1

Determination of Equilibrium Sorption Isotherm of Crackers by Using

GAB Model

By

Kirtiraj Kundlik Gaikwad

MS: Packaging

School of Packaging

Michigan State University, East Lansing USA

2

Determination of Equilibrium Sorption Isotherm of Crackers by Using

GAB Model

Kirtiraj K Gaikwad, Maria Rubino

School of Packaging, Michigan State University, East Lansing 48825 MI USA

ABSTRACT

Crackers are highly sensitive to moisture. Due to moisture shelf life of crackers is decreases. Sorption

isotherms give information about the sorption mechanism and the interaction of food with water. In this

study moisture sorption isotherms of crackers were determined using Licl, Mgcl, kno2, NaNo2,

(NH4)2So4, KNo3 with RH 12%, 33.20%, 48%, 64.20%, 80.30%, and 92% respectively. It is shown

that, increasing equilibrium moisture content with increase in relative humidity RH. The Guggenheim-

Anderson-de Boer (GAB) models were applied to fit the predicted data. The criteria used to evaluate the

goodness of fit of model were the percentage root mean square (RMS) which is 3.10. The GAB model

is considered suitable to predict the moisture sorption isotherm of crackers since it gave RMS value

Key Words: Crackers, sorption isotherms, GAB model.

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1 INTRODUCTION

Shelf-life determination is of great importance for the food industry to ensure that the consumer will

obtain a high-quality product for a certain period of time after purchase. For the delivery of a product

with maximum quality, the shelf-life of the packaged food product should be determined. (Ubonrat

Sirpatrawan2009) The quality of crackers is strictly related to their water content. Usually, when this

product is packaged, the water activity inside the package is generally as low as possible. During the

distribution and storage of the product, due to the difference between the water activity inside and

outside the package, water molecules permeate through the package leading to an increase of the internal

water activity. This causes an increase of the water content of the packed product and consequently a

decrease of its quality. The quality decay kinetics of these types of foods depends on several factors, the

most important being the characteristic of the packed product. (M.A. Del et al 2003). Moisture sorption

isotherms of these products are useful to determine their storage stability as well as to predict their shelf-

life since they give information about the equilibrium relationship between product moisture content and

water activity, at a given temperature and relative humidity.

An important role of packaging film is to reduce exchange of water between the product and the

environment the barrier property of packaging films depends on both molecule diffusion coefficient and

solubility of water in the matrix (R.S. Jagadish et. Al. 2011). Water activity (aw) is the most important

factor, affecting the durability of the packaging material. Water activity has the basic controlling factor

in the preservation of moisture sensitive material for food applications against microbiological,

chemical, and physical deterioration. Equations for modeling water-sorption isotherms are of special

interest in many aspects of food preservation by dehydration By the sorption isotherms which will

obtain from experimental data is necessary to predict the hygroscopic properties of the film. The

equilibrium moisture content is an important quantitative measure in the practice of food storage,

packaging. (Baldev Raj et al 2001) The GAB model is considered to be the most versatile sorption

model available in the literature. GAB models have been adopted as equations by the American Society

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of Agricultural Engineers for describing sorption isotherms. These models have been widely used in the

literature (U. Siripatrawan and P. Jantawat)

The objectives of this study is to determine the experimentally the equilibrium sorption isotherm and

and to model the sorption characteristics of crackers using GAB equations on the basis of moisture

adsorb by crackers. This product usually encounters loss of crispness due to moisture gain during

storage and distribution, with subsequent deterioration in product quality.

.

2 Materials and Methods

2.1 Materials:

Electronic weighing balance, Crackers, Buckets (to create Humidity Environment contains salt),

Vacuum oven, different salt like Licl, Mgcl, kno2, NaNo2, (NH4)2So4, KNo3 with RH 12%, 33.20%,

48%, 64.20%, 80.30%, 92% respectively, Aluminum dish etc.

2.2 Methods

2.2.1 Determination of Initial moisture content (IMC or Mi):

Aluminum dishes were taken (3 dishes) and weighed empty dish to get dish weight on electronic

weighing balance. 3.2124 +-2 gm Crushed crackers weighed on electronic balance to get initial weight

of crackers (Wi). Measured crackers were taken in aluminum dish and. Crackers were dried on 98-1000C

under 30 inches Hg in vacuum oven till weight of crackers not changing (about 5 hours). After certain

time weight of crackers were not change and this at this point, reweighed dishes to get final product

crackers (WD) or loss of moisture from crackers. Equation for calculation of initial moisture content (Mi)

is as follow

Mi =(Wi−WD)

WD (1)

Where, Wi is the initial weight of product and WD is the final weigh of product

2.2.2 Determination of Equilibrium moisture content (Me):

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Aluminum dishes were taken (18 dishes) and weighed empty dish to get dish weight on electronic

weighing balance. 3.2124 +-2 gm Crushed crackers weighed on electronic balance to get initial weight

of crackers. All weighed crackers were taken in keep in dish and reweighed to get sample +dish weight.

Applying same procedure each sample is weighed and recorded data. These dishes then placed in 6

different buckets witch contain different salt Licl, Mgcl, kno2, NaNo2, (NH4)2So4, KNo3 with RH

12%, 33.20%, 48%, 64.20%, 80.30%, 92% respectively. Total 18 samples used. i.e., in each salt solution

Bucket contains 3 samples. These samples are weighed initially 7 days period until no further change

in increase or decrease weight is observed. At this stage since no further weight gain or loss of

moisture is observed, it is assumed equilibrium has been reached. The equilibrium moisture content at

each specific relative humidity is determined based on following equation.

Me=We

Wi*(Mi + 1) − 1 (2)

Where, Wi is the initial weight of product, We is the final weigh of product, Mi is initial moisture content

and Me is equilibrium moisture content. Average the equilibrium moisture content value of replicate

samples for at specific relative humidity

Then using Me value plot the graph Me vs. Aw (RH/100). Other Graph were plotted for aw/Me vs Aw

by applying 2nd-polynomoal to get the value of α,β, γ. After getting values of α,β,γ. From equation k,

C, and Wm values were calculated by applying there formula

T = β 2/ (-α γ) +4 (3)

C = T√𝑇2 − 4𝑇/2 (4)

2.2.3 GAB model:

By using moisture sorption isotherm with the experimental data, we will successfully calculate three

constants in GAB model,k, C, and Wm and establish the equation for GAB model

The GAB equation was used to model water sorption of crackers as follows

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Wm

Me=

(1−kaw)∗(1−kaw+C∗kaw)

C∗kaw (5)

Where, Me - equilibrium moisture content of the product (dry basis), Aw - water activity (RH%/100).

Wm- the water content in the mono-layer in BET theory, C - Guggenheim constant, k- factor correcting

properties of the multi-layer molecules, with respect to the bulk liquid.

Predicted equilibrium moisture content were calculated by using GAB model and graph plotted the

moisture sorption isotherm by predicted moisture sorption isotherm

2.2.4 Data comparison:

Predicted data (GAB model) and experimental data were compared the by using following equation

RMS-√∑(

Mexp−Mcalc

Mexp)^2

N⁄ *100 (6)

Where Mexp: Experimental moisture content, Mcalc: Calculated moisture content, N: Number of

experimental unit. This RMS equation is fit in Mexp and Mcal by which we can compare both data with

each other

3 RESULTS AND DISCUSSIONS

3.1 Experimental Data:

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Calculation of the Initial Moisture Content (Mi):

Sample Initial weight of the

Crackers

Before Drying

Final weight of the

Crackers

After Drying

1 3.2758 3.0357

2 3.3477 3.1109

3 3.3957 3.1618

Salt (Chemical) RH (%) Sample

weight of Empty

dish (gm)

sample

(gm)

sample+dish

1/11/13 (Wi)

sample+ dish

(1/22/13) (gm)

samle + dish

1/29/13

sample

+dish 2/5/13

sample+dish

2/12/13

Licl 12% 5.4 1.3097 3.2124 4.5221 4.5317 4.5322 4.531 4.5306

5.5 1.3102 3.2413 4.5515 4.5581 4.5582 4.5586 4.5576

5.6 1.3151 3.2334 4.5485 4.5562 4.5567 4.5545 4.5502

Mgcl 33.20% 5.7 1.3205 3.2389 4.5594 4.6323 4.6327 4.633 4.6324

5.8 1.3258 3.2809 4.6067 4.6796 4.6803 4.6822 4.6801

5.9 1.3192 3.2744 4.5936 4.6666 4.668 4.6676 4.6671

kno2 48% 5.1 1.3219 3.2597 4.5816 4.6971 4.6974 4.6971 4.6962

5.11 1.3053 3.2624 4.5677 4.696 4.6968 4.6972 4.696

5.12 1.3201 3.2307 4.5508 4.6751 4.6753 4.6745 4.6737

NaNo2 64.20% 5.13 1.3095 3.2457 4.5552 4.771 4.7716 4.7738 4.7729

5.14 1.3351 3.2249 4.56 4.7729 4.7731 4.7753 4.7744

5.15 1.3247 3.2216 4.5463 4.7574 4.7576 4.7567 4.7589

(NH4)2So4 80.30% 5.16 1.2995 3.2725 4.572 5.9524 4.9583 4.9569 4.9571

5.17 1.3025 3.2726 4.5751 4.9505 4.9559 4.9543 4.9548

5.18 1.3027 3.2504 4.5531 4.9318 4.9361 4.93444 4.9334

KNo3 92% 5.19 1.3202 3.26 4.5802 5.2731 5.2642 5.2333 52001

5.2 1.288 3.2202 4.5082 5.1996 5.1865 5.13 5.1144

5.21 1.3166 3.2802 4.5968 5.2432 5.2401 5.199 5.1728

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Equation for Mi:

𝑀𝑖 = 𝑊𝑖−𝑊𝐷

𝑊𝐷

Where,

Wi – Initial Weight of the product

WD- Final Weight of the product

For Sample No 1: 𝑀𝑖 = 3.2758−3.0357

3.0357 = 0.079092gm

For Sample No 2 𝑀𝑖 = 3.3477−3.1109

3.1109 = 0.076119gm

For Sample No 3 𝑀𝑖 = 3.3957−3.1618

3.1618 = 0.073976gm

Average Mi = 0.076396 gm

3.2 Tabulated 𝐖𝐢 𝐖𝐞 and 𝐌𝐞 under different RH%:

Me= 𝑊𝑒

𝑊𝑖 (𝑀𝑖 + 1) − 1

Where,

Wi – Initial Weight of the product, Mi- Initial Moisture Content

Me - Equilibrium Moisture content We – final weight of product

Calculation For 12%RH (sample 5.4): Me= 4.5306

4.5515 (0.0763 + 1) − 1

= 0.078514 gm

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From above calculation we get following table for Wi, We and Me

Salt

(Chemical)

RH (%) Sample Initial Wt

(Wi)

Final wt

(We)

Equilibrium

Moisture Content

Me (Dry Basis)

Me Avg

Licl 12% 5.4 4.5221 4.5306 0.078514 0.078515

5.5 4.5515 4.5576 0.078075

5.6 4.5485 4.5502 0.077816

Mgcl 33.20% 5.7 4.5594 4.6324 0.093771 0.093772

5.8 4.6067 4.6801 0.094037

5.9 4.5936 4.6671 0.093736

kno2 48% 5.1 4.5816 4.6962 0.10353 0.103532

5.11 4.5677 4.696 0.10691

5.12 4.5508 4.6737 0.10565

NaNo2 64.20% 5.13 4.5552 4.7729 0.12805 0.128051

5.14 4.56 4.7744 0.12721

5.15 4.5463 4.7589 0.12621

(NH4)2So4 80.30% 5.16 4.572 4.9571 0.16701 0.167014

5.17 4.5751 4.9548 0.16561

5.18 4.5531 4.9334 0.16654

KNo3 92% 5.19 4.5802 52001 0.22988 0.229882

5.2 4.5082 5.1144 0.22485

5.21 4.5968 5.1728 0.21740

3.3 Moisture isotherm based on experimental data

Salt (Chemical) RH (%) Sample Equilibrium

Moisture Content

Me (Dry Basis)

Me Avg

(Exp)

Licl 12% 5.4 0.078514 0.078515

10

5.5 0.078075

5.6 0.077816

Mgcl 33.20% 5.7 0.093771 0.093772

5.8 0.094037

5.9 0.093736

kno2 48% 5.1 0.103531 0.103532

5.11 0.106913

5.12 0.105654

NaNo2 64.20% 5.13 0.128051 0.128051

5.14 0.127218

5.15 0.126211

(NH4)2So4 80.30% 5.16 0.167014 0.167014

5.17 0.165611

5.18 0.166548

KNo3 92% 5.19 0.229881 0.229882

5.2 0.224859

5.21 0.217408

Graph:

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Fig 1: Moisture isotherm Me vs. RH%

3.4 Plot of 2nd-polynomoal version of GAB model and corresponding equation, including the

converted data.

Salt (Chemical) RH (%) Me Avg (Exp) Aw Aw/Me

(gm moisture /

100gm dry

product)

Licl 12% 0.078515 0.120 1.52

Mgcl 33.20% 0.093772 0.332 3.54

kno2 48% 0.10353 0.481 4.63

NaNo2 64.20% 0.12805 0.642 5.01

(NH4)2So4 80.30% 0.16701 0.803 4.80

KNo3 92% 0.22988 0.920 4.00

0

5

10

15

20

25

0% 20% 40% 60% 80% 100%

Me

(gm

)

RH %

Me/ RH%

Series1

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Graph:

Fig 2: 2nd-polynomoal version of GAB model, Aw/Me vs Aw

3.5 Calculation of GAB parameter:

From above graph by 2nd-polynomoal equation we got the value of α, β, γ Values -12.363, 16.152 &

-0.3006 respectively

So first, Aw/Me = α(aw) 2 βaw γ

-12.363) + 16.152+ (-0.3006)

= 3.488

T= β 2/ (-α γ) +4

= ((16.152)2 /- ((-12.363)*(-0.3006)) +4)

= - 66.20

y = -12.363x2 + 16.152x - 0.3006

0

1

2

3

4

5

6

0 0.2 0.4 0.6 0.8 1

Aw

/Me

Aw

aw /Me VS aw

Series1

Poly. (Series1)

13

C = T√𝑇2 − 4𝑇/2

= −66.2004 √(−66.20)2 − 4 ∗ (−66.2004)/2

= 0.9853

β =1

Wm(1 −

2

C)

𝑾𝒎 =1

16152(1 −

2

0.985334)

= -0.06375

γ = 1

𝑊𝑚𝐶𝑘

k = 1

−0.06375∗0.9853∗(−0.3006)

= 52.95

α -12.363 T -66.20

β 16.152 C 0.9853

γ -0.3006 K 52.95

Wm -0.06375

3.6 Predicted data and experimental moisture isotherm

Calculation for Me by GAB Model

𝑊𝑚

𝑀𝑒=

(1 − 𝑘𝑎𝑤) ∗ (1 − 𝑘𝑎𝑤 + 𝐶𝑘𝑎𝑤)

𝐶𝑘𝑎𝑤

For Licl 12%

Rearranging above equation and putting values so we get,

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−0.06375

𝑀𝑒=

(1 − 52.95 ∗ 0.120) ∗ (1 − 52.95.∗ 0.12 + 0.9853 ∗ 52.95 ∗ 0.120)

0.9853 ∗ 52.95 ∗ 0.120

Me= 0.0822 gm moisture)/gm dry product

By applying above equation we get

Salt (Chemical) RH (%) Exp (Me) (gm

moisture/100 gm

dry product

Me by GAB

Model (gm

moisture)/(gm

dry product)

Licl 12% 0.078515 0.0822

Mgcl 33.20% 0.093772 0.089

kno2 48% 0.103532 0.104

NaNo2 64.20% 0.128051 0.129

(NH4)2So4 80.30% 0.167014 0.170

KNo3 92% 0.229882 0.224

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Graph: predicted (Fitted line) and experimental (scatter plot) Me vs. RH%

Salt (Chemical) RH (%) Exp (Me) (gm

moisture/100 gm

dry product

Me by GAB

Model (gm

moisture)/(gm

dry product)

Licl 12% 7.81 8.22

Mgcl 33.2% 9.37 8.97

kno2 48% 10.3 10.4

NaNo2 64.2% 12.8 12.9

(NH4)2So4 80.3% 16.7 17.0

KNo3 92% 22.9

22.4

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Fig 3: Predicted data and experimental moisture isotherm Me exp & Me GAB VS RH%

3.7 Calculation for RMS:

Predicted data (GAB model) and experimental data were compared the by using following equation

RMS-√∑(

Mexp−Mcalc

Mexp)^2

N⁄ *100

Where,

Mexp : Experimental moisture content

Mcalc : Calculated moisture content

N: Number of experimental unit

We have Mexp , Mcal and N value so by putting values in above formula we get.

0

5

10

15

20

25

0% 10% 20% 30% 40% 50% 60% 70% 80% 90% 100%

Me

(gm

)

RH%

Me exp & Me GAB vs RH%

Me exp

Me GAB

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RMS = 3.10

DISCUSSION

Moisture sorption isotherms describe the relationship between the equilibrium moisture content and the

water activity at constant temperatures and pressures. For food materials these isotherms give

information about the sorption mechanism and the interaction of food biopolymers with water. The

moisture sorption isotherms are extremely important in modeling the drying process, in design and

optimization of drying equipment, in predicting shelf-life stability, in calculating moisture changes

which may occur during storage and in selecting appropriate packaging material. Moisture sorption

isotherms are an important tool when formulating food to achieve specific qualities and attributes (Bell

and Labuza, 2000). Despite their value, traditional isotherms have been limited by their low resolution.

It is very helpful in making shelf life calculations, developing mixing models, modeling temperature

abuse, determining the integrity of a protective coating or layer, determining monolayer values, and

making accurate packaging calculations. GAB (Guggenheim- Anderson-de Boer) equation has been

applied successfully for the correlation of the equilibrium moisture content with the water activity of

food products and it is recommended by the european project COST 90 on Physical Properties of Foods.

(Z. B. Maroulis, 1988) The simplicity and physical meaning of the GAB model makes it very useful for

describing and interpreting water sorption isotherms for Food Application of the GAB model to food

isotherms has shown a good fit up to aw = 0.9 (Piotr P. Lewicki 1977) It has been shown that the GAB

equation fits food isotherms in that range as well as or better than other equations with four or more

terms The GAB equation can also describe water activity variation with temperature since W,, C and K

are exponential functions of inverse absolute It has become the standard sorption isotherm equation used

in Europe and is being established in US laboratories (Christine M. 1991) In this study we analyzed data

by two different way one is Me that is from experimental value and Me predicted from GAB model

from this data were compared with RMS 3.106875657 which is which is below 25%. It proves that the

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GAB model can successfully predict the moisture content under different RH. Guggenheim- Anderson-

de Boer (GAB model ) could use for establish sorption isotherm, providing the relationship between aw

and water content over a wide range of food products with different shapes of isotherms, under widely

varying conditions of temperature, moisture and water activity Water activity is a measure of the water

in a food (or other substance) available to organisms. Water activity is defined as the equilibrium

relative humidity (ERH) of this air divided by 100. The relationship between water activity and moisture

content at a given temperature is called the moisture sorption isotherm. This relationship is complex and

unique for each product due to different interactions between the water and the solid components at

different moisture contents. In conclusion, different products at different temperature have their certain

moisture isotherm, and the increase tendency of water activity always accompanied by an increase of

water content in the certain product.

4 CONCLUSIONS

It is shown that, increasing equilibrium moisture content with increase in relative humidity RH. The

GAB isotherm model was found to be adequate for the description of the isotherms of the crackers at the

different percent RH Moisture content control. It is show that moisture sorption isotherms have an

important role to play in the quantitative approach to the prediction of the shelf life of crackers or any

dried foods due to their sensitivity to moisture changes. The GAB isotherm model was found to

represent the predictable data satisfactorily for crackers. The analysis of the GAB equation proves that

the GAB model can successfully predict the moisture content under different RH.

ERROR ANALYSIS

1) Every time we analyze the weight of sample there is a chances of error while recording of data

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2) When we take sample out of salt solution bucket at that time there is change of relative humidity

percentage and it disturb the RH % around the sample.

3) We need to take precaution while handling sample during measurements. While taking sample dish

out of bucket we need to take precaution because sample dish are very light in weight so there is chance

of fall of sample in bucket while handling.

4) Bucket closure should be properly packed. If closure open then outside humidity affect the inside

humidity and it will not create expected humidity inside the bucket.

5) Due to high humidity like 90% there is chances of mold growth on the sample so it will also increase

the weight of sample if mold growth in large quantity

5 REFERENCES

1) U. Siripatrawan and P. Jantawat (2006) Determination of Moisture Sorption Isotherms of Jasmine Rice

Crackers Using BET and GAB Models Food Science and Technology International December 2006 vol. 12

no. 6 459-465

2) M.A. Del Nobile et al (2003) shelf life prediction of cereal-based dry foods packed in moisture-sensitive

films Journal Of Food Science—Vol. 68, Nr. 4, 2003.

3) R.S. Jagadish et al (2011) Properties and sorption studies of polyethylene oxide–starch blended films

Food Hydrocolloids Volume 25, Issue 6, August 2011, Pages 1572–1580.

4) Baldev Raj et al (2001) Moisture-sorption characteristics of starch/low-density polyethylene films.

Journal of Applied Polymer Science Volume 84, Issue 6, pages 1193–1202, 9 May 2002

20

5) Bell Leonard N., Labuza (2001) Moisture sorption: practical aspects of isotherm measurement and use

(2nd Ed.)

6) Z. B. Maroulis, et al (1988) Application of the GAB Model to the Moisture Sorption Isotherms for Dried

Fruits Journal ofFood Engineering 7 (1988) 63-78

7) Piotr P. Lewicki ( 1977) The applicability of the GAB model to food water sorption isotherms

International Journal of Food Science and Technology 1997, 32, 553-557 55

8) Christine M. (1991) Comparison of Regression Methods for Fitting the GAB Model to the Moisture

Isotherms of some Dried Fruit and Vegetables Journal of Food Engineering 13 ( 199 1) 115 - 13 3