Recommendations for the application of the model

In order to use the proposed model, some considerations have to be taken into account. One is related to the nomenclature used in this model. This point covers aspects from the units used to quantify measurements to the definitions of parameters. For example, the units for the transmission rate may vary according to the permeant and the standard. The WVTR and O2TR are normally expressed in different terms ( ݃ ή ݉ିଶ_{ή ݀ܽݕ}ିଵ _{and ݉ܮ ή ݉}ିଶ_{ή ݀ܽݕ}ିଵ respectively). In this project, the units were based on SI units, thus they correspond to ݉݋݈ ή ݉ିଶ_{ή ݏ}ିଵ _{for both permeants. This becomes important when comparisons between} experimental data and predictions are required. To avoid confusion, Table 7.2 presents the conversion between SI units and several other unit combinations.

Table 7.2 Conversion factor of permeability and transmission rate of water vapour and oxygen from the SI units to

several combinations of the units where ݉௣௘௥௠ is the molecular mass of the permeant (݃ ή ݉݋݈ିଵ), ݌௧௢௧ is the total pressure of the system (Pa) and ߠ temperature (ιܥ)

Variable Original Unit Conversion Factor Ref

Permeability (݉݋݈ ή ݉ ή ݉ିଶ_{ή ݏ}ିଵ_{ή ܲܽ}ିଵ₎ ݉݉݋݈ ή ܿ݉ ή ܿ݉ିଶ_{ή ݄}ିଵ_{ή ݇ܲܽ}ିଵ _{ʹǤ͹͹ͺ ൈ ͳͲ}ି଼ _a ݃ ή ݈݉݅ ή ݉ିଶ_{ή ݀ܽݕ}ିଵ_{ή ݉݉ܪ݃}ିଵ _{ʹǤʹͲͷ ൈ ͳͲ}ିଵଶ _݉ ௣௘௥௠ ൗ a ݉ܮ ή ݈݉݅ ή ݉ିଶ_{ή ݀ܽݕ}ିଵ_{ή ܽݐ݉}ିଵ _{͵ǤͶͻʹ ൈ ͳͲ}ିଶଶ_{ή ݌} ௧௢௧Τሺߠ ൅ ʹ͹͵ሻ a ݉ܮ ή ݈݉݅ ή ܿ݉ିଶ_{ή ݀ܽݕ}ିଵ_{ή ܽݐ݉}ିଵ _{͵ǤͶͻʹ ൈ ͳͲ}ିଵ଼_{ή ݌} ௧௢௧Τሺߠ ൅ ʹ͹͵ሻ a ݉ܮ ή ݈݉݅ ή ܿ݉ିଶ_{ή ݄}ିଵ_{ή ܽݐ݉}ିଵ _{͵Ǥʹͻ͹ ൈ ͳͲ}ିଵସ_{ή ݌} ௧௢௧Τሺߠ ൅ ʹ͹͵ሻ a ݉ܮ ή ݈݉݅ ή ܿ݉ିଶ_{ή ݏ}ିଵ_{ή ܽݐ݉}ିଵ _{ͳǤͳͺ͹ ൈ ͳͲ}ିଵ଴_{ή ݌} ௧௢௧Τሺߠ ൅ ʹ͹͵ሻ a ݉ܮ ή ݈݉݅ ή ܿ݉ିଶ_{ή ݏ}ିଵ_{ή ܲܽ}ିଵ _{ͳǤʹͲ͵ ൈ ͳͲ}ିହ_{ή ݌} ௧௢௧Τሺߠ ൅ ʹ͹͵ሻ a ݉ܮ ή ݈݉݅ ή ܿ݉ିଶ_{ή ݏ}ିଵ_{ή ܿ݉ܪ݃}ିଵ _{ͻǤͲʹ͵ ൈ ͳͲ}ିଽ_{ή ݌} ௧௢௧Τሺߠ ൅ ʹ͹͵ሻ a ܿ݉ሺܵܶܲሻ ή ݉݉ ή ݉ିଶ_{ή ݏ}ିଵ_{ή ܲܽ}ିଵ _{ʹǤʹͶͳ ൈ ͳͲ}଻ _b ܿ݉ሺܵܶܲሻ ή ݉݉ ή ݉ିଶ_{ή ݀ܽݕ}ିଵ_{ή ܽݐ݉}ିଵ _{ͳǤͻ͸ʹ ൈ ͳͲ}ଵ଻ _b ܿܿ ή ݈݉݅ ή ͳͲͲ݅݊ିଶ_{ή ݀ܽݕ}ିଵ_{ή ܽݐ݉}ିଵ _{ͶǤͻͺͶ ൈ ͳͲ}ଵ଻ _b ܤܽݎݎ݁ݎ ʹǤͻͻͲ ൈ ͳͲଵହ _b Transmission rate (݉݋݈ ή ݉ିଶ_{ή ݏ}ିଵ₎ ݃ ή ݉ିଶ_{ή ݀ܽݕ}ିଵ _{ͳǤͳͷ͹ ൈ ͳͲ}ିହ _݉ ௣௘௥௠ ൗ c ݉ܮ ή ݉ିଶ_{ή ݀ܽݕ}ିଵ _{ͳǤ͵ͻʹ ൈ ͳͲ}ିଵଶ_{ή ݌} ௧௢௧Τሺߠ ൅ ʹ͹͵ሻ c

To formulate dispersion coatings from simulations it is required to express the amount of filler in terms of mass or mass fraction. The model was designed to quantify the fillers in terms of the volume fraction with respect to the total volume of dispersion coating. The method of how to convert the amount of fillers into volume fraction was presented in the Chapter 2 Section 2.2. Thus, this method can be used in the backward direction to calculate the mass fraction and the total mass of fillers and latex required.

The model expresses the length of the fillers in terms of maximum Feret diameter. For this reason, it is recommended to verify whether the length data that are going to be used in the model correspond to this concept. Details of this parameter were presented in Chapter 3. In the same way, if information is derived from parameters such as aspect ratio or elongation of fillers, it is essential to check how those parameters were defined and compare them with the definition used in the model. As an example, the aspect ratio of filler may be calculated as the ratio between the length or a half of the length (maximum Feret diameter, equivalent diameter, or other reference length) over the thickness of fillers. Also, the similarities of the concept of some parameters may generate confusion due to their potential ambiguous definitions. For example, the aspect ratio and the elongation represent ratio between two lengths of the fillers. Thus, depending in the reference that is used to observe the fillers, care must be taken as to how those parameters were defined.

7.4 Discussion and conclusion

The sensitivity analysis showed that it is possible to use a model to evaluate different formulation of coatings. From this information, it is possible to optimise coating formulations to achieve required relative permeability. In this way, it was found that settling of the fillers in the coating or two coating layers represented an advantage in the reduction of relative permeability. This technique may reduce the material used for coating preparation and the occurrence of uncoated areas. In addition, the analysis indicated that the most important factor that affects the barrier properties of dispersion coating was the agglomeration of fillers. This observation was based on coatings with no uncoated areas. Future studies should be carried out to improve the dispersion of the fillers in the coating. The applicability of the model to optimise coating formulation must consider the definitions of the concepts used in the model in order to apply the correct information for running simulations.