4. Mass and Heat transfer

What are the three directions of mass transfer?

1. Migration (additives (in packaging) → food)

2. Scalping (flavour → package)

3. Permeation (O₂, CO₂, H₂O vapor through wall)

What is Fick’s first law?

• Describes the diffusion of a permeant through a polymer film

• Diffusion flux J is the amount of permeant diffusing per area per time through a plane perpendicular to the flow direction.

Fickian vs Non-fickian behavior

• Fickian = concentration independent diffusion coefficients

• Non-Fickian = Concentration dependent behavior

Three different steps of permeation through a polymer film

1. Sorption (Henry’s law)

2. Diffusion (Fick’s law)

• Is typically 10³ - 10⁴ x slower than the surface steps

• Therefore, D controls the overall transmission rate, not the surface equilibria

1. Desorption (Henry’s law)

Henry’s law formula

describes how much gas dissolves into a material at the surface.

Permeability coefficient formula

• D = Diffusion coefficient

• S = Solubility coefficient

What are diffusivity and solubility?

Mass flux vs mass flow rate

• Mass flux (Φ_m/A): the rate of mass transfer per unit area (kg.m^-2.s^-1)

• Mass flow rate (Φ_m): the amount of mass passing over unit time (kg.s^-1)

EVOH

• Used as a gas barrier layer - has really low GTR

• However it is humidity sensitive

• Water plasticises the EVOH matrix, increasing free
  volume and therefore diffusivity D, raising GTR
  dramatically

• Only works well in low humidity

Units thickness normalized flux, N

units transmission rate

Units permeance (R)

Units permeability coefficient (P)

What is GTR?

GTR stands for Gas Transmission Rate. It is a specific type of transmission rate (TR) used to measure the quantity of a gas (such as oxygen, nitrogen, or carbon dioxide) that passes through a packaging film

What are the two methods to measure GTR

• Method 1: ASTM D3985 coulometric sensor

  • Continuous carrier gas flow

  • High to ultra high barrier films

• Method 2: ASTM D1434

  • Closed cell

  • Differential pressure

How do you measure WVTR?

• Done using an ASTM E96 (gravimetric desiccant method)

EVOH (ethylene-vinyl alcohol) shows excellent O₂ barrier
at low humidity, but a poor O₂ barrier at high relative humidity. What is the physical reason?

• EVOH is a crystalline copolymer containing polar hydroxyl (-OH) groups.

• Under dry conditions, these -OH groups engage in intense hydrogen bonding between the polymer chains

• Because EVOH is a hydrophilic polymer, it readily absorbs water vapor when exposed to high relative humidity

• Once absorbed, the water molecules interact with the polar -OH groups and behave as a plasticizer within the polymer structure

How to calculate GTR?

1. Calculate flux: respiration rate * weight = total flux (ml/h)

2. Determine partial pressure: p_out - p_in = partial pressure

3. Rearrange: flux (ml/h) = GTR x partial pressure x area

How is GTR measured in laminate structures?

• Using resistance in series

How do you calculate total GTR?

Retort sterilization

Heat stability of packaging plastics

Zero, first and second order models

Factors affecting reactions

• Temperature

• Water activity

• Oxygen partial pressure

What can cause deviations in the Arrhenius equation?

• Changes in physical phase (e.g. freezing)

• Other reaction becomes dominant

• Water activity change with temperature

• pH change with temperature

• Solubility changes with temperature

• Catalyst is inactivated

Temperature UHT/Aseptic sterilized can

140 C

Temperature Retort

121 C

Temperature Pasteurization of PP pouches

~100 C

Temperature of making freezer/fridge LDPE bag

<100 C

A package shows a pressure decay of ΔP = 2 mbar over 20 seconds in a chamber with volume 1000 cm³. Assuming atmospheric pressure is 1000 mbar, which of the following best describes the effect of doubling the diameter of a cylindrical leak (pinhole) on the leak flow rate?