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Effect of Adsorption Conditions on Effective Diffusivityand Textural Property of Dry Banana Foam MatPreeda Prakotmak a , Somchart Soponronnarit a & Somkiat Prachayawarakorn ba School of Energy, Environment and Materials, King Mongkut's University of TechnologyThonburi , Bangkok, Thailandb Faculty of Engineering, Department of Chemical Engineering , King Mongkut's University ofTechnology Thonburi , Bangkok, ThailandPublished online: 27 Jun 2011.

To cite this article: Preeda Prakotmak , Somchart Soponronnarit & Somkiat Prachayawarakorn (2011) Effect of AdsorptionConditions on Effective Diffusivity and Textural Property of Dry Banana Foam Mat, Drying Technology: An InternationalJournal, 29:9, 1090-1100, DOI: 10.1080/07373937.2011.569044

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Effect of Adsorption Conditions on Effective Diffusivityand Textural Property of Dry Banana Foam Mat

Preeda Prakotmak,1 Somchart Soponronnarit,1 and Somkiat Prachayawarakorn21School of Energy, Environment and Materials, King Mongkut’s University of Technology Thonburi,Bangkok, Thailand2Faculty of Engineering, Department of Chemical Engineering, King Mongkut’s University ofTechnology Thonburi, Bangkok, Thailand

Foamed banana product, a crispy snack, can quickly adsorb themoisture from the moist air, leading to loss of textural property.The main purpose of this research was therefore to study moistureadsorption kinetics of dry banana foam mat and its texture qualitychange. The adsorption isotherm experiments were carried out witha standard static method using saturated salt solutions over a widerange of relative humidities from 32 to 82% and temperatures of 35,40, and 45�C. Three dry banana foam densities of 0.21, 0.26, and0.30 g/cm3 adsorbed water vapor under controlled conditions. Fick’ssecond law coupled with an optimization technique was used toestimate the effective moisture diffusivity at sorption conditions.Empirical equations with two and three constant parameters fordescribing the dependence of the effective moisture diffusivity onmoisture content were tested. The two constant parameters couldsuitably describe the variation of the effective moisture diffusivitywith moisture content. The initial foam density, relative humidity,and temperature significantly affected the effective moisture diffu-sivity. The banana foam mats for all densities lost their crispytexture at moisture content of 0.078 kg/kg db.

Keywords Adsorption kinetics; Capillary condensation;Crispness; Food foam; Snack

INTRODUCTION

Foam mat drying is a process in which a semi-liquidfood is whipped to form stable foams by incorporating alarge volume of air in the presence of a foaming agent,which acts as a foam inducer. It is then spread as a thinmat and exposed to drying air until the moisture contentof the product is reduced to certain level.[1,2] The dryingtime required for food foam is significantly shorter thanthat for non-foam because the development of porousstructure in the food foam reduces the mass transfer resist-ance.[1,3] Foaming has successfully been applied to somefruits such as apple juice,[4] mango,[5] star fruit,[6] blackcur-rant pulp,[7,8] and banana.[1,9] To produce a crispy banana

snack, the banana foam is usually dried to a moisture con-tent below 0.04 kg=kg db. At this moisture content, the par-tial pressure of water vapor inside the product is lower thanthat in the environment. Hence, the prolonged exposure ofthe product to ambient storage conditions can lead to theadsorption of moisture from the atmosphere into the pro-duct matrix. The uptake of moisture is commonly associa-ted with deleterious changes in quality. For crispy foodssuch as breakfast cereals, crispy breads, and popcorn, theirtextures become unacceptable at the moisture content of0.042–0.07 kg=kg db.[10] Ready-to-eat snacks and whitebread lose their crispness at a moisture content of about0.1 kg=kg db.[11,12]

Food products can adsorb moisture rapidly or slowlydepending on a partial pressure of water vapor in theexposed environment. The rate of flow of adsorbable gasesis known to be dependent on the adsorption condition. Ina single capillary tube, the amount of adsorption varies ina wide range, starting from negligible adsorption at verylow relative humidity to complete liquid filling at 100% rela-tive humidity. Between these two extreme points, it can div-ided into three regimes; that is, monolayer, multilayer, andcapillary condensation. In the whole range of relativehumidity, the range of moisture content corresponds to eachregime, which depends on the size and shape of the pore.Real porous materials, however, contain a distribution ofpore sizes and may experience different types of adsorption.At low relative humidity, monolayer adsorption is domi-nant.When the relative humidity increases, the material sur-face becomes increasingly covered with adsorbed moleculesand, simultaneously, the filling of liquid into smaller poresoccurs. The amount of pores that are filled with liquidincreases with increased relative humidity and eventuallythe entire pore volume is covered with liquid. Hence, in awide range of relative humidity, the both liquid and gasphases are present inside the porous materials.

As mentioned above, the coexistence of these two phasesmay affect the movements of liquid and gas inside the

Correspondence: Preeda Prakotmak, School of Energy,Environment and Materials, King Mongkut’s University ofTechnology Thonburi, 126 Pracha u-tid Road, Bangkok 10140,Thailand; E-mail: preeda_list@hotmail.com

Drying Technology, 29: 1090–1100, 2011

Copyright # 2011 Taylor & Francis Group, LLC

ISSN: 0737-3937 print=1532-2300 online

DOI: 10.1080/07373937.2011.569044

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porous material and subsequent transport property. Thegas relative permeability decreases and the liquid relativepermeability increases as the number of liquid-filled poresin porous material increase.[13] For a certain number ofliquid-filled pores, the gas relative permeability becomeszero but the liquid relative permeability still increases con-tinually. To describe the transport of water vapor inside thebanana foam during adsorption, it is convenient to includethe transport mechanism for each phase in a single trans-port property, namely, effective diffusivity.

The effective moisture diffusivity of food is known to beeither independent or dependent of moisture content.[14–18]

In the case where it independent of moisture content, theArrhenius relation is often used to represent its variationwith temperature. However, the dependence of the dif-fusion coefficient on moisture content is not clearly demon-strated. There is no general model for describing therelationship between effective diffusivity and moisturecontent.[19] Many empirical forms such as power law,polynomial, and exponential forms have frequently beenused to describe their relationships.[15–17] Nevertheless,the model for relating the effective diffusivity to moisturecontent of porous banana foam does not exist, and litera-ture data concerning the effect of relative humidity onmoisture diffusivity are limited. The objectives of this studywere therefore to select a suitable empirical equation of dif-fusivity; to investigate the influences of relative humidity,temperature, and foam density on the effective moisturediffusivity; and to explore the change of textural propertiesof the banana foam mat during adsorption.

MATERIALS AND METHODS

Dried Banana Foam Preparation

Gros Michel bananas (Musa sapientum L.) with amaturity stage of 5 corresponding to yellow peel and greentip were purchased from a local market. The total solublesolids of the banana was measured using an ATC-1E hand-held refractometer (ATAGO, Tokyo, Japan) at a tempera-ture of 23�C. The banana used in the experimentscontained total soluble solids content of 23–25 �Brix. Toprepare banana foam, the bananas were sliced and pre-treated by immersing them in 1 g=100 g sodiummetabisulfitesolution for 2min and rinsing them with distilled water for30 s[1] in order to prevent discoloration during the foamingprocess. One hundred grams of banana puree with 5 g freshegg albumen, used as a foaming agent, was whipped with aKitchenAid mixer (model no. 5K5SS, Strombeek-Bever,Belgium) at the maximum speed to produce foam densitiesof 0.3, 0.5, and 0.7 g=cm3. The banana foam density wasdetermined by measuring the mass of a fixed volume ofthe foam. The banana foam was poured slowly into a steelblock with dimensions of 45� 45� 42mm (W�L�H)and then placed on a mesh tray, which was covered with

aluminum foil. Then it was dried to about 0.03 kg=kg dbusing a tray dryer that was operated at 80�C and an air velo-city of 0.5m=s. The banana foam prepared from the initialfoam densities of 0.3, 0.5, and 0.7 g=cm3 could produce thedried banana foam densities of 0.21� 0.02, 0.26� 0.02,and 0.30� 0.02 g=cm3, respectively. The product thick-nesses after drying were 2.8� 0.15, 3.2� 0.1, and3.4� 0.1mm for banana foam densities of 0.21, 0.26, and0.30 g=cm3, respectively. Five replications were performedfor each banana foam density.

Adsorption Experiment

Moisture adsorption experiments were carried out usingthe static method. Samples were placed into the glass jarscontaining the saturated salt solutions (MgCl2 � 6H2O,Mg(NO3)2 � 6H2O, KI, NaCl, and KCl), which providedrelative humidity (RH) in range the of 32–82% at the cor-responding temperatures of 35, 40, and 45�C. All of the jarswere placed in a temperature-controlled oven with a pre-cision of�1�C (UFE500,Memmert, Schwabach,Germany).Samples were weighed at different exposure times rangingfrom 1 to 120 h. At RH> 74%, 1mL of toluene was heldin a vial and fixed in the glass jars in order to preventmicrobial sample spoilage.[20] The moisture content of eachsample after reaching the equilibrium condition was determ-ined by drying it in the hot air oven at 103�C for 3 h.[21] Atthis temperature, the percentage error of moisture contentdetermination was approximately 0.4% when compared tothe result obtained by the standard vacuum method.[1] Theexperiment at each adsorption condition was repeated threetimes and the mean value was reported.

SEM Photograph

The morphologies of dried banana foam mats werecharacterized using a scanning electron microscope(SEM; JSM-5600LV, JEOL Ltd., Tokyo, Japan) with anaccelerating voltage of 10 kV. Before photographing, thespecimens were cut into a dimension of 5� 5mm and thenglued onto the metal stub. The samples were coated withgold, scanned, and photographed at 15�magnification.

Image J (U.S. National Institutes of Health, Bethesda,MD) software was used to quantify the porous bananafoam characteristics such as pore diameter and pore area.An SEM image is composed of 8-bit greyscale pixels. Eachpixel of the SEM micrograph was assigned a value of grayintensity between 0 and 255. The SEM images were thensegmented into binary images based on a manual thresholdsetting using their grey-level histogram. The threshold set-ting consisted of finding the grey level of the histogram thatsuitably separates the classes associated with solids andpores. From this threshold setting, binary black-and-whiteimages can be created. The pixels with grey levels lowerthan the selected threshold were assigned as space, whichappeared black, and the pixels with grey levels above the

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selected threshold were set as solid, which appeared whitein the binary image. The pore diameter was estimated fromthe known pore area by counting the number of pixels filledin the specified space.

Texture Analysis

The effects of moisture content and storage temperatureon product textures were studied by a compressive testusing a texture analyzer model TA.XTplus (Stable MicroSystems, Surrey, UK). The banana foam with moisturecontent of 0.038 kg=kg db was used to adsorb water vaporat an RH of 74% and temperature of 24�C. After the pro-duct adsorbed water vapor for a predetermined time, thesample was examined for its textural properties. The plat-form table is attached with a hole plate (9mm diameter) fit-ted to the texture analyzer. The sample was placed on theplate and a direct force was applied to the sample using a5-mm spherical probe moving at a constant crossheadspeed of 2mm/s. Before the penetration test, the sampleswere exposed to the surrounding with RH of 35–45% forless than 20 s and the textural property of the samplesdid not change. From the force deformation curve, thehardness was defined at the maximum force of the curveand the crispness was characterized by the number of peaksand the slope of the first peak. The data were analyzed byanalysis of variance (ANOVA) using Duncan’s multiplerange test at P< 0.05. Twelve samples were used to deter-mine the textural properties and the average values of hard-ness and crispness were presented.

Determination of Effective Moisture Diffusivity

The banana foam mat used in the experiments haddimensions of 43� 43� 4mm. This sample size providedmoisture transport in the thickness direction because thematerial thickness was 10 times shorter than the othertwo dimensions. The change in product size due to swellingwas considered negligible during adsorption. The unsteady-state mass transfer equation for moisture diffusion withinan isotropic material with flat slab geometry is given by:

@ðqMÞ@t

¼ @

@xðDeff ðMÞ @ðqMÞ

@xÞ ð1Þ

or

@ðqMÞ@t

¼ Deff ðMÞ @2ðqMÞ@x2

þ @ðqMÞ@x

� @ðqDeff ðMÞÞ@x

ð2Þ

where q is the apparent density of dry banana foam (kg=m3),M is the moisture content (kg=kg db), t is time (s),Deff(M) isthe effective moisture diffusion coefficient (m2=s), and x isthe distance along the diffusion path (m). In this study, itwas assumed that the moisture distribution inside the sam-ple at the beginning was spatially uniform and the migration

of water vapor from the surrounding air to the sample sur-face occurred at the top surface. No moisture transferred atthe bottom because the bottom surface was placed on anopaque glass dish. From the above assumptions, the follow-ing initial and boundary conditions can be established:

M ¼ Min; 0 � x � L at t ¼ 0 ð3Þ

Deff �@ qMð Þ@x

� �¼ hmMwPvsat

RTRHsðMÞ � RHairð Þ;

x ¼ 0 at t > 0

ð4Þ

@ðqMÞ@x

¼ 0; x ¼ L at t > 0 ð5Þ

whereMin is the initial moisture content (kg=kg db), L is thethickness of the material (m),Mw is the molecular weight ofwater (18 kg=kmol), Pvsat is the saturated vapor pressure(Pa), T is the temperature of the solid (K), R is the perfectgas constant (8,314.3 J=kmol=K), and RHs(M) and RHair

are the relative humidity of air at the top surface of productand in the surrounding air, respectively. RHs(M) can bedetermined from the moisture adsorption isotherms andthe data are not reported in the present work. hm is theconvective mass transfer coefficient (m=s), which can bedetermined from the correlation proposed by[22]

Sh ¼ 0:646Re0:5 � Sc1=3 ð6Þ

Because the density of dry banana foam did not change dur-ing adsorption, the density can be cancelled out on both sidesof Eq. (2), and Eq. (2) can be written in a form of finite differ-ence scheme using forward difference for the first term on theright-hand side and central difference for the second term:

Mtþ1i �Mt

i

Dt¼ Dt

eff ;i

Mtiþ1 � 2Mt

i þMti�1

ðDxÞ2

!

þMt

iþ1 �Mti�1

2Dx

� �Dt

eff ;iþ1 �Dteff ;i�1

2Dx

� �for i ¼ 1 to N � 1

ð7Þ

where Dt is the time increment (s) and Dx is the distancebetween adjacent nodes (m). Equation (4) was discretizedusing the central difference and it can be expressed by

Dteff ;i � q

Mtiþ1 �Mt

i�1

2Dx

� �

¼ hmMwPvsat

RTRHsðMt

i Þ � RHair

� �for i ¼ N

ð8Þ

where MtNþ1 in Eq. (8) is the fictitious moisture content at a

fictitious node and N is the number of layers, as illustrated

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in Fig. 1. From Eq. (8), the value ofMtNþ1 can be calculated,

and this value was used to determine the moisture content atthe top surface,MN, at tþ 1 using Eq. (7). The discretizationof Eq. (5) with the backward difference formula givesMt

iþ1 ¼ Mti�1. Substituting Mt

i�1 in Eq. (7) with Mtiþ1, it

can then be written as follows:

Mtþ1i �Mt

i

Dt¼ 2Dt

eff ;0

Mtiþ1 �Mt

i

ðDxÞ2

!for i ¼ 0 ð9Þ

From Eq. (9), the value of Mtþ10 can be determined. In the

moisture calculation, the time increment of 0.01 s was usedand the sample thicknesses of 2.8, 3.2, and 3.4mm for therespective foam densities of 0.21, 0.26, and 0.30 g=cm3 weredivided into 105, 120, and 128 layers.

After the moisture content at every node is known,the average moisture content M(t)pre can be readily becalculated by integrating the calculated moisture profilethroughout the sample thickness and the trapezoidalnumerical integration was used:

M tð Þpre¼R L0 M tð ÞdxR L

0 dxð10Þ

Because the dependence of diffusivity on moisture contentcannot be described by any specific equation, three possibleempirical equations obtained from the literature[23–25] weretested with the moisture adsorption data:

Deff ðMÞ ¼ D0 expð�ðe1M þ e2M2ÞÞ ð11Þ

Deff ðMÞ ¼ D0 �MDx ð12Þ

Deff ðMÞ ¼ D0 expð�a �MÞ ð13Þ

where D0, Dx, e1, e2, and a are the constant parameters.The accuracy of the models was evaluated by root meansquared error (RMSE) and coefficient of determination

(R2). RMSE is defined as:

RMSE ¼ 1

NP� P

XPn¼1

ðMðtÞexp �MðtÞpreÞ2

" #1=2ð14Þ

where M(t)exp is the experimental average moisture contentof material at time t, M(t)pre is the predicted average moist-ure content, NP is the number of data points, and P is thenumber of parameters.

The lower the value of RMSE is, the better the goodnessof fit. In this work, a modified Nelder-Mead simplexmethod was used to estimate the constant parameters inEqs. (11), (12), and (13). The RMSE was set as the objec-tive function with a tolerance of 10�9. To help speed upthe convergence of optimization, the initial guess wasobtained from the least squares fits of the moisture diffusiv-ity data calculated from the method of slopes.[26] Themodel with the lowest value of RMSE and highest valueof R2 was considered the best model to correlate the experi-mental data.

RESULTS AND DISCUSSION

Morphology of Dry Banana Foam

The microstructures of dry banana foam mats charac-terized by SEM are shown in Fig. 2 and the pore size dis-tributions determined by the binary image of SEM forthree banana foam densities are shown in Fig. 3. It is clearfrom both figures that the sample with a foam density of0.21 g=cm3 had a larger proportion of large pores thanthe higher foam densities, whereas the foam density of0.30 g=cm3 exhibited a larger proportion of smaller pores.The proportion of the pores larger than 300 mm were about24, 10, and 4% for the foam densities of 0.21, 0.26, and0.30 g=cm3, respectively. From their pore size distributions,the void area fractions for the banana foam densities of0.21, 0.26, and 0.30 g=cm3 were 31, 26, and 23%, respect-ively. The void area fraction of banana foam sample at adensity of 0.30 g=cm3 was relatively small because therewere a small number of large pores.

Identification of Effective Moisture Diffusivity Model

Three empirical effective diffusivity models describingthe relationship between the effective diffusivity and moist-ure content were proposed and validated against the moist-ure adsorption data. Two experimental data sets for thedry banana foam density of 0.21 g=cm3 obtained at 40�Cand 66% RH and at 35�C and 83% RH were used to vali-date the effective diffusivity models. Figure 4 shows theeffective diffusivity–moisture relationship estimated fromEqs. (11)–(13) and their predictions of moisture uptake.As shown in Figs. 4a and 4d, the effective diffusivityvalues obtained from the diffusion models decreased withmoisture content, but their values were not identical. The

FIG. 1. Illustration for node positions in a banana foam mat.

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difference in Deff values among the three models was due tomathematics but not physics. The constant parameters foreach diffusion model are shown in Table 1. For all casesstudied, the models predicted the experimental data with

reasonable agreement; the R2 values of the three modelswere above 0.99 and their RMSE values were lower than0.008.

The predictions of moisture adsorption using threeeffective diffusivity models are shown in Figs. 4b and 4e,indicating that the moisture contents calculated from thediffusivity models were almost superimposed even thoughthe effective diffusivity values determined from the modelswere different. This implied that the extent of such differ-ence in the effective diffusivity values was insensitive tothe moisture content calculation, and thus it was difficultto identify the suitable model for predicting the moisturecontent from the values of RMSE and R2. One more cri-terion was thus needed to quantify the quality of the esti-mated constant parameters. In this study, the localrelative error (E) was used to identify the suitable diffusiv-ity model, and it is defined as:

EðtÞ ¼ 100MexpðtÞ �MpreðtÞ�� ��

MexpðtÞð15Þ

where Mexp(t) is the experimental moisture content at timet and Mpre(t) is the moisture content from prediction. If theestimation of moisture content was perfect, the value of Eat time t was zero. The values of E for the three empiricaldiffusion models are shown in Fig. 4c for 40�C and 66%RH and in Fig. 4f for 35�C and 83% RH, indicating thatthe values of E for Eqs. (12) and (13) were less than 2%throughout the exposure time, and the error from predic-tion using Eq. (11) varied during adsorption; the maximumerror, significantly higher than 2%, was found in the earlyadsorption stage.

The accurate prediction of adsorbed moisture in theearly adsorption period is very important for a crispy pro-duct because the product quickly loses its crispy texturewhen it adsorbs water vapor up to certain moisture con-tent. The banana foam will lose its crispiness at a moisturecontent of about 0.078 kg=kg db, as will be seen in the sec-tion on banana foam texture. From these results, it can bededuced that Eq. (12) or (13) was used to describe themoisture adsorption of banana foam. However, using Eq.(12) to predict moisture content during adsorption pro-vided E values for all adsorption times slightly lower thanthat using Eq. (13). This implied that Eq. (12) was a suit-able empirical model to describe the relationship betweeneffective moisture diffusivity and moisture content for drybanana foam.

Effect of Relative Humidity on Effective MoistureDiffusivity

The empirical equation of Eq. (12) was selected to studythe effect of relative humidity on the effective moisture dif-fusivity. Figure 5 shows the moisture adsorption at 35�C

FIG. 2. SEM micrographs of dry banana foam mats at different initial

foam densities (baseline is 1mm): (a) 0.21 g=cm3, (b) 0.26 g=cm3, and (c)

0.30 g=cm3.

FIG. 3. Pore size distribution of dry banana foam at various densities.

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and RH range of 32–83% for the banana foam densityof 0.21 g=cm3. As expected, the faster adsorption ratewas accomplished with higher relative humidity. The

predictions of moisture content using Eqs. (1) and (12)agreed well with the experimental data over a wide rangeof relative humidity values.

FIG. 4. Validation of the experimental and estimated moisture uptakes and the variation of effective diffusivity with moisture content of two selected

example cases: 40�C, 66% RH (left) and 35�C, 83% RH (right).

TABLE 1Estimated parameters of empirical models for selected conditions

Experimental conditions

40�C, 66% RH 35�C, 83% RHEstimatedparameters Equation (11) Equation (12) Equation (13) Equation (11) Equation (12) Equation (13)

D0 5.947� 10�10 8.908� 10�11 3.962� 10�10 1.709� 10�10 6.326� 10�11 1.236� 10�10

e1 11.108 — — 4.604 — —e2 �27.508 — — �7.172 — —Dx — �0.463 — — �0.244 —a — — �3.914 — — �1.210R2 0.996 0.999 0.999 0.995 0.998 0.998RMSE 0.0043 0.0013 0.0015 0.0081 0.0034 0.0038

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Figure 6 shows the changes of Deff with moisture con-tent at different values of RH and at adsorption tempera-tures of 35, 40, and 45�C for the dry banana foamdensities of 0.21, 0.26, and 0.3 g=cm3. The Deff value forthe dry banana foam densities was greatly increased withincreased moisture content in the range of RH of 31–48%and at all adsorption temperatures. The equilibrium moist-ure content of samples at these relative humidities wasgiven in a range of 0.08–0.15 kg=kg db. In this RH range,the water molecules were adsorbed on the pore surface witha small thickness. The adsorbed water acts as a plasticizer,which increases the molecular mobility of water in the solidmatrix. In addition to a plasticization effect, the flow ofwater vapor into the porous banana foam was notlimited. Hence, the effective moisture diffusivity wasremarkably increased as the moisture content increasedduring adsorption.

When the RH was higher than 48%, the plasticizationand vapor flow effects became less important and the trendof changing Deff with moisture content had large differ-ences among dry foam densities and adsorption conditions;that is, temperature and RH. At the dry banana foam den-sity of 0.21 g=cm3, the value of Deff shown in Fig. 6a for35�C and RH of 67 and 75% increased slightly withincreased moisture content. When the value of RH was83%, on the other hand, the value of Deff for this bananafoam density decreased with increased moisture content.At higher temperatures of 35�C together with RH above65%, the Deff decreased with increasing moisture contentas shown in Figs. 6b and 6c. For the other two dry bananafoam densities, the Deff shown in Figs. 6d and 6e for the drybanana foam density of 0.26 g=cm3 as well as Figs. 6f and6 g for the foam density of 0.3 g=cm3 were almostindependent of adsorbed moisture content at higher

temperatures of 35�C and at higher RH values of 66%.Such different moisture diffusivity trends may be relatedto the combined effects of physical characteristics of poresize and formation of liquid in the pores of the sample,and both factors affect the flows of water vapor and liquidinside the porous food sample, which will be describedbelow.

Because the adsorption was carried out at 35�C andhigher than 50% RH, some water vapor was incorporatedinto the banana sample, and some formed a thickerliquid film, which results in a smaller flux of water vaporflowing through the material and provided a slightincrease of Deff with increased moisture content. Whenthe adsorption temperature increased to 40 or 45�C,implying an increase of partial pressure, the rate of watervapor adsorption by the porous banana foam samplebecame faster, allowing more exterior pores to be filledwith water compared to adsorption at 35�C. Conse-quently, the water vapor is more difficult to transportthrough the sample, resulting in a decrease in Deff forthe dry banana foam density of 0.21 g=cm3 because thesample adsorbs more water vapor. For the samples withhigher foam densities, that is, 0.26 and 0.3 g=cm3, therelationship between Deff and adsorbed moisture contentwas independent, which was not similar to the case of thedry foam density of 0.21 g=cm3. Such differences in themoisture diffusivity curves are due to different porestructures between banana foam densities as depicted inFig. 3. With a larger proportion of small pores, corre-sponding to a size range of 5–100 mm, for the bananafoam densities of 0.26 or 0.3 g=cm3, it is possiblethat these small pores are occupied by the water with anumber close to the percolation threshold at which thevapor flow inside the pores is blocked. Hence, the flowof water into the pores inside the banana foam is onlygoverned by capillary flow and the Deff value, which inturn changes slightly with moisture content. Rocaet al.[27] carried out adsorption experiments at 84% RHand 20�C and found that the effective moisture diffusiv-ity of sponge cake with porosity of 86% exponentiallydecreased with increased moisture content and decreasedslightly for the sample of 52% porosity.

Effects of Temperature and Banana Foam Density onEffective Moisture Diffusivity

Figure 7 shows the changes of Deff with moisture con-tent at adsorption temperatures of 35, 40, and 45�C.As expected, the Deff values increased with increasedtemperature. Figures 8a and 8b show the Deff value forthree foam densities at an illustrated temperature of 35�Cand relative humidities of 32 and 50%, respectively. TheDeff values were relatively lower for the high banana foamdensity than for the low foam density. The difference inthe Deff values can be accounted for by the morphological

FIG. 5. Effect of values of relative humidity on moisture adsorption

kinetics at 35�C for the foam density of 0.21 g=cm3. Dash lines are the pre-

dictions; symbols represent experimental data.

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difference between three samples, as already explained.Highly porous food provides less diffusional flux resistanceand thus greatly facilitates the moisture transport to highlyporous foods, yielding high value of Deff.

Effect of Moisture Content on Banana Foam Texture

Figure 9 shows the force deformation curves of thebanana foam at adsorption temperature of 35�C and RHvalues of 48% and 74%. Eight banana foam mats at the

FIG. 6. Variation of effective diffusivity with moisture content at various relative humidities for foam densities of 0.21, 0.26, and 0.30 g=

cm3: (a) 0.21 g=cm3; (b) 0.21 g=cm3; (c) 0.21 g=cm3; (d) 0.26 g=cm3; (e) 0.26 g=cm3; (f) 0.30 g=cm3; and (g) 0.30 g=cm3.

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density of 0.26 g=cm3 were used to demonstrate howadsorption condition affects the textural property. Theadsorption time required to reach moisture content ofabout 0.05 kg=kg db was approximately 32 and 5min forthe corresponding values of 48 and 74% RH. The forcedeformation curves show irregular peaks that likely rep-resent subsequent fracture events of the pore structure.When direct force was applied to the sample, multiple frac-tures occurred due to the force required to pass through thepore voids of the dry banana foam sample, leading toirregular jaggedness of the curve. The jagged pattern ofthe force deformation curve reflects the crispy behaviorof the banana foam mats. As observed from this figure,the irregular jagged force-deformation curves are notice-ably different for the samples that were exposed to differentvalues of RH, and their curves can be classified into twogroups, namely, A and B. Group B, the sample exposedto 74% RH, was less crispy and tough, as indicated bylow jagged force and high maximum force. On the otherhand, the group A sample stored at 48% RH had a highjagged force and low maximum force, implying a samplewith a crispy texture. From the force deformation curves,it is clear that the adsorption rate affected the textural pro-perty, although the product moisture content for testingwas identical. This is because most water vapor adsorbed

at high relative humidity is present near the sample surface,and the resulting surface is wetted, which provides a lesscrisp product.

Figure 10 shows the curves of force versus displacementrecorded by the texture analyzer at different moisturecontents. The dry banana foam mat before water vaporadsorption had a moisture content of 0.039 kg=kg db andmultiple peaks in the force deformation curve. The original

FIG. 8. Effect of initial foam densities on effective diffusivity at 35�Cand relative humidities of (a) 32% and (b) 50%.

FIG. 7. Effect of temperatures on effective moisture diffusivity: (a)

q¼ 0.21 g=cm3 and (b) q¼ 0.26 g=cm3.

FIG. 9. Effect of adsorbed moisture on force-deformation curve for

foam density of 0.26 g=cm3.

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samples with a moisture content of 0.039 kg=kg db atbanana foam densities of 0.21, 0.26, and 0.30 g=cm3 hada different number of peaks, initial slope, and maximumforce as shown in Fig. 11. This indicates that the micro-structure of banana foams plays an important role in thetextural properties. When the sample adsorbs water vaporup to certain moisture content, the fracture pattern asshown in Fig. 10 is absent, revealing that the sample isnot expected to be crisp. In addition, it has a tough texture.

Figure 11 shows the textural properties of banana foamat moisture contents and the results of statistical analysisare shown in Figs. 11a–11c. The number of peaks wascounted when the force amplitude was greater than thethreshold value, which was set at 30 g (0.294N). The num-ber of peaks and initial slope for all foam densities signifi-cantly decreased with increased moisture content. Incontrast to the changes of the initial slope and number ofpeaks, the maximum force may increase or not change withmoisture content, depending on the foam density. At thefoam density below 0.26 g=cm3, an insignificant change inthe maximum force was observed in the moisture contentrange of 0.039–0.078 kg=kg db, but the maximum forcechanged significantly with moisture content for the foambanana density of 0.3 g=cm3, showing a higher maximumforce as the moisture content of the sample increased.

The lowest number of peaks were found at a moisturecontent of 0.078 kg=kg db, and it may be expected thatthe banana foam samples lose their crispy texture. Thismoisture content for the banana foam is given in samerange of other crisp products such as crispy breads, cereals,popcorn, and puffed corn,[10] and the moisture content ofcrisp products should not be higher than 0.07–0.08 kg=kgdb in order to preserve their textures.

CONCLUSION

Three empirical equations describing the dependence ofthe effective moisture diffusivity on moisture content weretested. The RMSE, R2 value, and local relative error weresuitably used as criteria to identify the appropriate effectivediffusivity model. From these criteria, among the threeempirical models tested, the relation between the Deff andmoisture content could be described adequately by Eq.(12). This proposed equation is simple and has the abilityto estimate the Deff values over a whole adsorption rangeof moisture content of banana foam mat. From theanalysis of adsorption data, the banana foam density,adsorption temperature, and relative humidity affected theDeff value. TheDeff value of every banana foam density rap-idly increased with increased moisture content at low rela-tive humidity and for all adsorption temperatures. Whenthe RH was higher than 50%, the Deff was constant,increased, or decreased with increased moisture content.Such Deff trends relate to the capability of the dry bananafoam to adsorb water vapor. A faster adsorption rate led

FIG. 10. Variation in force-deformation curve during compression test

at various moisture content levels for foam density of 0.21 g=cm3.

FIG. 11. Effect of moisture content and initial foam densities on (a)

number of peaks, (b) initial slope, and (c) maximum force of the banana

foam mats: the same letter means insignificant difference at P> 0.05.

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to the pores filling with liquid, resulting in a decrease in Deff

with moisture content for the low-density banana foam, butit was independent of moisture content for the high-densityfoam. The value of Deff was higher for adsorption at highertemperature and for lower foam density.

From the quality evaluation, it was found that the bananafoam mat was very hygroscopic and its crispness was verysensitive tomoisturemigration. The increase inmoisture con-tent of banana foam mat during adsorption decreased thenumber of peaks and initial slopes, implying less crispiness,but the maximum force increased, indicating a tough texture.The banana foam mats for all densities lost definitely theircrispy texture at moisture content of 0.078 kg=kgdb.

ACKNOWLEDGMENTS

The authors express their appreciation to the Com-mission on Higher Education, Thailand, for supportingthis research by a grant fund under the program StrategicScholarships for Frontier Research Network for thePh.D. Program Thai Doctoral Degree. This work was alsosupported in part by Thailand Research Fund and KingMongkut’s University of Technology, Thonburi, and theNational Science and Technology Development Agency.

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