LINK TO THE ORIGINAL PAGE CACHED IMAGE 01/11/2007 SAFE FOOD PACKAGING PORTAL

     getting started        notations        list of inputs        parameter form     FV MONOLAYER       FV MULTILAYER  

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1D DESORPTION SIMULATION STANDARD FINITE ELEMENT FORMULAITON for multi geometries (v. 1.02)

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)

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 paritioning

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: the 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 (see above for details)
Advanced users:   >>how to combine simulation and experiments  >>how to take a decision according to simulation results
Optimized codes:   >>Optimized FV MONOLAYER simulation  >>Optimized FV MULTILAYER simulation

parameter
value
unit
l_P
L_FP
kgF·kgP-1
K_FP
kgF·kgP-1
D_P
Bi
none
C_P0
t


<< The solution is calculated using a 2nd degree finite element technique and integrated over time by a variable order implicit scheme. As a result, the solution is expected
to be calculated very fast and accurately in time. However, the solution may be inconsident for low L_FP/K_FP values. If some inconsistency is suspected in the solution
(e.g. oscillation, value exceeding the equilibrium value), check the result with a superfine method. It uses an absolutely stable integration time scheme with a small
spatial discretization step. The alternatives to confirm the results are:
   to compare with the semi-analytical solution described in Vitrac and Hayert (2006)
   to compare with the solution obtained with a finite volume formulation (absolutely conservative but may be inaccurate in time), use the multilayer FV code with a
     single layer as input.

2007 by INRA\Olivier Vitrac