the case of themodi®ed BET model, the values of the coe�cient ofdetermination were highest. Minimum RMSE value wasfound for the modi®ed BET equation and maximumvalues were obtained for the Iglesias and Chirife equa-tion. So, the modi®ed BET equation was found to be thebest estimator for predicting the equilibrium moisture

content of pineapple, followed by the Chung and Pfostequation and the GAB equation. The observed andpredicted sorption isotherms using the modi®ed BETequation at temperatures of 20°C, 30°C, 40°C and 50°Care shown in Fig. 3. The agreements between the ob-served and predicted results were excellent for the rela-tive humidity range 11±97%. The parameters a and b arefound to be linearly dependent on temperature and thefollowing equation was developed to predict the sorp-tion isotherms of pineapple for the temperature range20±50°C and relative humidity range 11±97%.

Me � �21:579ÿ 0:2264� T �=�1ÿ �0:6809� 0:0024

� T � rh�: �4�The net isosteric heats of sorption for di�erent moisturecontents are shown in Fig. 4. The net isosteric heat ofsorption decreased with an increase in moisture content.A steep slope of the curve is observed at low moisturecontent. At low moisture contents, the heat of sorptionis higher than at high moisture contents. Tsami (1991)suggested that the rapid increase in the heat of sorptionat low moisture content was due to the existence ofhighly active polar sites on the surface of the food ma-

Table 4

Estimated coe�cient of determination and RMSE values of di�erent models for the sorption isotherm for pineapple at di�erent temperatures

Models R2 RMSE

20°C 30°C 40°C 50°C

1. Smith (1947) 0.909 0.914 0.914 0.902 3.938

2. Chung and Pfost (1967) 0.957 0.975 0.988 0.903 2.332

3. Henderson (1952) 0.944 0.938 0.946 0.935 3.352

4. Modi®ed BET (1996) 0.999 0.999 0.999 0.998 0.614

5. Iglesias and Chirife (1981) 0.771 0.755 0.763 0.804 7.942

6. Day and Nelson (1965) 0.978 0.972 0.996 0.976 3.521

7. GAB (Van den Berg, 1984) 0.965 0.984 0.983 0.981 3.126

Fig. 3. Observed (Mo) and predicted (Mp) sorption isotherms of

pineapple by modi®ed BET method at di�erent temperatures.

106 M.D. Hossain et al. / Journal of Food Engineering 48 (2001) 103±107

terial which are covered with water molecules forming amono-molecular layer. The net isosteric heat of sorptionof water in pineapple can be expressed mathematicallyas power function of moisture content,

Qst � 29:765Mÿ1:1656e �R2 � 0:9967�: �5�

This mathematical relationship may be used to calculatethe heat of sorption of pineapple for various moisturecontents.

4. Conclusions

Higher sorption isotherms were observed at lowertemperatures. The experimental data was ®tted to sevenisotherm models. The modi®ed BET model was foundto be the best-®t model to describe the sorption iso-therms of pineapple in the temperature range 20±50°Cand relative humidity range 11±97.5%. So the modi®edBET model may be used to estimate sorption isothermsof pineapple. The heat sorption of pineapple decreaseswith an increase in moisture content and is found to be apower function of moisture content.

References

Bala, B. K. (1991). Physical and thermal properties of malt. Drying

Technology, 9(4), 1091±1104.

Balaban, M. O., Zurith, C. A., Singh, R. P., & Hayakawa, K. (1987).

Estimation of moisture sorption and improved criteria for evalu-

ating moisture sorption equations for foods. Journal of Food

Process Engineering, 10, 53±70.

Brunauer, S., Emmett, P. H., & Teller, E. (1938). Adsorption of gases

in multi-molecular layers. Journal of American Chemical Society,

60, 309±319.

Chirife, J., & Iglesias, H. A. (1978). Equations for ®tting water

sorption isotherms of foods. 1. A review. Journal of Food

Technology, 13, 159±174.

Chung, D. S., & Pfost, H. B. (1967). Adsorption of vapour by cereal

grains and their products. Transactions of the ASAE, 10(4), 549±

557.

Coulson, J. M., & Richardson, J. F. (1975). Chemical Engineering

(Vol. 3, 5th ed., pp. 506±519). Oxford: Pergamon Press.

Day, D. L., & Nelson, G. L. (1965). Desorption isotherms for wheat.

Transactions of the ASAE, 8(2), 293±296.

Dincer, T. D., & Esin, A. (1996). Sorption isotherms for macaroni.

Journal of Food Engineering, 27, 211±228.

Henderson, S. M. (1952). A basic concept of equilibrium moisture.

Agricultural Engineering, 33(1), 29±33.

Hossain, M. A., Bala, B. K., Sarkar, R. I., & Sarkar, M. A. R. (1998).

Experimental investigation on equilibrium moisture contents for

chilli. Journal of the Institution of Engineers, Bangladesh (Agricul-

tural Engineering Division), 25/AE(1), 94±100.

Iglesias, H. A., & Chirife, J. (1976). Prediction of the e�ect of

temperature on water sorption isotherm of food materials. Journal

of Food Technology, 11(2), 109±116.

Iglesias, H. A., & Chirife, J. (1978). Isosteric heats of water vapour

sorption on dehydrated foods. Part 1. Analysis of the di�erential

heat curves. Lebensmittel-Wissenscha� und Tecnolgie, 9, 116±122.

Iglesias, H. A., & Chirife, J. (1981). An equation for ®tting uncommon

water sorption isotherms in foods. Lebensmittel-Wissenscha� und

Tecnolgie, 14, 111±117.

Labuza, T. P. (1968). Sorption phenomena in foods. Food Technology,

22, 263±272.

Labuza, T. P. (1975). Interpretation of sorption data in relation to the

state of constituent water. In R. Duckworth (Ed.), Water Relations

in Foods (pp. 155±172). New York: Academic.

Lomauro, C. J., Bakshi, A. S., & Labuza, T. P. (1985). Evaluation of

food moisture sorption isotherm equations. Part 1. Fruit, vegetable

and meat products. Lebensmittel-Wissenscha� und Tecnolgie, 18,

111±117.

Okos, M. R., Narsimhan, G., Singh, R. K., & Weitmauuer, A. C.

(1992). Food dehydration. In D. R. Heldman, & D. B. Lund (Eds.),

Hand Book of Food Engineering (pp. 437±562). New York: Marcel

Dekker.

Rahman, M. S., & Labuza T. P. (1999). Water activity and food

preservation. In M. S. Rahman (Ed.), Handbook of Food Preser-

vation (pp. 339±382). New York: Marcel Dekker.

Smith, S. E. (1947). Sorption of wheat vapour by high polymers.

Journal of the American Chemical Society, 69, 646±651.

Tsami, E. (1991). Net isosteric heat of sorption in dried fruits. Journal

of Food Engineering, 14, 327±335.

Ven den Berg, C. (1984). Description of water activity of foods for

engineering purpose by means of the GAB model of sorption. In B.

M. McKemenne (Ed.), Engineering and Food (Vol. 1, pp. 311±321).

London: Elsevier Applied Science.

Wexler, A., & Hasegawa, S. (1954). Relative humidity±temperature

relationships of some saturated salt solutions in the temperature

range 0° to 50°C. Journal of Research National Bureau of

Standardization, 53A, 19±25.

Young, J. F. (1967). Humidity control in the laboratory using salt

solutions: a review. Journal of Applied Chemistry, 17, 241±245.

,

Fig. 4. Net isosteric heat of sorption for di�erent moisture contents.

M.D. Hossain et al. / Journal of Food Engineering 48 (2001) 103±107 107