Trends in Food Science & Technology 29 (2013) 135e141

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Estimating the

needed amount of

desiccant, water or

moistener to adjust

the equilibrium water

activity of dry

powder mixtures

Nancy Redman-Fureya, Mark D.

Normandb and Micha Pelegb,*aThe Procter & Gamble Company, Mason Business

Center, 8700 Mason Montgomery Road, Mason, OH

45040-9760, USAbDepartment of Food Science, Chenoweth Laboratory,University of Massachusetts, Amherst, MA 01003, USA

(Tel.: D1 (413) 545 5852; fax: D1 (413) 545 1262;

e-mail: micha.peleg@foodsci.umass.edu)

Prior to their mixing, further processing or packaging, indus-

trial pharmaceutical and food powder formulations, or their

individual components, are sometimes equilibrated under

controlled humidity conditions in order to reach a water activ-

ity level deemed desirable and safe. Occasionally, there is

a need to lower this water activity by adding a desiccant, or

raise it through free moisture adsorption or adding a moistener.

If the components do not interact chemically, the system is

closed, the moisture in the free space negligible and the tem-

perature practically constant, the amount of water gained or

lost by the mixture’s components is determined by a simple

moisture balance equation, which can be used to translate

the exchanged moisture into the mass of a given desiccant

or moistener needed. To find this mass, one needs to know

the mixture’s initial composition, the ingredients’ masses and

moisture contents (in order to calculate their dry mass), and

their moisture sorption isotherm equations. The latter can be

of any kind, including polynomial, and there is no limit on

the number of their coefficients. Knowledge of the desiccant’s

moisture content, if not zero, or moistener’s initial moisture

contents, or water activity, and its moisture sorption isotherm

equation is also needed. The calculation of the overall

amounts of water exchanged and corresponding amount of

desiccator or moistener needed has been automated and can

be performed with a Microsoft Excel� spreadsheet especially

written for the purpose and posted as freeware on the Internet.

IntroductionMaintaining proper water activity level in dry foods andpharmaceutical products is essential to their physical,chemical and microbial stability and to guarantee theirshelf life. Many food and pharmaceutical products aremulti-component mixtures in the form of loose relativelylarge particulates (notably breakfast cereals and snacks),loose or encapsulated powder (e.g., cake, beverage orsoup mixes, or controlled release drugs) and tablets (e.g.,soup cubes, and many prescription and over the counterpills). Since the mixture’s components need not be all atthe same water activity initially, moisture migration be-tween them is quite common. Where the dry mixture’scomponents do not interact chemically in a manner that af-fect their water sorption pattern, and the temperature re-mains practically constant, one can estimate theequilibrium water activity that the mixture will reach ina closed system (hermetically sealed package or container)by solving a mass balance equation numerically (Peleg &Normand, 1992). The calculation can be done with pro-grams written in Mathematica� and MS Excel� that areavailable as freeware on the Internet (http://people.umass.edu/aew2000/WaterAct/wateractivity.html). To find theequilibrium water activity of a given mixture, the user en-ters each ingredient’s mass, initial moisture contents andmoisture sorption isotherm equation. The program then cal-culates and displays the equilibrium water activity, and alsothe changes in the moisture contents of the individual ingre-dients, i.e., which gained or lost moisture and by howmuch. This program can be useful to manufacturers whomix the ingredients without adjusting their water activity,by revealing whether the mixture’s water activity at equili-bration will be at a safe or unsafe level. Since the

Moistening (aw initial < aw new)

Equilibration @ aw initial

A B C DIngredients:

Mixing

Mixture@ aw initial

Mixing

Mixture@ aw new

Moistener

Fig. 2. Schematic example of how a dry powder mixture’s water activ-ity can be raised through exposure to a humid atmosphere or admix-

ture of a moistener.

136 N. Redman-Furey et al. / Trends in Food Science & Technology 29 (2013) 135e141

calculation method is solely based on mass balance consid-erations, the program is unable to tell how fast the calcu-lated equilibrium water activity level will be approached.But since in practice the mixture’s components are usuallyfairly dry to start with, this is rarely if ever an issue.

Another type of calculation is needed when the ingredi-ents are mixed after their equilibration at a given water ac-tivity but the target water activity for the mixture isdifferent. This requires that the mixture will have to be fur-ther dried using a desiccant, for example, or wetted by al-lowing it to absorb moisture directly or through theadmixture of a ‘moistener’. Examples of such scenariosare shown schematically in Figs. 1 and 2. Notice that anyvery dry ingredient can serve as a ‘desiccant’ and anywet ingredient as a ‘moistener’. The question that arisesin such situations is how much desiccant should be addedin case the mixture’s target water activity is lower thanthat of the initial, or how much pure water ought to be ab-sorbed, or moistener added, if the target water activity ishigher than the initial.

The objective of this work was to write the mass balanceequations for such scenarios and use them to develop soft-ware for doing the calculations routinely in an industrialenvironment.

Principle and methodConsider a list of ingredients A, B, C,. N, having a dry

mass, wA, wB, wC, .wN, all having the same initial wateractivity, aWInitial. Their moisture sorption isotherms are allknown and expressed algebraically in the form of m(aW)vs. aW, i.e., mA(aW), mB(aW), mC(aW),., or mN(aW) vs.

Desiccation ( aw initial

> aw new )

Equilibration @ aw initial

A B C DIngredients:

Mixing

Mixture@ aw initial

Mixing or addition

Mixture@ aw new

Desiccant

Fig. 1. Schematic example of how a dry powder mixture’s water activ-ity can be lowered through admixture of a dry desiccant.

aW, where each of the m(aW)’s is the ingredient’s moisturecontent on a dry basis at a given water activity aW, ex-pressed as grams of water per gram or per 100 grams ofdry matter.

The mixture’s total initial moisture contents in grams,MInitial, is:

MInitial ¼ wAmAðaWInitialÞ þwBmBðaWInitialÞ þ wCmCðaWInitialÞþ.þwNmNðaWInitialÞ ð1Þ

At the target or ‘new’ water activity, aWNew, the moisturecontents in grams, MNew, will be:

MNew ¼ wAmAðaWNewÞ þwBmBðaWNewÞ þwCmCðaWNewÞþ.þwNmNðaWNewÞ ð2Þ

Thus if aWNew < aWInitial, the total amount of water to beremoved from the original ingredients is DM ¼ Minitial �Mnew. Or, if one wants to monitor the change in the individ-ual ingredients e see below:

DM ¼ wA½mAðaWInitialÞ �mAðaWNewÞ� þwB½mBðaWInitialÞ�mBðaWNewÞ� þwC½mCðaWInitialÞ �mCðaWNewÞ� þ.

þwN½mnðaWInitialÞ �mNðaWNewÞ� ð3ÞProvided that the system is closed, the conditions prac-

tically isothermal and the amount of moisture in the freespace between the particles negligible, this amount of mois-ture, DM, is to be absorbed by a desiccant, Des, as demon-strated schematically in Fig. 3. For the calculation of theamount of desiccant needed, its moisture sorption iso-therm’s equation mDes(aW) ought to be known and also itsinitial water activity, aWDesInitial, or moisture contents mDe-

s(aWDesInitial). But since the desiccant is usually added verydry, both aWDesInitial and the corresponding moisture

Fig. 3. Simulated (exaggerated) example of how a dry desiccant pres-ence lowers the water activity of a dry powder mixture. The moisturesorption isotherm of the desiccant is at the top and that of the original

mixture at the bottom.

Fig. 4. Simulated (exaggerated) example of how a wet moistener pres-ence raises the water activity of a dry powder mixture. The moisturesorption isotherm of the moistener is at the bottom and that of the orig-

inal mixture at the top.

137N. Redman-Furey et al. / Trends in Food Science & Technology 29 (2013) 135e141

contents mDes(aWDesInitial) are expected, but do not have tobe, practically zero.

Theoretically, when the new equilibrium water activity,aWnew, is reached, the desiccant has absorbed the moisturelost by the mixture’s components. Therefore

DM ¼ wDes½mDesðaWnewÞ �mDesðaWDesinitialÞ� ð4Þ

or

wDes ¼ DM

mDesðaWnewÞ �mDesðaWDesinitialÞ ð5Þ

where DM is the mass of water to be desorbed from themixture and absorbed by the desiccant in grams and wDes

the desiccant’s dry mass needed to reduce the mixture’s wa-ter activity to the wanted level aWNew, also in grams.

Where aWNew > aWInitial, the extra needed moisture canbe absorbed directly by the mixture through equilibration,or provided by the admixture of a wet ingredient servingas a moistener.

In this case, the total amount of water to be added to theoriginal mixture’s ingredients is:

DM ¼ wA½mAðaWNewÞ �mAðaWInitialÞ� þwB½mBðaWNewÞ�mBðaWInitialÞ� þwC½mCðaWNewÞ �mCðaWInitialÞ� þ.

þwN½mNðaWNewÞ �mNðaWInitialÞ� ð6ÞThis is the amount of water that will be absorbed di-

rectly by the mixture ingredients if left to equilibrate atthe new water activity aWNew.

An added moistener Moi can release this moisture pro-vided it has been introduced at a water activity higherthan the targeted, i.e., aWHMoiInitial > aWNew, as shown sche-matically in Fig. 4.

If the humidifying ingredient’s moisture sorption iso-therm equation mMoi (aW) is known, the amount of waterthat it will release to the mixture per gram dry weight

would be mMoi (aWHumInitial) � mMoi (aWNew). Hence, thetheoretical dry mass of the moistener needed to raise themixture’s water activity to the wanted aWNew will be:

wMoi ¼ DM

mMoiðaWMoiInitialÞ �mMoiðaWNewÞ ð7Þ

Notice that the initial mixture before desiccation ormoistening can be treated as a single component witha moisture sorption isotherm mMix(aw) given by:

mMixðawÞ ¼Pn

i¼1

wimiðawÞPn

i¼1

wi

ð8Þ

where the wi’s are the dry masses of the ingredients A,B, C, . N, here labeled i ¼ 1, 2, 3, . n, and the mi(aw)’sare their corresponding moisture sorption isotherm equa-tions. This can be seen in Figs. 3 and 4 where the mixtureis represented by a single moisture sorption isotherm e seebelow.

Eqs. (1)e(8) and the moisture sorption isotherm equa-tions are all formulated on a dry mass basis. In practice,the initial moisture contents of an ingredient is usuallyknown or determined on a wet basis, which can be usedto calculate the dry mass, w, be it of any particular ingredi-ent of the original mixture, wi, of the desiccant, wDes, or themoistening ingredient, wMoi, with the formula:

w¼Ww100�%Mwb

100ð9Þ

where Ww is the original “wet mass” and %Mwb the percentmoisture contents on a wet weight basis.

Once the dry mass of each component has been deter-mined, it can be combined with the corresponding moisturesorption isotherm equation and inserted into the formulas to

138 N. Redman-Furey et al. / Trends in Food Science & Technology 29 (2013) 135e141

calculate the values of wDes or wMoi. If and when needed,wDes and wMoi can be converted into the correspondingwet masses in the following manner. The moisture contentson a dry weight basis mdb can be calculated using the mois-ture sorption isotherm equation, i.e., mdb ¼ mdb(aW) whereaW can be the equilibration water activity of any ingredient,or the initial water activity of the moistener,aWMoiInitial, for example. The moisture on a dry weight ba-sis can be converted into the moisture contents in percenton a wet basis, %Mwb, with the formula:

%Mwb ¼ 100mdb

1þmdbð10Þ

Fig. 5. Partial view of the MS Excel� spreadsheet arranged to calculate the ammixture to a des

The corresponding wet mass, Ww, will then be:

Ww ¼ wð1þmdbÞ ð11ÞAll the calculations with the above mass balance equa-

tions are arithmetic, which makes them particularly amena-ble to programing and presentation in a spreadsheet format,such as in the widely used MS Excel�.

The programThe program to perform the calculations discussed in the

previous section has been posted on the Internet, in theform of a freely downloadable MS Excel� workbook,

ount of desiccant needed to lower the water activity of a dry powderired level.

139N. Redman-Furey et al. / Trends in Food Science & Technology 29 (2013) 135e141

see: http://people.umass.edu/aew2000/WaterAct/DesMoi.html. A screen display of part of the spreadsheet to calcu-late of the total water exchanged and the amount of desic-cant to be added is shown in Fig. 5 and to calculate theamount of moistener in Fig. 6. Except for the details, thedifference is that Fig. 5 shows a case where the chosen ‘Ini-tial water activity’ is higher than the ‘New water activity’while in Fig. 6 it is the other way around. The program en-ables the user to create a library of up to 15 ingredients,3 desiccants and 3 moisteners. Entering zero as the initialmass of an ingredient, desiccant or moistener will eliminateit from the calculation. The spreadsheet has instructionsthat appear as pop-up notes upon pointing the mouse at

Fig. 6. Partial view of the MS Excel� spreadsheet arranged to calculate the amixture to a des

cells having a red triangle in their upper right corner.They also explain how to use the program and how ingre-dients and their moisture sorption isotherm equations canbe added to or removed from the library, temporarily or per-manently. For the actual calculation, when the pertinent in-gredients’ cells are active, the user’s input, in both thedesiccation and moistening cases, is their initial masses,their initial moisture contents or water activity and the de-sired new water activity.

Based on the difference between the initial and new wa-ter activities, the program identifies the case, i.e., whethera desiccant or moistener is needed for the water activity ad-justment. The program then performs the calculations using

mount of moistener needed to raise the water activity of a dry powderired level.

Fig. 7. The fit of Eq. (12) to moisture sorption data generated with othermodel equations originally derived from experimental data. [Noticethat in the case of the desiccant, the second term might be superfluous

for the practical range of its application.]

140 N. Redman-Furey et al. / Trends in Food Science & Technology 29 (2013) 135e141

the mass balance equations listed and discussed in the pre-vious section, the moisture sorption isotherm equations ofup to three desiccants or moisteners, their initial water ac-tivity or moisture contents, and the new (target) water activ-ity of the mixture. There are no limitations on themathematical form of the moisture sorption isotherm equa-tions as long as they do not lead to a prohibited mathemat-ical operation such as division by zero, or an attempt tocalculate the logarithm of zero or a negative number. Themoisture sorption isotherm equations can be based on

Fig. 8. The screen display of the Wolfram Demonstration that calculates thea desired level, with added arrows to indica

models from the literature, such as the BET, GAB, Hender-son’s or Oswin’s (Iglesias & Chirife, 1982; Wolf, Spiess, &Jung, 1985), or ad hoc empirical. Notable among the latterare polynomial expressions of any degree, which are themost convenient for fitting laboratory sorption data (Peleg& Normand, 1992). A double power law equation can bea convenient alternative too (Peleg, 1993), see below. Thereis also no limit on the number of adjustable model param-eters. All that counts is that the chosen moisture sorptionisotherm equation faithfully describes the moisture sorptionpattern in the pertinent water activity range.

Although the settings shown in the Figs. 5 and 6 are pri-marily for pre-equilibrated mixtures, the program allowsone or several ingredients to be entered at a different initialwater activity from the rest.

The advantage of the presented program is not only thatit enables routine calculations in an industrial environmentbut also that it enables one to examine the theoretical con-sequences of hypothetical scenarios where the mixture’scomposition and/or the ingredients’ initial conditions arealtered. The program also allows comparing the perfor-mance of different desiccants or moisteners added at dif-ferent initial moisture contents or water activities andevaluate their quantitative implications. Although not in-tended for this purpose, the program also allows estimat-ing the amount of moisture gained or lost througha permeable package during storage (DM ) that will resultin raising or lowering the mixture’s water activity toa given level.

amount of desiccant needed to lower the water activity of a powder tote the moisture movement directions.

141N. Redman-Furey et al. / Trends in Food Science & Technology 29 (2013) 135e141

Another way to assess themoisture gained or lost is the in-teractiveWolframDemonstration “EquilibriumWaterActiv-ity of Binary DryMixtures” (http://demonstrations.wolfram.com/EquilibriumWaterActivityOfBinaryDryMixtures/), butit requires some working familiarity with nonlinearregression.

With the dry mass of the mixture’s ingredients calcu-lated, and their moisture sorption isotherm equationsknown, one can use Eq. (8) to write the mixture’s moisturesorption isotherm equation and generate a set of mMixture

(aW) vs. aW data with it. [These data appear on the secondsheet of the workbook, which is not shown in Figs. 5 and 6,but are plotted as a continuous curve on the first sheet e seefigures]. These mixture soption data can then be fitted withthe flexible semi-empirical double power model (Peleg,1993):

mðaWÞ ¼ k1an1W þ k2a

n2W ð12Þ

where the k’s and n’s are the adjustable parameters.The same can be done with the desiccant or moistener’s

generated data using their moisture sorption isotherm equa-tions, which are also listed on the second sheet and plottedon the first. The fit of Eq. (12) to such data is demonstratedin Fig. 7.

Once the k’s and n’s of both the mixture and desiccant ormoistener have been calculated, and so the mixture’s wetmass, their values can be used to estimate the amount ofdesiccant or moistener needed with the above mentionedWolfram Demonstration. This is done by entering theirk’s and n’s and the mixture’s mass and its k’s and n’s.Once entered, the desiccant or moistener’s slider is movedon the screen until the desired equilibrium water activitylevel is reached. The slider’s position and correspondingregistered mass is the needed amount. Actually, the plotsshown in Figs. 3 and 4 were generated using the WolframDemonstration’s code slightly modified to focus on a wateractivity range, which is pertinent to certain industrial for-mulations. Obviously, this is a somewhat cumbersome pro-cedure, clearly unfit for routine calculations. But once thesorption parameters have been calculated, it allowsa much faster examination of hypothetical scenarios bysimply moving sliders on the screen.

A new Wolfram Demonstration entitled “Dehydration bya Desiccant”, specifically written for calculating the amountof desiccant needed to lower the water of a particular ingredi-ent or the mixture as a whole, can be found at http://demonstrations.wolfram.com/DehydrationByADesiccant/. Itsscreen display is shown in Fig. 8. In this case themoisture sorp-tion isotherm of the ingredient or mixture is described by

a generic version of the GAB equation while that of the desic-cant by a single power term version of Eq. (12) e see figure.

It ought to be reiterated that the described method of cal-culation and resulting programs are all based on a staticmass balance model. Hence they provide no indication asto how long it will take the mixture to approach the newequilibrium water activity. This will depend on the ingredi-ent’s chemical character, physical state and initial moisturecontents. Therefore if of interest, the moisture’s exchangerate will have to be determined experimentally.

AcknowledgmentContribution of the Massachusetts Agricultural Experi-

ment Station at Amherst.The authors express their thanks to Kate Poiesz, Julie

Mathews and The Proctor & Gamble Corporation for sug-gesting the study and the encouragement to pursue it.

List of symbols

A, B, C, ., N reference to an ingredient (subscript)aw water activityDes desiccant (subscript)i index of an ingredient (subscript)k1, k2 coefficients in Eq. (12)M absolute moisture contents (g)m or mdb moisture contents on a dry basisMoi moistener (subscript)Mwb moisture contents on a wet basisn1, n2 powers (scaling factors) in Eq. (12)w dry mass (g)Ww wet mass (g)DM absolute moisture added or removed (g)

References

Iglesias, H. A., & Chirife, J. (1982). Handbook of food isotherms:Water sorption parameters for food and food components. NewYork: Academic Press.

Peleg, M. (1993). Assessment of a four parameter general model forsigmoid moisture sorption isotherms. Journal of Food ProcessEngineering, 16, 21e37.

Peleg, M., & Normand, N. D. (1992). Estimation of the water activityof multicomponent dry mixtures. Trends in Food Science andTechnology, 3, 157e160.

Wolf, W., Spiess, W. E. L., & Jung, G. (1985). Sorption isotherms andwater activity of food materials. New York: Elsevier.