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 MONOLAYER MATERIALS 1D DESORPTION SIMULATION Compliance testing emphasis The solution is calculated using a Finite Volume. A Finite Element code is also available. Advanced users:   >>how to combine simulation and experiments  >>how to take a decision according to simulation resultsRelated tool:   >>FV MULTILAYER simulation
 FAST FINITE VOLUME FORMULATION (v. 1.01)
 NOTATIONS

Notations ( physical formulation, dimensionless equations)
NAME DESCRIPTION
_F
food or food simulant
_P
plastics or polymer

_FP

ratio in F and in P
M
migrant or diffusant
0
initial
slab
sheet or planar packaging (most common)
cylindrical
cylinder (L_FP gives the internal radius)
spherical
sphere (L_FP gives the internal radius)

 INPUTS

List of input parameters (Hierarchisation: geometry, thermodynamics, transport, initial concentration, contact time)
NAME PHYSICAL PROPERTY / UNITS / MAIN ASSUMPTION / SAFE VALUE
l_P

plastic thickness [ SI unit = m)] - ONE SINGLE SIDE CONTACT

No safety value (must be measured)

L_FP

mass dilution factor [SI unit: kgF/kgP)] - NO SIDE EFFECT (1D TRANSPORT)
= mass of F / mass of P   >>mass balance details

No safety value (must be measured)   >>3D»1D approximations

K_FP

partition coefficient [SI unit: (kgM/kgF)/(kgM/kgP)] - DESORPTION EQUILIBRIUM OBEYS TO HENRY's LAW
= concentration in F at equilibrium / concentration in P at equilibrium    NB: equilibrium=no more mass transer (no gradient/no flux)

Safety value = 1000 (almost complete extraction at equilibrium)   >>Illustration of partitioning

D_P

diffusion coefficient [SI unit: m²/s] - THE FOOD/SIMULANT DOES NOT INTERACT WITH THE POLYMER

Safety value = must be [over]estimated or measured at a temperature higher than the conditions of use.
>>For a rough overestimate, use: Piringer Calculator

Bi

dimensionless mass Biot number=h·l_P/D_P [no unit] - h with SI unit m/s= EXTERNAL MASS TRANSFER RESISTANCE DUE TO FOOD TEXTURE/ABSENCE OF STIRRING

Safety value = 1000 (almost no external mass transfer resistance)   >>Illustration of uncertainty on Bi values, combined effects

C_P0

initial concentration in P [SI unit: kgM/kgP] - ASSUMES AN HOMOEGENOUS AND UNIFORM INITIAL CONCENTRATION

Safety value = 5000 ppm   >>maximum recommended concentrations

t

contact time [SI unit s] - NO REACTION AND NO MASS LOSSES DURING DESORPTION

Default value = 10 days (according to monolayer regulation for storage at ambient temperature, the maximum storage time can be used instead). Note that D_P and Bi must be overestimated respectively to their expected values at the tested temperature (e.g. 40°C).   >>Illustration of effect of dimensionless time in worst case conditions

 PARAMETER FORM

Assumptions partitioning Diffusion‡ Food texture
Reduce migration estimate by introducing additional knowledge
Increase migration estimate
 static form
parameter value unit
l_P
L_FP kgF·kgP-1
C_P0
t

 normal fine super fine hyper fine << Choose here the accuracy of the solution("normal" is always recommended as a first guess).Results are open in a new window

©2007 by INRA\Olivier Vitrac

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