Mathematical modelling of active packaging systems for horticultural products : a thesis presented in partial fulfilment of the requirements for the degree of Doctor of Philosophy in Packaging Technology at Massey University, New Zealand (2008)

Active packaging systems can offer significant advantages in preventing quality loss in&#13;\nhorticultural products through control of microbial and/or physiological activity. By&#13;\ndelivering and sustaining volatile active agents at effective levels in a package atmosphere,&#13;\nsignificant shelf life extension can thus be achieved. Design of these systems is&#13;\ncomplicated by the number of possible package, product, active agent and carrier&#13;\ncombinations that can be employed and the significant interactions that may occur between&#13;\nthese components. Mathematical modelling can be used to simplify system design and&#13;\nreduce the number of experimental trials required to achieve optimal active packaging&#13;\nsystems. In this study a generalised modelling methodology was developed and validated&#13;\nto facilitate the design of active controlled volatile release packaging systems for&#13;\nhorticultural products.&#13;\nThe modelling methodology was developed using an example system which comprised&#13;\ntomatoes packed under a modified atmosphere (MA; 5 % (v/v) CO2 and 10 % (v/v) O2) in&#13;\na LDPE bag with a polymer film sealed sachet containing silica gel pre-saturated with the&#13;\nantifungal agent hexanal. Experimental trials showed that for this system a target sustained&#13;\nhexanal concentration of 40-70 ppm was required. This was shown to be (i) the minimum&#13;\ninhibitory concentration (MIC) for controlling Botrytis cinerea growing on tomatoes stored&#13;\nat 20°C and ~99%RH, (ii) to have only a relatively minor influence on the postharvest&#13;\nquality of tomatoes under these active MA conditions, and (iii) to promote only a small&#13;\napparent uptake of hexanal from the atmosphere by the tomatoes.&#13;\nThe effective hexanal permeabilities of Tyvek , LDPE and OPP sachet films were&#13;\ncharacterised using the isostatic method and shown to exhibit a dependence on both&#13;\ntemperature (10 and 20°C) and concentration (over a range of 0.01-0.22 mol m[superscript -3). Average&#13;\npermeabilities decreased in the order of Tyvek &gt; LDPE &gt; OPP, respectively, at all&#13;\ntemperatures at comparable hexanal partial pressures.&#13;\nHexanal sorption isotherms for silica gel at both 10 and 20ºC were determined using the&#13;\ngravimetric method and were reasonably well described by the Langmuir equation. The&#13;\nequilibrium amount adsorbed was significantly reduced at the higher temperature but the pre-adsorption of water vapour on hexanal uptake on silica gel showed no uniform trend on&#13;\nthe sorption characteristics suggesting that multicomponent sorption is complex.&#13;\nA generalised modelling methodology was developed through conceptualising key mass&#13;\ntransfer processes involved in these active MA packaging systems. Quantitative methods&#13;\nfor deciding the relative importance of each process were established together with&#13;\nguidelines for when simplifying assumptions could be made. This information was&#13;\nformalised into a decision tree to allow appropriate assumptions to be made in model&#13;\nformulation without unacceptable loss of model accuracy. Methods to develop generalised&#13;\nequations from these assumptions to describe changes in the sachet, package headspace&#13;\nand outer bag film with respect to an active agent and MA gases were then identified.&#13;\nThe mathematical modelling methodology was applied to the example hexanal release&#13;\nactive MAP tomato packaging system. For these systems there was a high initial peak in&#13;\npackage headspace concentration during the first 24 h which declined to a quasi steadystate&#13;\nconcentration over a period of days. The quasi steady-state headspace concentrations&#13;\nwere generally in the MIC range and were well predicted by the model. Interactions&#13;\nbetween water vapour and silica gel may have been responsible for the relatively higher&#13;\nhexanal concentration at the onset of release from the Tyvek sachet (a highly porous&#13;\nmaterial). However the influence of water vapour (&gt;95% RH in the MA bag containing&#13;\ntomatoes) during the quasi steady-state period appeared to be insignificant for all sachet&#13;\nfilms.&#13;\nThe model was successfully applied to a range of packaging configurations and storage&#13;\ntemperatures. A lack of fit was evident between model predictions and experimental trials&#13;\nduring the initial (unsteady-state) stages of the release pattern for both headspace vapour&#13;\nconcentrations and adsorbed mass on the silica gel. These differences were attributed to (i)&#13;\nmodel input uncertainties, chiefly with regard to the estimated coefficients of both the&#13;\nLangmuir isotherm equation and film permeability, and (ii) overestimated effective&#13;\npermeability values predicted by extrapolation of the concentration dependence of film&#13;\npermeability beyond the conditions for which the permeability was measured. These&#13;\nresults suggest improved models for the effective permeabilities of the films, quantified&#13;\nunder a range of vapour concentrations and concentration gradients, are required for better&#13;\ndescribing fluxes across the sachet film.&#13;\nDespite these limitations, the model did describe the general release pattern. The model was then used to pose a range of ‘what-if’ scenarios investigating the release patterns&#13;\npredicted for different active packaging designs. This analysis gave useful insights into how sorption isotherm shape and package/sachet design parameters can be manipulated to&#13;\nachieve different volatile release platforms.&#13;\nThe work clearly demonstrated the importance of accurate data for permeability of volatile&#13;\ncompounds through polymer films and for sorption of the active agent on the carrier phase.&#13;\nMore work on characterising these systems is recommended to further improve modelbased&#13;\ndesign methods for active MAP systems.&#13;\nOverall the generalised methodology developed can be confidently adopted for&#13;\nconstructing a mathematical model that provides sufficient accuracy and simplicity to be implemented for designing active packaging systems for horticultural and food products.