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 MULTILAYER MATERIALS 1D DESORPTION SIMULATION Compliance testing emphasis The standard 2nd degree finite element method is still available for comparison.Advanced users:   >>How to take a decision with different sources of uncertainty Related tool:   >>FV MONOLAYER simulation
 FAST FINITE VOLUME FORMULATION (v. 1.01)
 NOTATIONS

The optimized finite volume discretization scheme is decribed here. Additionnaly, an introduction to finite volume methods can be found in Wikipedia.

NAME DESCRIPTION
_F or layer 0
food or food simulant
_Pi
layer i of plastics or polymer (layer 1 is in contact with F)

_FP

ratio in F and in P
M
migrant or diffusant
0
initial

 INPUTS

List of input parameters (Hierarchisation: geometry, thermodynamics, transport, initial concentration, contact time)
NAME PHYSICAL PROPERTY / UNITS / MAIN ASSUMPTION / SAFE VALUE
l_Pi thickness of the layer i [ SI unit = m)] - ONE SINGLE SIDE CONTACT
No safe value (must be measured)
L_FP Overall volume dilution factor [SI unit: m³/m³)] - NO SIDE EFFECT (1D TRANSPORT)
= volume F / volume of P
Be avare that a mass dilution factor is used for monolayers but it not practical here for computation.
No safe value (must be measured)   >>3D»1D approximations
rho_ density [SI unit: (kg/m³) - since ratios of density are used, other units are also possible] - NB: k_ and rho ARE USED AS k_/rho_
If your concentrations are expressed in mass/mass (usual case), you must assign realistic densities to achieve accurate results..
No safe value (must be measured)
k_F
k_Pi
phenomenological coefficient (Henry like coefficient such that the partition coefficient between i and j is K_ij = kj /ki [SI unit: (kgM/kgj)/(kgM/kgi)] DESORPTION EQUILIBRIUM OBEYS TO HENRY's LAW
This formulation converts concentrations into dimensionless partial pressures, pi=ki·Ci, which are continuous between materials. The equilibrium condition corresponds to uniform pi values.
Safe choice = k_Pi>1000.k_F (almost complete extraction at equilibrium)   >>How to handle uncertainty on k values
D_Pi diffusion coefficient in Pi [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 an overestimate, use: Piringer Calculator
Bi dimensionless mass Biot number [no unit] - EXTERNAL MASS TRANSFER RESISTANCE DUE TO FOOD TEXTURE/ABSENCE OF STIRRING/MASS TRANSFER IN FOOD
Bi=h.D_iref·rho_iref/(k_iref·l_iref) with iref layer with maximal transport resistance [(k_i·l_i)/(D_i·rho_i)]
NB: The internal solver use a dimensionless formulation based on the layer with a maximum transport resistance.

Safety value = 1000 (almost no external mass transfer resistance)
C0_Pi initial concentration in Pi [SI unit: kgM/kgP] - ASSUMES AN HOMOEGENOUS AND UNIFORM INITIAL CONCENTRATION IN THE LAYER _Pi
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 (use the maximum shelf life combined with the maximum storage temperature)

 PARAMETER FORM

 TIPS‡ Order: _F=Food, _P1=layer in contact with food To remove a layer: assign its length to 0 or delete it static form
parameter unit _F _P1 _P2
l -
L_FP
kgF·kgP-1 - -
rho kg·m-³ or g·cm-³
k variable
D
-
Bi none - -
C0
-
t - -

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