DEVELOPMENT OF A STANDARD FOOD PACKAGE MOISTURE TRANSFER MODEL
4.5 MODEL VALIDATION
4.5.3 Results and Discussion
4.5.3.3.2 Single Perforation in a Single Layer Packaging System
A package system consisting of a polymer liner with a single perforation containing SMP was simulated. Values of system inputs for the simulation are summarised in Table 4-10.
Table 4-10: Summary of system inputs used for validation of the moisture isotherm component of the model for a single layer system with a single perforation.
Parameter Description Symbol Units Value *
General system inputs
Mass of solids in SMP kg
Initial moisture content of SMP (kg water).(kg solids)−1
Ambient temperature K ( ) Ambient relative humidity % ( )
Surface area of packaging m2
( )
Number of layers - 1
Total area of perforation(s) m2 ( )
Diameter of perforation m GAB isotherm parameters
Moisture content of monolayer for GAB isotherm
(kg water).(kg
solids)−1
0.051 Guggenheim constant for GAB
isotherm
- 12.11
Constant for GAB isotherm - 1.08 Properties of layer 1 of packaging
film
Thickness of layer 1 of packaging film m ( )
Solubility of water vapour in layer 1 of packaging at reference temperature
mol.m -3
.Pa-1 0.001 Reference temperature of solubility of
water vapour in layer 1 of packaging
K ( )
water vapour in layer 1 of packaging material
Permeability of water vapour in layer 1 of packaging at reference
temperature
mol.m.m −2
.s−1.Pa−1 ( )
Activation energy of permeation of water vapour in layer 1 of packaging material
J.mol
-1 ( )
Reference temperature of diffusivity of water vapour in layer 1 of
packaging
K ( )
* Error values represent a 95% CI relative to the mean.
A comparison of model predictions and experimental results for the single layer non- perforated system is shown in Figure 4-29.
Figure 4-29: Comparison of moisture content of SMP ((kg water).(kg solids)−1) versus time (hours) for a polymer liner with 1 perforation at 26.6°C and 76.5% ambient RH as predicted by the standard food package model and measured experimentally. Error bar at 0 hours represents 95% CI of initial experimental mass. Model 95% CI limits represent extreme predictions based on 95% CIs of system inputs.
0.060 0.062 0.064 0.066 0.068 0.070 0.072 0 50 100 150 200 250 300 350 400 M o istu re c o n te n t ((k g w ate r).(kg so lid s) −1) Time (h) Sample 1 Sample 2 Sample 3 Sample 4 Sample 5 Sample 6 Model 95% CI
As can be seen, there was excellent agreement between model predictions and experimental measurements for the single polymer liner containing a single perforation. Like the non-perforated system (Section 4.5.3.3.1), the water vapour transfer rate also remained relatively linear, suggesting a relatively constant water vapour pressure in the package headspace during the trial period. Therefore a polymer liner containing 20 perforations was also considered for validation.
4.5.3.3.3 Multiple Perforations in a Single Layer Packaging System
A polymer liner with 20 perforations containing SMP was simulated. Values of system inputs for the simulation were the same as for the single perforation system (Table 4-10), except the total area of perforations was increased 20-fold ((1.04 ± 0.14) × 10-7 m2). A comparison of model predictions and experimental results is shown in Figure 4-30.
Figure 4-30: Comparison of moisture content of SMP ((kg water).(kg solids)−1) versus time (hours) for a polymer liner with 20 perforations at 26.6°C and 76.5% ambient RH as predicted by the standard food package model and measured experimentally. Error bar at 0 hours represents 95% CI of initial experimental mass. Model 95% CI limits represent extreme predictions based on 95% CIs of system inputs.
0.06 0.07 0.08 0.09 0.10 0.11 0.12 0.13 0 50 100 150 200 250 300 350 400 M o istu re c o n te n t ((k g w ate r).(kg so lid s) −1) Time (h) Sample 1 Sample 2 Sample 3 Sample 4 Sample 5 Sample 6 Model 95% CI
Again there was excellent agreement of model predictions with experimental results. In this case the water vapour transfer rate was clearly not linear, suggesting a change in the water vapour pressure in the package headspace. The experimentally measured increase in mass of sample 5 appears somewhat high relative to the other samples, however this was well within the 95% confidence interval of model predictions.
Based on the predicted moisture content of the SMP, it was calculated using the moisture sorption isotherm that the water activity of the SMP increased from 0.286 to 0.490 over the simulated period. This water activity range covers a relatively large proportion of the applicable range reported by the source of 0.115 to 0.538 (Joupila & Roos, 1994), suggesting that the model is correctly predicting the water vapour pressure in the package headspace.
4.6
SUMMARY
In this chapter, the development of a standard food package moisture transfer model was presented. The standard food package system contains a single individual packaging layer that may consist of multiple layers with different properties in direct
contact. Moisture transfer occurs by permeation through the packaging, as well as diffusion through perforations. Key underlying assumptions for the standard system include
instantaneous water vapour transfer in air, in the food product, and at the surface of the food product and packaging, negligible mass of water in the package headspace, and that the system can accurately be represented by one-dimension. A mathematical model was formulated and solved numerically using MATLAB® software. Error checks and validation against experimental observations were carried out, which suggested the model can accurately predict real-world observations for food packaging systems of interest.