## Leakage

### Quick Start

If you have a great barrier film packaging your product but have a small leak from some sort of pinhole, then the effectiveness of the packaging will be greatly reduced. Here we do some simple calculations to see the relative effects of packaging and pinholes.

Factor Value Factor Value Factor Value Factor Value
Pack Width cm Pack Height cm Pack Seam mm Hole r μm
Area cm² RH % WVTR g/m²/day OTR ml/m²/day
Pack H2O g/pack/d Pack O2 cc/pack/d Pinhole H2O Pa.m³/s Pinhole O2 Pa.m³/s
Pinhole H2O g/pack/d Pinhole O2 cc/pack/d H20 % from pinhole O2 % from pinhole

### Leakage calculations

We have a pack of width W and height H sealed with a seam length l in which there's a hole of radius r

Water or oxygen at a pressure difference of ΔP can leak in through the hole at a rate, Q that depends on the diffusion coefficient, D, in air. Q is given by:

Q=DΔP(πr^2)/l

These fluxes are in units of Pa.m³/s and ΔP is either the partial pressure of oxygen (fixed at 0.21 atm) or that of water which depends on the RH. We can convert these into g (or cc) per pack per day.

Oxygen values are all with respect to 21% O2. If you have a package OTR measured with pure O2, multiply by 0.21.

The packaging itself has a WVTR and OTR in g or cc/m²/day, which we can also convert to the amount coming through the area of the package. If you have values in other units then use the Permeability app to do the conversion.

Knowing the total coming through, we can find the % leakage due to the pinhole. It is often a high %, telling us that a small pinhole from, say, a poor heatseal can dominate shelf-life considerations.

### Acknowledgement

My thanks to Dr Yves Wyser of Nestlé for providing the background theory and the worked example (the default values when you first run the app) used in the app. Responsibility for errors/limitations are mine.