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iglesias1976

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HkCTOR
Departamento
de Industrias,
Universidad
A. IGLESIAS
Facoltad
and JORGE
de Ciencias
de Buenos Aires,
Exactas
CHIRIFE
y Naturales
Buenos Aires, Argentina
A MODEL FOR DESCRIBING THE
WATER SORPTION BEHAVIOR O F FOODS
ABSTRACT
A multilayer adsorption equation, originally developed for physical adsorption on nonuniform surfaces,is used to describe the water sorption
behavior of a great variety of foods and food components. Characteristic parameters of the sorption equation, for each of the products
tested, were computed. A comparison was made between Halsey’s equation and Henderson’s classical one. Literature data for 220 food isotherms, comprising 69 different materials, were utilized to compare
both equations. It was found that in most casesHalsey’s equation has a
better fit than Henderson’s.
INTRODUCTION
ALTHOUGH
several mathematical equations have been reported in the literature for describing water sorption isotherms
of food materials (Henderson, 1952; Becker and Sallans, 1956;
Labuza, 1968; Agrawal et al., 1969; Nellist and Hughes, 1973)
none of them has been able to give accurate results throughout
the whole range of water activity and for different types of
foods. Eqtiations for fitting water sorption isotherms in foods
are of special interest in many aspects of food preservation by
dehydration. Among them it may be mentioned the prediction
of the shelf life of a dried product in a packaging material
(Karel et al., 1971; Labuza et al., 1972) or the prediction of
drying times of foodstuffs (King, 1968).
Recently (Iglesias et al., 1975a), have shown that a multilayer adsorption equation, originally developed by Halsey
(1948) could be used to describe the water sorption behavior
of a large number of foods and food components. This equation was shown to be applicable to the range of water activity
of about, 0.10 < A, < 0.80, which covers most of the practical applications. Halsey’s equation is,
p/p,, = exp (-a/RT or)
(1)
where, p/p0 = Aw = water activity; a, r = parameters; 0 =
coverage, % dry basis; and X, =
X/X, ; X = equilibrium
monolayer value, same units as X. Halsey (1948) deduced Eq
(1) assuming that the potential energy of a molecule varies as
the inverse rth power of its distance from the surface. He also
stated that the magnitude of parameter r characterizes the
type of interaction between the vapor and the solid. If r is
large, the attraction of the solid for the vapor is very specific
and does not extend far from the surface; when r is smaller the
forces are more typical Van der Waals and are able to act at a
greater distance.
In order to investigate the real magnitude of the applicability of Halsey’s equation in the food area, it is now applied
to a great variety of foods not previously investigated. Furthermore, Halsey’s equation is quantitatively
checked against
Henderson’s model (Henderson, 1952) which is a widely used
model relating water activity and amount of sorbed water.
Experimental data from the literature comprising over 200
984-JOURNAL
OF FOOD SCIENCE-
Volume 41 (1976)
isotherms and corresponding to 69 different
were utilized to compare both equations.
food materials,
RESULTS & DISCUSSION
FOR PURPOSES of curve fitting,
form,
Eq (1) may be put in the
In In PO/p = -rln 0 + In a’
(2)
where, a’ = a/RT.
A plot of In In pa/p vs 0 should be a straight line from
which the parameters r and a’ may be calculated. Monolayer
values were obtained by applying BET equation (Labuza,
1968) to the experimental data of sorption isotherms. As it
was mentioned (Iglesias et al., 1975a) the monolayer value is
not essential for fitting purposes; if X, is not desired to be
used, 19 may be replaced by X, and Eq (2) will also fit the
experimental data ‘yielding a different value for parameter a’.
The,parameters r and a’ were calculated using a lineal regression program in an IBM 360/50, 128 K computer. Table 1
shows the calculated values.
A widely used model relating water activity and amount of
sorbed water in foods is due to Henderson (Henderson, 1952;
Lafuente and Piiiaga, 1966; Labuza, 1968; Agrawal et al.,
1969; Chen and Clayton, 1971; Nellist and Hughes, 1973;
Singh and Oj ha, 19 74),
1 - A, = exp - (k Xn)
(3)
which may be written as,
ln[-ln(l-A,)]=nlnX+lnk
(4)
where, n, k = parameters.
A piot of In [- In (1 - A,)] vs amount sorbed should give
a straight line from which the parameters n and k may be
calculated. A least squares analysis was used to obtain the
values of parameters n and k which are shown on Table 2. It
could appear somewhat strange to compare Halsey’s equation
with Henderson’s, when recently Iglesias and Chirife (1976)
showed that in most cases two or three “localized isotherms”
may be distinguished when applying Eq (4). However, for fitting purposes the ,utility of Henderson’s equation would be
severely restricted if two or more pairs of constants were
needed to define, the sorption isotherm. For this reason, the
experimental data were fitted with Eq (4), and although this
resuited in a loss of accuracy, the error introduced in this way
may be in several cases small enough for fitting purposes.
In order to evaluate the goodness of fit of Halsey’s and
Henderson’s equations as applied to the experimental data, a
statistical analysis (which is not included here) was performed.
WATER SORPTION
From this analysis onlv the %(ErrorL,
is shown here in Table
3. This %(Error)avg means an aver&g of the % relative differences between the experimental and calculated values at
several (usually eight) equally spaced water activites over the
range examined. Analysis of the results presented in Table 3
clearly indicate that in most cases Halsey’s equation has a
better fit than Henderson’s In over 220 isotherms comprising
69 different food materials it was found that in 70.4% of the
cases examined Halsey’s equation yields a %( Error)avg smaller
Table l-Constants
BEHA VIOR OF FOODS-985
than Henderson’s equation. For 7.7% of the cases both equations give a similar %(Error)avg, i.e., the %(Error)avg for both
equations does not differ by more than 10%.
CdNCLUSIONS
IN AGREEMENT with previously reported results (Iglesias et
al., 1975a) it was found that Halsey’s equation describes reasonably well equilibrium
moisture contents for the various
r and a’ in Halsey’s
equationa
XITI
Range of
Product
Specs
A,
Temp
OC
g/lOOg
(d.b.1
X02
Range of
r
a’
Product
Specs
A,
Temp
“C
g/lOOg
(d.b.1
Adsorption
Desorption
Adsorption
Desorption
Adsorption
Desorption
0.10-0.80
0.1 O-0.80
0.05-0.80
0.10-0.80
0.05-0.70
0.10-0.80
5
5
25
25
45
45
4.8
5.1
4.2
4.6
3.6
4.5
1.407
1.681
1.273
1.528
1.006
1.308
1.580
2.088
1.544
1.890
1.357
1.519
Chicken,
raw
0.1 o-0.60
0.1 o-0.70
0.1 o-0.70
0.1 O-0.80
0.05-0.80
0.1 O-0.80
5
5
45
45
60
60
8.3
8.5
5.0
5.2
3.7
freeze-dried
Adsorption
Desorption
Adsorption
Adsorption
freeze-dried
Adsorption
Desorption
Adsorption
Desorption
Adsorption
Desorption
0.05-0.80
0.10-0.80
0.05-0.80
0.05-0.70
25
25
45
60
3.2
3.3
2.7
0.89
1.194
1.496
0.9840
0.8664
1.546
2.211
1.253
1.715
Chives
freeze-dried
Adsorption
Adsorption
0.05-0.80
0.05-0.70
Cinnamon
Adsorption
Adsorption
0.05-0.80
0.05-0.69
25
45
4.0
3.1
0.7610
0.8253
1.374
1.404
Adsorption
Desorption
Adsorption
Desorption
Cardamom
Desorption
Adsorption
0.20-0.80
0.10-0.80
5
25
8.1
5.9
2.574
1.833
2.598
1.881
Cloves
Cardamom
Adsorption
0.05-0.80
45
45
60
4.7
5.1
3.9
1.383
1.447
1.588
1.513
Anise
Avocado
Banana
Celery
Chamomile
Cheese, Edam
0.10-0.80
0.05-0.70
0.10-0.70
0.10-0.70
0.05-0.80
0.1 O-0.80
0.05-0.80
5
25
45
45
60
6.3
6.2
3.4
3.6
3.2
1.083
1.025
0.8668
0.8667
0.8579
1.398
1.295
1.459
1.389
1.406
Adsorption
Desorption
Adsorption
Desorption
Adsorption
Desorption
Adsorption
0.10-0.80
0.10-0.80
0.10-0.80
0.10-0.80
0.05-0.80
0.10-0.80
0.05-0.70
5
5
25
25
45
45
60
6.2
7.2
6.2
6.9
4.1
4.0
2.9
1.403
1.748
1.403
1.644
1.024
1.083
1.121
1.573
2.022
1.573
1.839
1.417
1.584
1.563
freeze-dried
Adsorption
Desorption
0.05-0.80
0.10-0.80
25
25
3.3
3.5
1.035
1.263
1.337
1.796
Cheese,
Emmental
freeze-dried
Adsorption
Desorption
Adsorption
0.05-0.80
0.104.80
0.05-0.80
25
25
45
3.3
3.7
2.2
1.141
1.469
0.9251
1.380
1.828
1.022
Chicken,
freeze-dried
Desorption
Adsorption
Desorption
Adsorption
Desorption
0.20-0.70
0.10-0.70
0.1 o-0.80
0.05-0.80
0.10-0.80
5
45
45
60
60
8.4
4.7
5.6
3.3
3.7
2.113
1.228
1.741
1.148
1.311
1.886
1.349
2.015
1.425
1.638
cooked
3.8
1.130
1.632
1.326
1.575
1.427
1.423
25
60
6.1
1.4
1.103
0.8106
1.553
1.509
0.10-0.70
0.20-0.70
0.1 o-o,70
0.20-0.70
25
25
45
45
6.1
7.0
4.7
5.4
1.758
2.082
1.444
1.667
1.785
1.922
1.461
1.647
Adsorption
Desorption
Adsorption
Adsorption
Adsorption
0.10-0.80
0.10-0.70
0.05-0.80
0.05-0.80
0.05-0.70
5
5
25
45
60
5.0
5.7
4.1
3.3
1.6
2.209
2.132
1.702
1.362
1.321
2.266
2.343
1.887
1.629
1.737
Coriander
Desorpt ion
Desorption
Desorption
0.20-0.80
0.20-0.80
0.1 O-0.80
5
25
45
7.0
6.1
4.3
2.859
2.456
1.483
2.375
2.231
1.507
Eggplant
freezedried
Adsorption
Adsorption
Adsorption
0.1 o-0.70
0.1 o-o. 70
0.05-0.70
25
45
60
6.7
5.3
1.8
1.052
0.7367
0.6858
1.394
0.8758
1.063
freeze-dried
Adsorption
0.1 O-0.60
45
4.9
1.112
1.181
Fennel
Adsorption
Desorption
Adsorption
Desorption
Adsorption
Desorption
0.05-0.70
0.1 O-0.80
0.05-0.70
0.1 O-0.80
0.05-0.70
0.1 O-0.80
5
5
25
25
45
45
2.8
4.3
2.8
3.4
2.5
2.5
0.9534
1.732
0.9534
1.366
0.9185
1.033
1.279
1.843
1.279
1.594
1.242
1.306
Ginger
Adsorption
Desorption
Adsorption
Desorption
Adsorption
Desorption
0.1 o-0.70
0.20-0.70
0.10-0.70
0.10-0.80
0.10-0.70
0.10-0.80
5
5
25
25
45
45
7.4
8.2
7.0
6.8
4.7
4.7
1.844
2.448
1.835
2.224
1.443
1.507
1.645
2.480
1.611
2.272
1.485
1.668
Grapefruit
freeze-dried
Desorption
Adsorption
0.10-0.70
0.05-0.70
5
60
5.8
1.9
0.9574
0.6752
1.702
1.194
1.477
1.709
freeze-dried
Adsorption
Adsorption
Adsorption
Desorption
Adsorption
a’
0.953
1.489
1.072
1.255
1.045
1.054
freeze-dried
Desorption
Adsorption
r
Egg. Paste
Table 1 (continued)
,
986--JOURNAL
OF FOOD SCIENCE-
Volume 41 (1976)
Table 1 (continued)
A,
Temp
“C
XIII
g/lOOg
id.b.)
Range of
Product
specs
Table 1 (continued)
XIII
Range of
r
a’
Hibiscus
Adsorption
Desorption
0.05-0.70
0.1 O-O. 70
25
25
2.2
3.2
0.6631
0.7798
Laurel
Adsorption
Adsorption
Desorption
Adsorption
0.05-0.70
0.05-0.80
0.10-0.80
0.05-0.70
25
45
45
60
4.5
3.1
4.5
2.6
1.318
1.164
1.349
1.404
1.493
i ,498
1.264
1.449
Lentil
Adsorption
Desorption
Adsorption
Adsorption
Desorption
0.10-0.70
0.20-0.70
0.10-0.70
0.10-0.70
0.1 O-0.80
5
5
25
45
45
7.5
9.3
6.9
5.2
5.2
1.613
2.253
1.611
1.297
1.377
1.635
2.011
1.667
1.391
1.404
Mushrooms,
Boletus
Adsorption
Desorption
Adsorption
Desorption
Adsorption
0.05-0.70
0.10-0.70
0.05-0.70
0.10-0.70
0.05-0.70
5
5
25
25
60
4.1
5.6
4.1
5.4
2.9
0.8945
1.068
0.8945
0.9595
0.8493
1.461
1.451
1.481
1.261
1.229
Mushrooms,
Pfifferling
Adsorption
Desorption
0.05-0.70
0.10-0.80
25
25
4.9
5.0
0.9365
1.140
1.407
1.717
Nutmeg
Adsorption
Desorption
Adsorption
Desorption
Adsorption
Desorpt ion
Adsorption
0.1 o-o. 70
0.1 o-o. 70
0.05-0.80
0.1 O-0.80
0.1 o-0.70
0.1 O-0.80
0.05-0.80
5
5.4
5
25
25
45
46
60
6.5
4.5
4.7
3.7
3.9
2.7
2.193
2.547
1.910
2.184
1.342
1.661
1.322
2.067
2.111
1.843
2.135
1.375
1.639
1.466
Paranut
Adsorption
Desorption
Adsorption
Adsorption
Desorption
0.05-0.70
0.1 O-0.80
0.05-0.80
0.05-0.80
0.1 O-0.80
5
5
25
60
60
2.2
2.5
1.8
1.1
1.2
1.549
2.342
1.597
1.056
1.323
1.643
2.383
1.722
1.292
1.790
Pear
Desorption
0.20-0.70
25’
10.8
0.8131
0.8640
Pear
freeze-dried
Adsorption
Desorption
0.1 O-0.60
9.1
9.1
0.7417
0.7417
0.9875
0.1 O-0.60
25
25
0.9875
Adsorption
Desorption
Adsorption
Adsorption
Desorption
Adsorption
Desorption
0.05-0.70
0.10-0.80
0.05-0.70
0.05-0.80
0.10-0.80
0.05-0.80
0.10-0.80
5
5
25
45
45
60
60
1.9
2.0
1.9
1.6
1.7
0.85
0.94
1.330
1.975
1.330
1.221
1.800
0.932
1.083
1.461
2.399
1.461
1.192
2.227
1.242
1.457
Peppermint
Adsorption
Desorption
Adsorption
Desorption
0.1 O-0.80
0.1 O-0.80
0.10-0.80
0.1 O-0.80
5
5
25
25
6.8
7.9
6:8
7.1
1.725
2.384
1.725
2.159
1.598
2.379
1.598
2.277
Peppermint
Adsorption
Desorption
Adsorption
0.1 O-0.80
0.1 O-0.80
0.05-0.70
45
45
60
4.7
4.5
3.2
1.293
1.415
1.338
1.432
1.777
1.448
Radish
freeze-dried
Adsorption
Adsorption
Desorption
Adsorption
Adsorption
0.05-0.70
0.05-0.70
0.10-0.70
0.05-0.70
0.05-0.70
5
25
25
45
60
6.0
5.4
5.9
3.5
2.1
0.8323
0.8350
0.8328
0.7542
0.7368
1.417
1.437
1.328
1.435
1.404
Pekanut
1.410
7.338
Product
Radish,
hot
Specs
A,
Temp
‘C
gllOOg
(d.b.1
r
a’
freeze-dried
Adsorption
Desorption
Adsorption
Adsorption
Desorption
0.1 o-o. 70
0.10-0.80
0.1 O-0.80
0.05-0.80
0.1 O-0.80
!i
7.3
5
25
45
45
6.9
6.8
4.5
4.6
1.363
1.660
1.441
1.034
1.047
1.586
2.184
1.628
1.333
1.389
freeze-dried
Adsorption
Desorption
Adsorption
0.05-0.80
0.1 O-0.80
0.05-0.80
45
45
60
5.2
5.7
4.2
1.296
1.368
1.090
1.620
1.729
1.438
Sweet
marjoram
Adsorption
Desorption
Adsorption
Desorption
Adsorption
Desorption
Adsorption
0.1 O-0.80
0.1 O-0.80
0.05-0.80
0.1 O-0.80
0.05-0.80
0.1 O-0.80
0.05-0.70
5
5
25
25
45
45.
60
6.3
7.4
4.6
5.2
3.0
3.1
2.1
1.907
2.369
1.431
1.574
1.114
1.122
1.154
1.968
2.698
1.734
1.873
1.610
1.550
1.534
Thyme
Adsorption
Desorption
Adsorption
Desorption
Adsorption
Desorption
Adsorption
0.10-0.80
0.10-0.70
0.05-0.80
0.1 O-0.80
0.05-0.80
0.1 O-0.80
0.05-0.70
5
5
25
25
45
45
60
5.6
7.0
4.7
4.9
3.5
3.6
3.1
1.748
2.090
1.513
I.771
1.293
1.307
1.430
1.837
2.071
1.722
2.146
1.759
1.782
back muscle
freeze-dried
Adsorption
Desorption
Adsorption
Desorotion
0.05-0.80
0.1 O-0.80
0.05-0.80
0.10-0.70
45
45
60
60
4.3
4.4
3.3
4.4
1.251
1.575
1.194
1.514
1.449
2.092
1.619
1.501
back muscle
freeze-dried
Desorption
Adsorption
Desorption
Adsorption
Desorption
0.10-0.70
0.05-0.80
0.1 o-0.70
0.05-0.80
0.10-0.80
5
45
45
60
60
8.8
4.3
8.8
3.5
3.5
1.592
1.078
1.573
0.9679
0.9772
1.620
1.443
1.596
1.378
1.388
Adsorption
Desorption
Adsorption
Desorption
Adsorption
Desorption
Adsorption
0.10-0.70
0.20-0.80
0.1 O-0.80
0.1 O-0.80
0.1 O-0.80
0.10-0.80
0.05-0.70
5
5
25
25
45
45
60
7.3
9.1
6.5
7.0
3.7
3.5
2.9
1.941
3.284
1.947
2.338
1.389
1.474
1.486
1.961
3.515
2.086
2.664
1.676
2.003
1.660
freeze-dried
Adsorption
Desorption
Adsorption
Desorption
Adsorption
0.05-0.60
0.1 o-0.70
0.05-0.80
0.1 O-0.80
0.05-0.80
5
5
25
25
45
5.2
5.4
4.1
4.2
3.0
0.8501
1.110
1.022
1.036
1.025
1.292
1.542
1.424
1.404
1.302
Salsify
Trout,
cooked
Trout,
raw
Winter
savory
Yoghurt
a Reference:
Wolf
et al. (1973)
1.864
WATER SORPTION
Table 2-Constants
n and k in Henderson’s
equation
Temp
OC
Adsorption
Desorption
Adsorption
Desorption
Adsorption
Desorption
0.1 O-0.80
0. I o-0.80
0.05-0.80
0. IO-O.80
0.05-0.70
o.Io-0.80
5
5
25
25
45
45
1.566
1.597
1.739
1.414
1.445
0.02013
0.00756
0.02051
0.01286
0.03865
0.02809
Apple
Desorption
0.05-0.70
19.5
7.178
0.03372
Avocado
freeze-dried
Adsorption
Desorption
Adsorption
Adsorption
0.05-0.80
0.10-0.80
0.05-0.80
0.05-6.70
5
5
45
60
1.492
1.692
I.183
1.288
0.03659
0.02051
0.087I 3
0.18741
a
a
freeze-dried
Adsorption
Adsorption
0.05-0.80
0.05-0.60
25
45
0.9440
1.352
0.06416
0.04848
c
freeze-dried
Adsorption
0.05-0.80
25
1.586
0.01498
d
freeze-dried
Adsorption
0.10-0.85
room
1.349
0.02612
Ref
Anise
Banana
Bean
Beef, raw
Cabbage
Specs
n
7.891
k
0.05-0.60
37
I .058
0.05720
Desorption
Adsorption
Adsorption
Desorption
Adsorption
0.20-0.80
0.10-0.80
0.05-0.80
0.10-0.80
0.05-0.70
5
25
45
45
60
2.446
2.062
1.718
1.610
2.224
0.00105
0.00487
0.01464
0.01824
0.00837
Carrots
Desorption
0.05-0.70
19.5
1.314
0.02497
Celery
freeze-dried
Adsorption
Adsorption
Adsorption
Desorption
Adsorption
0.10-0.70
0.10-0.70
0.05-0.80
0.10-0.80
0.05-0.80
5
25
45
45
60
1.335
1.244
1.116
0.9795
I.148
0.02239
0.03014
0.05345
0.07452
0.05494
Cellulose,
microcryst.
Chamomile
Cheese,
Edam
Cheese,
Emmental
Chicken,
cooked
Chicken
cooked
Product
added 7% oil
Desorption
0.1 O-0.80
37
I .a95
0.01531
a
a
a
a
a
a
a
Adsorption
Desorption
Adsorption
Desorption
Adsorption
Desorption
Adsorption
0.10-0.80
0.1 O-0.80
0.10-0.80
0.10-0.80
0.05-0.80
0.1 O-0.80
0.05-0.70
5
5
25
25
45
45
60
1.574
1.952
1.574
1.861
1.301
1.237
1.647
0.01314
0.00375
0.01314
0.00527
0.03614
0.04026
0.03325
a
a
freeze-dried
Adsorption
Desorption
0.05-0.80
0.10-0.80
25
25
1.294
1 ,438
0.05235
0.03211
a
a
a
freeze-dried
Adsorption
Desorption
Adsorption
0.05-0.80
0.10-0.80
0.05-0.80
25
25
45
b
Desorption
0.10-0.80
19.5
a
a
a
a
a
freeze-dried
Desorption
Adsorption
Desorption
Adsorption
Desorption
0.20-0.70
0.10-0.70
0.1 O-0.80
0.05-0.80
0.10-0.80
5
45
45
60
60
.413
.679
.054
0.04427
0.02079
0.15761
1 .972
0.00394
2.291
1.491
1.985
1.473
1.522
0.00165
0.02731
0.00694
0.03707
0.02949
Temp
J&f
32
Specs
a
a
a
a
a
a
freeze-dried
Adsorption
Desorption
Adsorption
Desorption
Adsorption
Desorption
0.10-0.60
0.10-0.70
0.19-0.70
0.1 O-0.80
0.05-0.80
0.10-0.80
5
5
45
45
60
60
I .288
1.863
1.322
1.406
I .361
1.220
0.02280
0.00397
0.03337
0.02304
0.03590
0.04924
a
a
freeze-dried
Adsorption
Adsorption
0.05-0.80
0.05-0.79
25
60
1.410
I ,228
0.01531
0.12413
Cinnamon
a
a
a
a
Adsorption
Desorption
Adsorption
Desorption
0.10-0.70
0.20-0.70
0.10-0.70
0.20-0.70
25
25
45
45
2.176
2.234
1.745
1.778
0.00371
0.00277
0.01712
0.01275
Cloves
a
a
a
a
a
Adsorption
Desorption
Adsorption
Adsorption
Adsorption
0.10-0.80
0.10-0.70
0.05-0.80
0.05-0.80
0.05-9.70
5
5
25
45
60
2.494
2.692
2.165
1.726
I.951
0.00270
0.00123
0.00712
0.02278
0.06471
Cod, raw
9
Adsorption
0.10-0.75
30
1.493
0.01265
Coriander
a
a
a
Desorption
Desorption
Desorption
0.20-0.80
0.20-0.80
0.10-0.80
5
25
45
2.631
2.381
1.614
0.00120
0.00264
0.02412
Corn
h
h
h
h
h
h
Desorption
Desorption
Desorption
Desorption
Desorption
Desorption
0.10-0.80
0.1 O-0.90
0.10-0.90
0.20-0.80
0.20-0.80
0.20-0.80
4.5
15.5
30
38
50
60
2.449
2.233
2.240
2.137
I .a78
2.000
0.00104
0.00219
0.00288
0.00455
i
Adsorption
0.20-0.80
25
1.611
0.01526
a
freeze-dried
Adsorption
0.10-0.60
45
1.455
0.03320
b
Desorption
0.10-0.80
19.5
1.753
0.01805
a
a
a
freeze-dried
Adsorption
Adsorption
Adsorption
0.10-0.70
0.10-0.70
0.05-0.70
25
45
60
I .321
0.9027
0.9640
0.02099
0.10435
0.19431
a
a
a
a
a
a
Adsorption
Desorption
Adsorption
Desorption
Adsorption
Desorption
0.05-0.70
0.10-0.80
0.05-0.70
0.10-0.80
0.05-0.70
0.10-0.80
5
5
25
25
45
45
1.310
1.896
1.310
1.497
1.239
1.108
0.06940
0.01238
0.06940
0.03696
0.09015
0.10587
j
i
i
Adsorption
Adsorption
Adsorption
0.10-0.80
0.10-0.80
0.10-0.80
25
35
42
2.334
2.260
2.079
0.00367
0.00507
0.00829
Gelatin
k
Adsorption
0.20-0.90
25
I .587
0.00799
Ginger
a
a
a
a
a
a
Adsorption
Desorption
Adsorption
Desorption
Adsorption
Desorption
0.10-0.70
0.20-0.70
0.10-0.70
0.1 O-0.80
0.10-0.70
0. IO-O.80
5
5
25
25
45
45
2.231
2.636
2.237
2.472
1.762
1.680
0.00252
0.00063
0.00286
0.00136
0.01604
0.01596
a
a
freeze-dried
Desorption
Adsorption
0.10-0.70
0.05-0.70
5
60
1.224
I ,008
0.02316
0.14190
Chicken,
raw
Egg albumin,
heat coag.
Egg. paste
Egg, whole
f
Range of
Ref
Chives
freeze-dried
Absorption
Cardamom
OF FOODS-987
Table 2 (continued)
A,
Range of
Product
BEHAVIOR
Egg-plant
Fennel
Fish protein cont.
Grapefruit
Table 2 (continued)
”
k
0.00998
0.00960
988-JOURNAL
OF FOOD SCIENCE-Volume
41 (1976)
Table 2 (continued)
Range of
Product
Ref
Specs
A,
Table 2 (continued)
Temp
“C
Range of
n
k
Green pea
b
Desorption
0.05-0.80
19.5
1.824
0.00708
Hibiscus
a
a
Adsorption
Desorption
0.05-0.70
0.10-0.70
25
25
0.945
1 .015
0.10777
o.oaoI 5
Laurel
a
a
a
a
Adsorption
Adsorption
Desorption
Adsorption
0.05-0.70
0.05-0.80
0.10-0.80
0.05-0.70
25
45
45
60
I ,844
1.472
1.486
2.012
0.01298
0.03913
0.03240
0.03067
a
a
a
a
a
Adsorption
Desorption
Adsorption
Adsorption
Desorption
0.10-0.70
0.20-0.70
0.10-0.70
0.10-0.70
0.10-0.80
5
5
25
45
45
1.974
2.414
1.992
1.612
1.509
0.00412
0.00093
0.00452
0.01852
0.02215
I
I
freeze-dried
Adsorption
0.10-0.70
23
1.163
0.03829
m
Adsorption
freeze-dried
0.05-0.80
20
1.232
0.03056
Lentil
Maltose
Mushrooms,
A. bisporus
Mushrooms,
Boletus
Mushroom
Boletus
0.05-9.75
19.5
I .a72
0.00503
a
a
a
a
a
freeze-dried
Adsorption
Adsorption
Desorption
Adsorption
Adsorption
0.05-0.70
0.05-0.70
0.10-0.70
0.05-0.70
0.05-0.70
5
25
25
45
60
1.165
1.210
1.060
I .098
1.110
0.02798
0.02782
0.04115
0.05381
0.09561
a
a
a
a
a
freeze-dried
Adsorption
Desorption
Adsorption
Adsorption
Desorption
0.10-0.70
0.10-0.80
0.10-0.80
0.05-0.80
0.10-0.80
5
5
25
45
45
1.685
1.877
1.602
1.312
I.183
0.00790
0.00417
0.01042
0.03331
0.04396
Radish
Radish,
b
Desorption
0.10-0.80
19.5
2.271
0.00149
k
k
Adsorption
Adsorption
0.05-0.80
0.05-0.80
25
40
1.438
1.393
0.01127
0.01339
1.272
1.195
Salmon,
1.193
0.03544
0.03913
0.07847
5
5
25
25
45
45
60
2.689
3.031
2.355
2.417
1.626
I.819
1.679
0.00174
0.00056
0.00493
0.00390
0.03245
0.01922
0.04029
Orgeat
c
freeze-dried
Adsorption
0.10-0.80
25
1.642
freeze-dried
o
Adsorption
0.10-0.80
37
1.372
0.02693
a
a
a
freeze-dried
Adsorption
Desorption
Adsorption
0.05-0.80
0.10-0.80
0.05-0.80
45
45
60
1.639
1.551
1.392
0.01256
0.01395
0.02974
k
Adsorption
0.20-0.90
25
1.544
0.01490
Salsify
Serum albumin,
horse
p
Adsorption
0.035-0.84
21.1
2.768
0.00052
Soybean
Sorghum
n
Adsorption
0.10-0.80
30
1.175
0.09164
Spinach
q
Adsorption
0.05-0.75
37
1.484
0.01996
r
freeze-dried
Adsorption
0.20-0.80
47
0.8755
0.07732
a
Adsorption
0.10-0.80
5
0.00344
marjoram
a
a
a
Desorption
Adsorption
Desorption
0.10-0.80
0.05-0.80
0.10-0.80
5
25
25
2.145
2.681
1 .%I 6
1.777
0.00057
0.01069
0.01019
Sweet
marjoram
a
a
a
Adsorption
Desorption
Adsorption
0.05-0.80
0.10-0.80
0.05-0.70
45
45
60
1.420
1.261
1.606
0.04058
0.05667
0.06312
Sugar beet
s
s
s
Desorption
Desorption
Desorption
0.05-0.70
0.05-0.70
0.05-0.70
20
35
47
1.325
1.264
1.117
0.02404
0.03385
0.04782
Sugar beet root
Water insol
components
s
s
Adsorption
Adsorption
0.10-0.80
0.1 O-0.80
35
47
1.953
1.900
0.00503
0.00780
Thyme
a
a
a
a
a
a
a
Adsorption
Desorption
Adsorption
Desorption
Adsorption
Desorption
Adsorption
0.10-0.80
0.10-0.70
0.05-0.80
0.10-0.80
0.05-0.80
0.10-0.80
0.05-0.70
5
5
25
25
45
45
60
1.937
2.635
1.903
2.018
1.660
1.483
2.103
0.00708
0.00092
0.00919
0.00633
0.02046
0.03014
0.01351
a
a
a
a
freeze-dried
Adsorption
Desorption
Adsorption
Desorption
0.05-0.80
0.10-0.80
0.05-0.80
0.10-0.70
45
45
60
60
1.540
1.794
1.563
1.929
0.02419
0.01156
0.02812
0.01352
0.02117
a
Adsorption
0.65-0.70
5
2.144
0.03348
Desorption
Adsorption
Adsorption
Desorption
0.10-0.80
0.05-0.80
0.05-0.80
0.10-0.80
5
25
60
60
2.591
2.001
1.350
1.536
0.01356
0.05250
0.21802
0.14849
c
freeze-dried
Adsorption
0.05-0.80
25
1.600
0.01497
a
Desorption
0.20-0.70
25
0.8685
0.06416
a
a
freeze-dried
Adsorption
Desorption
0.10-0.60
0.1 O-0.60
25
25
1 .OOl
1.001
0.04600
0.04600
a
a
a
a
a
a
a
Adsorption
Desorption
Adsorption
Adsorption
Desorption
Adsorption
Desorption
0.05-0.70
0.10-0.80
0.05-0.70
0.05-0.80
0.10-0.80
0.05-0.80
0.10-0.80
5
5
25
45
45
60
60
1.814
2.205
I.814
1.416
2.045
1.229
1.270
0.06826
0.03082
0.06826
0.14983
0.04959
0.31318
0.26001
a
a
a
a
a
a
a
Adsorption
Desorption
Adsorption
Desorption
Adsorption
Desorption
Adsorption
0.10-0.80
0.10-0.80
0.1 O-0.80
0.1 O-0.80
0.10-0.80
0.10-0.80
0.05-0.70
5
5
25
25
45
45
60
i .a92
2.665
i .a92
2.455
1.447
1.625
1.846
0.00621
0.00058
0.00621
0.00120
0.02744
0.01723
0.02534
Pear
raw
Sucrose
a
a
a
a
Pea
hot
Rice, cooked
25
25
60
0.10-0.70
0.10-0.70
0.05-0.80
0.10-0.80
0.10-0.70
0.10-0.80
0.05-0.80
Peppermint
Desorption
0.05-0.70
0.10-0.70
0.05-0.70
Adsorption
Desorption
Adsorption
Desorption
Adsorption
Desorption
Adsorption
Pekanut
b
Adsorption
Desorption
Adsorption
a
a
a
a
a
a
a
Pear
Pork, raw
a
a
a
Nutmeg
k
0.00289
0.02667
0.04725
0.03544
0.02472
0.02668
0.02622
”
2.075
1.413
1.203
1.272
1.337
1.341
I .282
“C
19.5
25
30
5
5
25
25
Temp
0.10-0.80
0.10-0.70
0.20-0.75
0.05-0.70
0.10-0.70
0.05-0.70
0.1 O-0.80
A,
Desorption
Adsorption
Adsorption
Adsorption
Desorption
Adsorption
Desorption
Specs
b
m
n
a
a
a
a
Ref
Potato
Salmin
Mushrooms
Pfifferling
Paranut
Product
Sweet
Trout,
cooked
Table 2 (continued)
-
iVATER
SORPTION
Table 2 (continued)
Trout,
Ref
raw
Specs
A,
Range of
“C
k
n
a
a
a
a
a
freeze-dried
Desorption
Adsorption
Desorption
Adsorption
Desorption
0.10-0.70
0.05-0.80
0.10-0.70
0.05-0.80
0.1 O-0.80
5
45
45
60
60
1.961
1.338
1.940
1.250
1.127
0.00310
0.03202
0.00330
0.04743
0.06239
Walnut kernels
shelled
t
Adsorption
0.10-0.90
22.5
2.583
0.02200
Wheat
u
Desorption
0.13-0.88
50
1.781
0.00957
Wheat, flour
v
v
v
v
Adsorption
Adsorption
Adsorption
Adsorption
0.12-0.89
0.13-0.90
0.13-0.90
0.15-0.90
20.2
30.1
40.8
50.2
2.201
2.069
1.965
1.780
0.00241
0.00383
0.00547
0.00993
a
a
a
a
Adsorption
Desorption
Adsorption
Desorption
0.10-0.70
0.20-0.80
0.1 O-0.80
0.10-0.80
5
5
25
25
2.452
3.231
2.183
2.662
0.00129
0.00010
0.00285
0.00069
Winter
savory
Table 3-Comparison
applied to foods and food
of Halsey’s
components
and
Henderson’s
equations
Halsey
%(Error)avg
Henderson
%(Errorlavg
Adsorption
Desorption
Adsorption
Desorption
Adsorption
Desorption
5
5
25
25
45
45
3.0
2.5
4.4
1.7
4.6
4.0
7.6
8.7
11.0
10.2
9.3
7.9
Apple
Desorption
19.5
5.5
22.7
Avocado
Adsorption
Desorption
Adsorption
Adsorption
25
25
45
60
4.8
4.3
9.8
8.2
11.9
13.4
1 1.4
22.3
Adsorption
Adsorption
25
45
6.5
9.2
Bean
Adsorption
25
Beef, raw
Adsorption
room
Cabbage
Adsorption
37
2.5
9.7
Cardamon
Desorption
Adsorption
Adsorption
Desorption
Adsorption
5
25
45
45
60
4.2
2.0
5.5
4.5
5.9
0.53
6.1
9.0
8.6
6.1
Carrot
Desorption
19.5
4.3
18.5
Celery
Adsorption
Adsorption
Adsorption
Desorption
Adsorption
5
25
45
45
60
4.7
6.5
2.6
2.9
7.4
5.3
5.0
22.4
17.3
25.1
Desorption
37
5.0
6.1
Anise
Banana
Cellulose,
microcrys.
Specs
Product
Ref
specs
e
f
g
h
i
j
k
Mizrahi
Labuza
”
k
Adsorption
Desorption
Adsorption
0.10-0.80
0.10-0.80
0.05-0.70.
45
45
60
1.571
1.571
2.031
0.02598
0.02598
0.02185
a
a
a
a
a
freeze-dried
Adsorption
Desorption
Adsorption
Desorption
Adsorption
0.05-0.60
0.10-0.70
0.05-0.80
0.10-0.80
0.05-0.80
5
5
25
25
45
1.318
1.395
1.293
1.166
1.283
0.02990
0.02149
0.03656
0.04930
0.06157
Wolf
et al. (1973)
Taylor
(1961)
Lafuente
and Pihaga
d MacKenzie
Temp
OC
a
a
a
Yoghurt
a
b
c
A,
and Luvet
(1966)
(1967)
et al. (1970)
and Rutman
(1968)
Jason (1958)
men and Clayton (1971)
Benson
and Richardson
(1955)
Rasekh et al. (19711
BUII (1944)
1 Flink
and Karal
(1972)
m lglesias
(1973)
n Saravacos
(1967)
0 Martinez
and Labuza
(I 968)
p Fenton
(1941)
9 Makower
and Dahority
(1943)
r lglesias
et al. (I 975c)
S lglesias
et al. II 975b3
t Rockland (1957)
u Becker and Sallans (I 956)
”
Bushuk
and
Winkler
(1967)
as
Table 3 (conthued)
Temp
‘C
Product
OF FOODS-989
Table 2 (continued)
Range of Temp
Product
BEHAVIOR
Specs
Temp
‘C
Halsey
%(Error)avg
Henderson
%(Error)avg
Adsorption
Desorption
Adsorption
Desorption
Adsorption
Desorption
Adsorption
5
5
25
25
45
45
60
2.3
2.6
2.3
1.7
2.8
1.7
2.8
8.2
5.9
8.2
8.3
18.4
14.0
Il.8
Cheese, Edam
Adsorption
Desorption
25
25
6.0
4.3
14.5
14.8
Cheese, Emmental
22.8
15.3
Adsorption
Desorption
Adsorption
25
25
45
5.9
3.0
16.8
11.4
12.1
8.9
Chicken,
cooked
Desorption
19.5
3.3
6.1
1.8
12.0
Chicken,
cooked
2.7
11 .o
Desorption
Adsorption
Desorption
Adsorption
Desorption
5
45
45
60
60
2.8
5.8
1 .l
5.6
4.1
0.28
3.1
7.7
13.6
12.8
Chicken,
raw
Adsorption
Desorption
Adsorption
Desorption
Adsorption
Desorption
5
5
45
45
60
60
5.4
3.3
4.5
2.0
4.4
3.8
3.1
3.9
5.2
9.7
16.6
4.8
Chives
Adsorption
Adsorption
25
60
2.3
8.6
15.3
21.4
Cinnamon
Adsorption
Desorption
25
25
3.9
3.5
2.1
0.36
Cinnamon
Adsorption
Desorption
45
45
5.9
3.9
1.7
0.28
Product
Chamomile
-
99%JOURNAL
OF FOOD SCIENCE-Volume
41 (1976)
Table 3 (continued)
Product
Specs
Temp
“C
Table 3 (continued)
Halsey
%(Error)avg
Henderson
%(Error)avg
Product
Specs
Temp
“C
Halsey
%(Error)avg
Henderson
%(Error)avg
Cloves
Adsorption
Desorption
Adsorption
Adsorption
Adsorption
5
5
25
45
60
3.2
2.7
4.1
4.3
4.9
4.1
3.4
7.3
10.1
11.7
Mushrooms,
Boletus
Adsorption
Desorption
Adsorption
Desorption
Adsorption
5
5
25
25
60
3.8
3.2
3.8
3.4
5.5
14.5
7.4
14.5
7.4
11.4
Cod, raw
Adsorption
30
5.1
6.0
Coriander
Desorption
Desorption
Desorption
5
25
45
5.0
2.6
5.0
1.3
1.9
5.0
Mushrooms,
Pfifferling
Adsorption
Desorption
25
25
2.1
3.3
12.3
13.7
Nutmeg
Desorption
Desorption
Desorption
Desorption
Desorption
Desorption
4.5
15.5
30
38
50
60
3.1
3.7
3.9
4.9
6.1
5.5
2.5
3.2
3.9
2.5
2.0
1.5
Adsorption
Desorption
Adsorption
Desorption
Adsorption
Desorption
Adsorption
5
5
25
25
45
45
60
4.2
5.1
5.9
3.4
5.6
4.3
6.7
0.52
1.3
4.2
3.4
2.2
4.9
1 1 .o
Orgeat
Adsorption
25
6.2
5.4
Paranut
Adsorption
Desorption
Adsorption
Adsorption
Desorption
5
5
25
60
60
5.9
3.5
4.3
8.9
6.6
3.5
6.7
7.9
21.7
15.9
Adsorption
25
3.5
23.1
Pear
Desorption
25
4.7
4.3
Pear
Adsorption
Desorption
25
25
6.2
6.2
5.4
5.4
Pekanut
Adsorption
Desorption
Adsorption
Adsorption
Desorption
Adsorption
Desorption
5
5
25
45
45
60
60
6.9
3.0
6.9
12.3
2.2
8.9
6.9
4.2
6.0
4.2
5.2
7.9
12.0
16.3
Adsorption
Desorption
Adsorption
Desorption
Adsorption
Desorption
Adsorption
5
5
25
25
4.0
2.9
4.0
1.4
4.5
2.9
4.5
6.5
45
45
60
3.1
2.2
6.4
8.6
11.3
5.9
Desorption
Adsorption
Adsorption
19.5
25
30
4.4
3.7
4.2
5.3
6.0
3.7
Egg albumin
heat coag.
Adsorption
25
6.5
2.9
b-8. paste
Adsorption
45
7.5
0.34
Egg, whole
Desorption
19.5
5.8
3.6
Egg plant
Adsorption
Adsorption
Adsorption
25
45
60
2.7
10.9
6.6
6.7
7.5
14.7
Fennel
Adsorption
Desorption
Adsorption
Desorption
Adsorption
Desorption
5
5
25
25
45
45
7.1
4.7
7.1
4.6
8.5
7.3
8.4
4.5
8.4
6.7
8.3
8.8
Fish protein
cone
Adsorption
25
4.3
4.1
Fish protein
cone
Adsorption
Adsorption
35
42
5.0
7.1
3.7
3.5
Gelatin
Adsorption
25
5.1
6.6
Ginger
Adsorption
Desorption
Adsorption
Desorption
Adsorption
Desorption
5
5
25
25
45
45
5.1
3.5
4.7
3.4
5.1
2.8
1.0
1.1
2.0
3.4
2.3
6.6
Grapefruit
Desorption
Adsorption
5
60
5.2
5.9
14.8
18.9
Pork, raw
Desorption
19.5
3.9
7.5
Green pea
Desorption
19.5
1.8
18.4
Radish
Hibiscus
Adsorption
Desorption
25
25
7.5
3.3
23.8
15.8
Laurel
Adsorption
Adsorption
Desorption
Adsorption
25
45
45
60
5.3
3.4
5.5
5.3
5.2
12.7
8.0
10.0
Adsorption
Adsorption
Desorption
Adsorption
Adsorption
5
25
25
45
60
6.1
1.4
1.3
3.2
7.2
14.3
16.2
12.2
19.8
22.5
Adsorption
Desorption
Adsorption
Adsorption
Desorption
5
5
25
45
45
4.8
3.3
3.9
3.7
4.6
Adsorption
Desorption
Adsorption
Adsorption
Desorption
5
5
25
45
45
3.7
2.1
3.1
4.8
2.5
4.3
9.4
7.0
14.2
13.5
Adsorption
23
2.5
Adsorption
20
5.8 ’
Lentil
Maltose
Mushrooms
A. bisporus
1.9
0.47
2.4
4.3
6.6
Peppermint
Potato
Radish,
hot
Rice, cooked
Desorption
19.5
5.2
2.5
Salmin
Adsorption
Adsorption
25
40
5.8
6.8
19.2
20.1
Adsorption
37
6.4
8.0
8.6
22.2
Salmon,
raw
\
I
I
I
-
WATER
Table 3 (continued)
Product
Specs
Temp
“C
Halsey
%(Error)avg
Henderson
%(Error)a,g
Salsify
Adsorption
Desorption
Adsorption
45
45
60
3.3
0.52
3.6
11.1
10.2
14.0
Serum albumin,
horse
Adsorption
25
5.8
10.6
Sorghum
Adsorption
21.1
5.3
6.7
Soybean
Adsorption
30
5.6
10.3
Spinach
Adsorption
37.
4.0
16.5
Sucrose
Adsorption
47
5.8
4.9
Sweet marjoram
Adsorption
Desorption
Adsorption
Desorption
5
5
25
25
2.6
1 .J
3.2
1.5
5.7
5.7
9.8
Adsorption
Desorption
Adsorption
45
45
60
3.6
3.6
5.3
1 4.2
1 1.3
Sugar beet root
Desorption
Desorption
Desorption
20
35
3.9
5.8
8.8
1 1.9
1 3.0
Sugar beet root,
water insol
fraction
Adsorption
Adsorption
47
7.2
7.7
Thyme
Adsorption
Desorption
Adsorption
Desorption
Adsorption
Desorption
Adsorption
5
5
25
25
45
45
60
3.4
2.5
3.9
1.3
1 .J
1 .o
4.0
10.9
11.1
Adsorption
Desorption
Adsorption
Desorption
45
45
60
60
6.4
2.6
4.1
3.8
11.1
16.2
8.3
Desorption
Adsorption
Desorption
Adsorption
Desorption
5
45
45
60
60
4.4
5.5
4.5
4.6
3.2
2.4
13.1
2.6
18.2
16.2
Adsorption
22.5
2.3
9.1
Sweet marjoram
Trout,
Trout,
cooked
raw
Walnut kernels,
’ shelled
47
35
8.9
7.5
14.7
1.9
0.95
5.3
2.9
8.6
9.0
13.7
9.4
Wheat
Desorption
50
5.0
3.7
Wheat, flour
Adsorption
Adsorption
Adsorption
Adsorption
20.2
30.1
40.8
50.2
1.6
2.5
3.1
3.3
8.8
14.6
8.1
Winter
Adsorption
Desorption
Adsorption
Desorption
5
5
25
25
2.6
1 .J
2.4
3.7
0.87
Adsorption
Adsorption
45
60
7.5
7.7
10.4
Adsorption
Desorption
Adsorption
Desorption
Adsorption
5
5
25
25
45
4.6
4.2
3.5
1 .9
5.3
7.9
Yoghurt
savory
7.9
1.4
6.1
6.3
7.9
8.5
16.1
13.4
13.3
SORPTION
BEHAVIOR
OF FOODS-991
foods examined. The food materials tested in the present
work, as well as those reported earlier (Iglesias et al., 1975a, b,
c), have water sorption characteristics which are representative
of almost all types of foods and food components, i.e., vegetables, meats, fruits, oilseeds, spices, cereals, milk products,
sugars, proteins and other food polymers. Isotherms analyzed
amounted to 220 comprising 69 different materials. It was
found that in most cases the proposed Halsey’s equation has a
better fit than Henderson’s,
After analyzing so much data one would like to draw conclusions about the physicochemical mechanism responsible for
the depression of water activity in food materials. The observed agreement between experimental data and Eq (2) would
suggest the validity of the physical adsorption model proposed
by Halsey (1948) previously mentioned. However, the situation is not so simple because the moisture sorption isotherms
of foods represent the integrated hygroscopic properties of
numerous constituents, and the depression of water activity is
due to a combination of factors each of which may be predominant in a given range of water activity in a given food
(Karel, 1973). Furthermore,
the water sorption process in
foods is a complex one. As a polymer sorbs water it undergoes
changes of constitution, dimensions and other properties (Mac
Laren and Rowen, 1951). Water sorption also leads to phase
transformations
of the sugars contained in the food (Karel,
1973). For these reasons it is difficult to draw conclusions
about the intimate nature of the binding processes involved in
the process of water sorption in foods. Consequently, we may
conclude that the main value of Halsey’s equation consists in
that it is a good mathematical description of the various degrees of binding of water which occur over the range of water
activities at which the equation applies. It is interesting to note
that Halsey’s equation with r = 2 has the same form as the
Harkins-Jura isotherm (Labuza, 1968),
In p/p0 = B - A/X=
where, B, A = constants. The limited usage of the Harkins-Jura
equation in the food area (Labuza, 1968) is easily explained
by inspecting the r values showed in this work and a previous
one (Iglesias et al., 1975a); it is seen that the r = 2 only
characterizes the sorption behavior of few products.
REFERENCES
Agrawal,
K.K., Clan,
B.L. and Nelson, G.L. 1969. Investigation
into
the theories of desorption
isotherms
for rough rice and peanuts. 1.
ASAE paper No. 69-890.
Becker. H.A. and Sallans, H.R. 1956. A study of the desorption
isctherms of wheat at 25OC and 5O’C. Cereal Chem. 33: 79.
Benson. S.W. and Richardson,
R.L. 1955. A study of hysteresis in the
sorotion
of solar eases bv native and denatured
oroteins.
J. Am.
Chem. Sot. f7: 2585.
Bull, H.B. 1944. Adsorption
of water vapour by proteins. J. Am. Chem.
sm. 66: 14.
Bushuk. W. and Winkler, C.A. 1957. Sorption of water vapour on wheat
flour. starch and eluten Cereal Chem. 34: 73.
Chen, C.‘S. and Clayton,
J.T. 1971. The effect of temperature
on sorption isotherms
of biological materials. Trans. ASAE 14: 927.
Fenton, F.C. 1941. Storage of grain sorghums. Agric. Engng. 22: 185.
Fish, B.P. 1958. Diffusion
and thermodynamics
of water in potato
starch geI. In “Fundamental
Aspects of the Dehydration
of Foodstuffs”
Sot. Chem. Ind. 143.
FIink, J.M. and Karel, M. 1972. Mechanisms
of retention
of organic
volatiles in freeze-dried
systems. J. Food Technol. 7: 199.
Halsey, G. 1948. Physical adsorption
on nonuniform
surfaces. J. Chem.
Physics 16: 931.
Henderson.
S.M. 1952. A basic concept of eauilibrium
moisture. Agric.
Engng 33: 20.
Iglesias, H.A. 1973. Thesis. Facultad de Ciencias Exactas y Natwales,
Universidad
de Buenos Aires. Argentina.
Iglesias, H.A., Chirife, J. and Lombardi,
J.L. 1975a. An equation for
correlating
equilibrium
moisture content in foods. J. Food Tecbnol.
10: 289.
Iglesias, H.A.. Chirife,
J. and Lombardi,
J.L. 1975b. Water sorption
isotherms in sugar beet root. J. Food Technol. 10: 299.
Iglesias, H.A.. Ch%fe.
J. and Lombardi.
J.L. 1975c. Comparison
of
water vapour sorption
by sugar beet root components.
J. Food
Technol. 10: 385.
992-JOURNAL
OF FOOD .SCIENCE-Volume
41 (1976)
Iglesias, H.A. and Chirife. J. 1976. On the local isotherm concept and
modes of moisture binding in food products.
J. Agric. Food Chem.
24: 77.
Jason, A.C. 1958. A study of evaporation
and diffusion processes in the
drying of fish muscle. In “Fundamental
Aspects of the Dehydration
of Foodstuffs.”
Sot. Chem. Ind. 103.
Karel. M., Mizrahi, S. and Labuza, T.P. 1971. Computer
prediction
of
food storage. Modem Pkg. 44: 54.
Karel, M. 1973. Recent research and development
in the field ofblow
moisture and intermediate
moisture foods. CRC Critical Reviews in
Food Technol. Feb.: 329.
King, C.J. 1968. Rates of moisture
adsorption
and desorption
in
porous, dried foodstuffs.
Food Technol. 22: 509.
Labuza, T.P. 1968. Sorption
phenomena
in foods. Food Technol.
22:
15.
Labuza, T.P. and Rutman, M. 1968. The effect of surface active agents
on sorption
isotherms
of a model food system. Can. J. Chem.
Engng. 46: 364.
Labuza, T.P., Mizrahi, M. and Karel, M. 1972. Mathematical
models for
optimization
of flexible
film packaging of foods for storage. Trans.
ASAE, p. 150.
Lafuente,
B. and Pitiaga.
F. 1966.
Humedades
de equilibria
de
productos
liofilizados.
Rev. de Agroq. y. Tecnol. de Alimentos
6:
113.
MacKenzie.
A.P. and Luyet. B.J. 1967. Water sorption
isotherms from
freeze-dried
muscle fibers. Cryobiology
3: 341.
Makower,
B. and Dahority,
G.L. 1943. Equilibrium
moisture content of
dehydrated
vegetables. Ind. Eng. Chem. 35: 193.
Martinez.
F. and Labuza, T.P. 1968. Rate of deterioration
of freezedried salmon as a function
of relative humidity.
J. Food Sci. 33:
241.
Mizrahi,
S., Labuza, T.P. and Karel, M. 1970. Computer-aided
predic
tions of extent of browning
in dehydrated
cabbage. J. Food Sci. 35:
799.
Nellist, M.P. and Hughes, M. 1973. Physical and biological processes in
the drying of seeds. Seed Sci. and Technol. 1: 613.
Piriaga, F. anh Lafuente.
B. 1965. Horchata en polvo. 1. Humedades de
eauilibrio
de la horchata
liofilizada
Rev. de Agroa.
_. v Tecnol. de
Aiim. 5: 99.
Rasekh, J.G., Stillings. B.R. and Dubrow,
D.L. 1971. Moisture adsorp
tion of fish orotein
concentrate
at various relative humidities
and
temperatures
J. Food Sci. 36: 705.
Rockland,
L.B. 1957. A new treatment
of hygroscopic
equilibria.
Food
Res. 22: 604.
Salwin, H. and Slawson, V. 1959. Moisture transfer in combinations
of
dehydrated
foods. Food Technol. 13: 715.
Saravacos, G.D. and Sticnhfield,
R.M. 1965. Effect of temperature
and
pressure
on the sorption
of water vapour by freeze-dried
food
materials. J. Food Sci. 30: 779.
Saravacos, G.D. 1967. Effect of the drying method on the water sorption of dehydrated
apple
and potato. J. Food Sci. 32: 81.
Saravacos, G.D. 1969. s&ption
and diffusion
of water in dry soybeans.
Food Technol. 23: 145.
Singh. R.S. and Ojha T.P. 1974. Equilibrium
moisture
content
of
groundnut
and chillies. J. Sci. Fd. Agric. 25: 451.
Taylor. A.A. 1961. Determination
of moisture equilibria in dehydrated
foods. Food Technol. 15: 536.
Wolf, W., Spiess. W.E.L. and Jung. G. 1973. Die Wasserdampfsorptionsisothermen
einiger, in der Liter&w
bislang wenig beticksichtigter
LebensmitteL
Lebensm. -Wiss. u. Technol. 6: 94.
Msreceived
8/8/75;revised
3/19/76;accepted
3121176.
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