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

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Active packaging systems can offer significant advantages in preventing quality loss in horticultural products through control of microbial and/or physiological activity. By delivering and sustaining volatile active agents at effective levels in a package atmosphere, significant shelf life extension can thus be achieved. Design of these systems is complicated by the number of possible package, product, active agent and carrier combinations that can be employed and the significant interactions that may occur between these components. Mathematical modelling can be used to simplify system design and reduce the number of experimental trials required to achieve optimal active packaging systems. In this study a generalised modelling methodology was developed and validated to facilitate the design of active controlled volatile release packaging systems for horticultural products. The modelling methodology was developed using an example system which comprised tomatoes packed under a modified atmosphere (MA; 5 % (v/v) CO2 and 10 % (v/v) O2) in a LDPE bag with a polymer film sealed sachet containing silica gel pre-saturated with the antifungal agent hexanal. Experimental trials showed that for this system a target sustained hexanal concentration of 40-70 ppm was required. This was shown to be (i) the minimum inhibitory concentration (MIC) for controlling Botrytis cinerea growing on tomatoes stored at 20°C and ~99%RH, (ii) to have only a relatively minor influence on the postharvest quality of tomatoes under these active MA conditions, and (iii) to promote only a small apparent uptake of hexanal from the atmosphere by the tomatoes. The effective hexanal permeabilities of Tyvek , LDPE and OPP sachet films were characterised using the isostatic method and shown to exhibit a dependence on both temperature (10 and 20°C) and concentration (over a range of 0.01-0.22 mol m[superscript -3). Average permeabilities decreased in the order of Tyvek > LDPE > OPP, respectively, at all temperatures at comparable hexanal partial pressures. Hexanal sorption isotherms for silica gel at both 10 and 20ºC were determined using the gravimetric method and were reasonably well described by the Langmuir equation. The equilibrium 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 the sorption characteristics suggesting that multicomponent sorption is complex. A generalised modelling methodology was developed through conceptualising key mass transfer processes involved in these active MA packaging systems. Quantitative methods for deciding the relative importance of each process were established together with guidelines for when simplifying assumptions could be made. This information was formalised into a decision tree to allow appropriate assumptions to be made in model formulation without unacceptable loss of model accuracy. Methods to develop generalised equations from these assumptions to describe changes in the sachet, package headspace and outer bag film with respect to an active agent and MA gases were then identified. The mathematical modelling methodology was applied to the example hexanal release active MAP tomato packaging system. For these systems there was a high initial peak in package headspace concentration during the first 24 h which declined to a quasi steadystate concentration over a period of days. The quasi steady-state headspace concentrations were generally in the MIC range and were well predicted by the model. Interactions between water vapour and silica gel may have been responsible for the relatively higher hexanal concentration at the onset of release from the Tyvek sachet (a highly porous material). However the influence of water vapour (>95% RH in the MA bag containing tomatoes) during the quasi steady-state period appeared to be insignificant for all sachet films. The model was successfully applied to a range of packaging configurations and storage temperatures. A lack of fit was evident between model predictions and experimental trials during the initial (unsteady-state) stages of the release pattern for both headspace vapour concentrations and adsorbed mass on the silica gel. These differences were attributed to (i) model input uncertainties, chiefly with regard to the estimated coefficients of both the Langmuir isotherm equation and film permeability, and (ii) overestimated effective permeability values predicted by extrapolation of the concentration dependence of film permeability beyond the conditions for which the permeability was measured. These results suggest improved models for the effective permeabilities of the films, quantified under a range of vapour concentrations and concentration gradients, are required for better describing fluxes across the sachet film. Despite 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 predicted for different active packaging designs. This analysis gave useful insights into how sorption isotherm shape and package/sachet design parameters can be manipulated to achieve different volatile release platforms. The work clearly demonstrated the importance of accurate data for permeability of volatile compounds through polymer films and for sorption of the active agent on the carrier phase. More work on characterising these systems is recommended to further improve modelbased design methods for active MAP systems. Overall the generalised methodology developed can be confidently adopted for constructing a mathematical model that provides sufficient accuracy and simplicity to be implemented for designing active packaging systems for horticultural and food products.
Active packaging systems, Horticultural products, Packaging technology, Mathematical models