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Analytica Chimica Acta 552 (2005) 218225Analysis and modelling of wicking through carton liquid packagingLong Lina, Helio R. JorgebaDepartment of Colour and Polymer Chemistry, The University of Leeds, Leeds, West Yorkshire LS2 9JT, UKbDepartment of Chemical Engineering, University of Quimbra, Quimbra, PortugalReceived 9 April 2005; received in revised form 2 July 2005; accepted 26 July 2005Available online 31 August 2005AbstractOne of the more important issues in carton liquid packaging systems is the wicking of liquid content through the carton (usually coatedwith polymeric films) packaging. A suitable carton packaging for liquid content should have slow rate of wicking to provide satisfactorilylong shelf life of the packaged product. In this study, the phenomenon of wicking of various liquid products, through coated carton packaging,was investigated. Thus, methods for the analysis of wicking through carton packaging had been developed. Mathematical models relatingthe rate of wicking to the physicalchemical properties of the liquid content and of the carton board were proposed. Model parameters for awidely used carton packaging material were obtained based on experimental data. The models obtained were proven capable of giving reliablecorrelation of the rate of wicking to the physicalchemical parameter of the liquid content and of the coated carton packaging. 2005 Elsevier B.V. All rights reserved.Keywords: Wicking; Diffusion; Particle size analysis; Modelling of wicking; Carton packaging1.enwide,usedmaterialscoatingstondifpackagingproducts.agingproperties.3temssizecontent.0003-2670/$doi:10.1016/j.aca.2005.07.063IntroductionCellulose based materials have long been used as morevironmentally friendly materials for packaging. World-the total weight of cellulose based packaging materialsis similar to the total weight of all other packagingused 1,2. Recent development in the polymericfor carton boards has made it possible to use car-board in the packaging of liquid products. One of theficulties in selecting suitable coated car ban board for theof liquid products is the large variety of the liquidEach liquid product to be contained in carton pack-has its own unique chemical and physicalchemicalIt was demonstrated, in a previous publication, that the nature of wicking through liquid packaging sys-is significantly influenced by the viscosity, the particleand size distribution and the surface tension of the liquidCorresponding author. Tel.: +44 780 361 5583; fax: +44 113 343 2947.E-mail address: l.linleeds.ac.uk (L. Lin).ablecoatedareatent,totheconsuming,thatarecarton,resistancetheaddsthephysicalchemicalthesuchcartonbe see front matter 2005 Elsevier B.V. All rights reserved.From the point of view of the packaging industry, suit-approaches for the rapid evaluation of the suitability ofcarton materials for the packaging of liquid productsdesirable. Currently, in order to evaluate the suitability ofcoated carton packaging material for a particular liquid con-laboratory tests, i.e. wicking test, have to be carried outestablish the rate of wicking of the liquid product throughcarton packaging material. Such tests are relatively time-which is particularly true considering the facta significant number of parameters of the carton materialof concern. Such parameters include the thickness of thethe thickness of the polymeric coating, the chemicalof the polymeric coating, the barrier properties ofpolymeric coating. The wide variety of the liquid contentsignificant complexity to the problem.Therefore, a mathematical model accurately describingrelationship between the rate of wicking and the variousproperties of the polymeric coating, ofcarton board and of the liquid product is desirable. Usinga model, rapid evaluation of the suitability of the coatedfor packaging for a particular liquid containment canmade.Chimicaablegents,majorwicking,filmforalcoholbarrierliquidproductselse2.containmentcartoncreasing,cartonaretonsstrengthenedcessesthusintocoatedthatthetheThecartonproductpinholessidemostalongpreFig. 2. The corners of the triangle flaps where most mechanical and thermaldisturbance occurs.3. Modelling and prediction of wickingthe concept3.1. Establishment of mathematical modelsMathematical modelling of diffusion of liquid and gasthrough polymeric barrier materials has been reported else-where 58. Various models have been developed to simulatethe diffusion of moisture through cellulose based packagingmaterials 914.In particular, several models have been developed forthe sorption and diffusion of moisture through heteroge-L. Lin, H.R. Jorge / AnalyticaCarton boards, being cellulosic in nature, have consider-affinity to aqueous liquids, such as fruit juices, deter-paints, etc. Consequently, wicking becomes one of theproblems in liquid packaging. To alleviate the extent ofcarton boards are usually coated with a polymericto improve the barrier property. Typical polymers usedsuch purpose include poly(ethylene), ethylene-vinylcopolymers and poly(propylene). Such polymericcoatings also need to be chemically resistant tocontainment. Details of the effects of the liquidon the polymeric coatings have been publishedwhere 4.Preparation of carton packaging for liquidFor the purpose of forming desirable container, the coatedboards have to be subjected to die-cutting, die-erecting, and sealing (usually by heating). A typicalpackage and relevant die-cutting and creasing patternschematically illustrated in Fig. 1.In the production process, the creased and cut flat car-are folded to form a three-dimensional structure that isby heat sealing. The folding and heating pro-are likely to cause damage to the polymeric coatingcreating fractures and pinholes. In the packaging shownFig. 1, the corners of the triangle flaps are usually subjectedmost mechanical and thermal disturbance (Fig. 2).There are also likely to be pinholes in the polymeric filmon the carton base. In practice, it is often inevitablethe liquid content migrate into the carton through eitherpinholes or the cracks in the coating in contact withliquid product (usually the inside of the packaging).liquid product will then continue to travel through thebase, usually along the grain direction. The liquidwill eventually emerge from the other side throughor crack in the polymeric film coated on the otherof the packaging. It should be emphasised that thelikely route of migration of the liquid product is thatthe grain direction, a fact that has been establishedviously 4.Fig. 1. A carton package and relevantActa 552 (2005) 218225 219neous media, such as paper and carton 1521. However,there exist very few reports on sorption and diffusion ofliquid containing particles, such as detergents and fabricconditioners. Thus, mathematical models for the simulationof the relationship between the rate of wicking and thephysicalchemical parameters of the coated carton board andof the particulated liquid content needed to be established.In this study, only the flow in the direction of the grain ofcarton board was considered. This was because that therate of diffusion across the grain was usually relativelyinsignificant, comparing to that along the grain. As such, thestructure of the carton board can be considered as porousmedium consisting of a bundle of cylindrical capillary tubes.die-cutting and creasing pattern.220 Chimicaena22ratecartonhwhereappropriateliquidadvisportionalboard/liquiduid,liquid,rootWwhereWthethecoefoftained,betweenitintendedfreematterrepresentedwickingminedtensionandThus,latetheWuiddeterminedthehaeacheboardingresulting3.2.modellingparameterscartonprocedures:L. Lin, H.R. Jorge / AnalyticaAssuming quasi-steady creeping flow, wicking phenom-is commonly described by the theory developed by Lucasand Washburn 23. Thus, the relationship between theof wicking and the physicalchemical properties of theboard and of the liquid can be simulated using Eq. (1):=parenleftbigg cos 22parenrightbigg1/2t1/2(1)h is the nominal distance travelled by the liquid, antortuosity factor of the carton board, and theviscosity and density, respectively, is the dynamicancing contact angle of the liquid on carton board, and the liquid surface tension.From Eq. (1), it can be seen that the rate of wicking is pro-to the square root of time, for any individual cartonassembly. Consequently, for any individual liq-weight gain of the carton board due to the wicking ofW, should also be directly proportional to the squareof time elapsed, by a factor of W0, as shown in Eq. (2): W0t1/2(2)0=parenleftbigg cos 22parenrightbigg1/2(3)It can be seen, from Eq. (3), that W0is a function ofphysicalchemical properties of the carton board and ofliquid contained. For convenience, W0is termed wickingficient throughout this paper.To this point, it has been established that the weight gainthe carton board, as a result of wicking of the liquid con-is proportional to the square root of the time of contactthe carton board and the liquid contained. However,has to be pointed out that the LucasWashburn theory wasto describe wicking phenomenon involving particle-liquids. As most liquid detergent contains particulateof significant size, modification to the wicking model,by Eq. (3), was needed.Based on past experience 4, it was dear that the rate ofof liquid detergent through carton board is deter-by several factors including viscosity, density, surfaceand particle size distribution of the liquid detergentthe physicalchemical properties of the carton board.the following model (Eq. (4) was proposed to simu-the relationship between the wicking coefficient, W0andphysicalchemical properties of the liquid contained, i.e., , and :0= c1c2c3c4c5(4)In Eq. (4), is the particle size characteristics of the liq-detergent and c1c5are the constants whose values areby the physicalchemical interactions betweenliquid detergent and the carton board. All other symbolsve the same significance as defined previously. Clearly,liquid detergent will have a unique set of parameters, ,theEq.Wgent,parametersofcoefindependentthatboardgent4.4.1.rateActa 552 (2005) 218225, , and , representing its physicalchemical properties rel-vant to wicking phenomenon. On the other hand, each cartonwill have a set of unique constants, c1c5, represent-its physicalchemical interactions with liquid detergent,in various degrees of wicking.Model acquisition and predictionTo this point, it is clear that the essence of the proposedand prediction approach is two-folds, namely:to define any liquid detergent by a unique set of parametersincluding , , , andto define the barrier properties of the carton board (againstliquid detergent migration) by a unique set of parametersc1c5.For any individual liquid detergent, the parameters , ,and could be obtained through laboratory analysis. Therepresenting the barrier effect of any individualboard, i.e. c1c5, could be obtained via the followingselect several liquid detergents of various physicalchemical nature, i.e. , , , ,select the carton board of interest,carry out laboratory tests to acquire the rate of wick-ing of each liquid detergent (details of testing proceduresare given later), represented by weight gain of the car-ton board after being in contact with the liquid detergent,andcompute the coefficients c1c5, by numerical optimisationor least-square fitting of Eq. (4).At this point, a model simulating the rate of wicking ofliquid detergents through the carton board investigated,(5), could be obtained:= c1c2c3c4c5t1/2(5)Using Eq. (5), the rate of wicking of any liquid deter-through any carton board, could then be predicted sincesuch as , , , , and c1c5were available. Onethe advantages of such a model was that the value of theficients c1c5was unique to individual carton board thusof the liquid detergent. In other words, providedthe values of the coefficients c1c5for a type of cartonwere available, the rate of wicking of any liquid deter-(recognised by the model as a set of parameters , , ,) could be predicted using Eq. (5).ExperimentalMaterials and equipmentInvestigation of the migration phenomenon and of theof migration was carried out using six commercialChimicaFig.4.4.fieldcometers4.5. Procedure for the measurement of particle size andsize distributionA COULTER N135 particle size analyser supplied byBeckman Coulter Ltd., High Wycombe, Buckinghamshire,UK was used for the analysis of particle size and size distri-bution.4.6. Procedure for the evaluation of the rate of wickingThe rate of wicking of liquid detergent through cartonL. Lin, H.R. Jorge / Analyticaliquid detergents, hereafter known as DlD6, and one typeof carton board, all supplied by Field Group, Killingworth,Newcastle Upon Tyne, UK. It should be pointed out thatthe current paper was intended to report a methodology,rather than a complete set of models, for the prediction ofwicking of liquid product through carton packaging. Assuch, only one type of carton board was investigated. Themethod reported could be used to predict wicking behaviourof other types of carton board. From the point of view ofboard structure, there are only a limited number of differentcarton boards in commercial use. Therefore, a library ofmodels for the prediction of wicking for most commerciallyavailable carton boards could be established with relativeease.The physicalchemical properties of the liquid detergentswere analysed. Such physicalchemical properties includedthe density, the surface tension, the viscosity and the particlesize and size distribution. The procedures for the determina-tion of these properties and of the rate of wicking are detailedas follows.4.2. Procedure for the measurement of the specificgravity of the liquidThe specific gravity of the liquid detergent, , is definedas the mass per unit volume. The measurement of the specificgravity of the liquid detergent involved weighting a knownvolume of test liquid and then calculating the specific gravityby dividing the mass of liquid by the volume of liquid. Dur-ing this investigation, 100 cm3volumetric flasks were usedto measure precisely 100 cm3of liquid detergent. An OhausExplorer Pro EP214D analytical balance, accurate to fourdecimal points, supplied by Fisher Scientific UK Ltd., Lough-borough, UK, was used to obtain the weight of the 100 cm3liquid detergents.The temperature of the liquid detergents in the volumetricflask was maintained at 20C during each measurement usinga water-bath having refrigeration capability. The weight ofthe 100 cm3liquid detergent was measured three times andaverage taken.4.3. Procedure for the measurement of surface tensionThe surface tension of a liquid is defined as “the force act-ing over the surface per unit length of surface perpendicularto the force”.Several methods for the measurement of the surfacetension, such as, capillary rise, Wilhelmy plates and drop-weight, are available. During this study, platinum ringmethod was used Thus, a du Nouy tensiometer, a surface ten-sion torsion balance supplied by Torsion Balance Supplies,Malvern Wells, Worcestershire, UK, was employed. Fivemeasurements for each liquid sample were carried of whichthe average was taken as the surface tension of the liquidsample.boardcartoncontactin-householderFig.andtemperatureforbothwithwicking,wFig.Acta 552 (2005) 218225 2213. Schematic illustration of the in-house built device for wicking tests.Procedure for the measurement of viscosityFor the determination of viscosity of the liquids, a Brook-model DV-II+ viscometer (supplied by Brookfield Vis-Ltd., Harlow, Essex, UK) was used.was determined by measuring the weight gain of theboard of defined dimension of which one end was inwith the liquid detergent, over a period of time. Anbuilt device, Fig. 3, was used for wicking tests. Thefor the carton samples is shown, in greater details, in4.The open-topped glass jar containing the carton samplethe liquid detergent was placed in an electric oven withcontrol.Carton board was cut to strips of dimensions 3 cm 7cmwicking tests. For the evaluation of the rate of wicking,edges along the length of the carton samples were sealedwax. However, for the investigation of the potential ofun-sealed carton samples were also used.The temperature of the test cabinet, i.e. the electric oven,as maintained at 25C. The humidity of the test cabinet was4. Schematic illustration of the in-house built holder for carton sample.222 ChimicaTPhysicalLiquiddeterD1D2D3D4D5D6maintainedousinsuredcarton24samplesweighedof5.5.1.deterofTemplopropertysize.oughbehabetigatedparticleparameter5.2.aresimaterial.DereleandeftigreaterL. Lin, H.R. Jorge / Analyticaable 1chemistry properties of the liquid detergentsgentDensity, (kg/m3)Surface tension, (N/m)Viscosity, (Pa s)Particle sizea, (106m)1075 0.0315 0.537 2.11023 0.0319 0.265 5.41019 0.0333 0.022 2.11262 0.027 1.120 3.61001 0.037 0.112 7.2994 0.0329 0.065 35.0aSize of 95% of particles.at 50%, using a total of 1000 cm3saturated aque-solution of sodium hydrogen sulphate (1 g/cm3), placedthe cabinet.The weight of each of the four carton samples was mea-and recorded prior to placing into the glass jar. Thesamples were taken out of the glass at an interval ofh. The excess liquid detergent was wiped off the cartonusing soft tissues. The carton samples were thenbefore returning to the glass jar for the continuationthe wicking tests.All six liquid detergents were subjected to wicking test.Results and discussionPhysicalchemical properties of the liquidgentsThe specific gravity, the surface tension and the viscosityeach of the six liquid detergents investigated are given inable 1.It can be seen, from Table 1, that the liquid detergentsyed for the investigation reported here had variousattributes, in particular the viscosity and particleSuch a variation of the property attributes enabled a thor-investigation of the relationship between the wickingviour and the prop