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T7 · Transport / BarrierPlastic Packaging EngineeringGATE 2027 Syllabus (XE5)Shop-Floor Standard
Fickian Film Oxygen Transmission Rate (OTR)
Calculates the steady-state volumetric flux of oxygen gas passing through a flexible packaging film per unit area per day (cc/m²/day).
Mathematical Canonical Relation
Plain Formula: OTR = (P_O2 * DeltaP) / t
Live Engineering Parameter Solver
Input your production or test values below for instant, verified output.
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P_O2
Range: 0.01 – 3000 cc·mil/(m²·day·atm)
DeltaP
Range: 0.05 – 1 atm
t_mil
Range: 0.1 – 10 mil
Calculated Engineering Result:
0.32 cc/(m²·day)
Engineering Verification:High-barrier food packaging classification.
When & Where to Apply
Use when designing food, snack, or pharmaceutical multi-layer packaging to determine barrier layer thickness required for target shelf-life.
Common Engineering Pitfalls
- Confusing material permeability coefficient PO2 with total film transmission rate OTR
- Ignoring relative humidity effects on EVOH moisture sensitivity
Physical Assumptions & Validity Limits
- Steady-state Fickian diffusion
- Henry’s law gas solubility relationship
- Constant gas partial pressure differential
Variable Symbols, SI Units & Dimensional Specifications
| Symbol | Variable Meaning | SI Unit | Typical Industrial Range |
|---|---|---|---|
| OTR | Oxygen transmission rate | cc/(m²·day) | — |
| P_{O2} | Permeability coefficient | cc·mil/(m²·day·atm) | 3.0 |
| \Delta p | Oxygen partial pressure difference | atm | 0.21 |
| t | Barrier layer thickness | mil (1 mil = 25.4 μm) | 2.0 |
Worked Industrial Numerical Example: EVOH vs LLDPE Barrier Packaging OTR Comparison
Problem Statement:
Compare the OTR of (a) a 2.0 mil LLDPE film (PO2 = 2,500 cc·mil/m²·day·atm) versus (b) a 0.2 mil EVOH barrier layer (PO2 = 0.05 cc·mil/m²·day·atm) under ambient air (0.21 atm O2).
Step-by-Step Numerical Solution:
- LLDPE OTR = (2500 * 0.21) / 2.0 = 262.5 cc/(m²·day)
- EVOH OTR = (0.05 * 0.21) / 0.2 = 0.0525 cc/(m²·day)
Final Answer: LLDPE = 262.5 cc/m²/day; EVOH = 0.0525 cc/m²/day
💡 Engineering Interpretation: A 0.2 mil (5 micron) EVOH layer provides a 5,000x barrier improvement over PE, preventing lipid oxidation in snack food.
Authoritative Technical Reference & Source Provenance
Plastic Packaging: Materials, Processing, Applications by O. G. Piringer & A. L. Baner (Wiley-VCH, 2008), 2nd Edition, Page 110-118.
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