Dimensionless correlations for estimating the permeability of perforated packaging films to oxygen

Several methods have been applied to estimate the permeance provided by perforations for perforated-mediated modified atmosphere package design. However, no dimensionless correlations have been proposed that comply with the principles of dynamic similarity and could therefore be applied with confidence to different packaging systems. The purpose of this work was to apply the Buckingham π theorem and obtain a generic correlation that obeys the principles of dynamic similarity. A correlation between the Stanton number (St) and the Schmidt (Sc) and Peclet (Pe) numbers was proposed and fitted to a set of 46 datapoints. The results showed that the correlation could be simplified to a proportionality between St and the reciprocal of Pe with a proportionality constant of 0.863. That implied that the influence of the perforation diameter was so dominant that the mass transfer coefficient (which is the same as the permeance given by the perforations) was simply proportional to the reciprocal of the perforation diameter, within the experimental variability. This result was validated with an additional set of 10 experiments. Mass transfer coefficients varied between 1 and 6 cm/s.