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
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
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
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.