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. 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