x-ray computer tomography€¦ · x-ray computer tomography effect of morphology on water sorption...
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X-ray Computer Tomography
Effect of morphology on water sorption in cellular solid foods Erik Esveld
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Modeling of moisture diffusion In products like bread, crackers, snacks Crispness
Quickly lost due to water uptake Difficult to control for composite products
How does the material and structure
affect the moisture uptake and transport ? Fit stepwise sorption with effective diffusivity ? Interpretation and predictive power limited !
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Model based on material and structure 53%
80% 89%
99%
Material ESEM + isotherm Sorption data
Structure XRT
SPI-MRI water content profiles Suitable for bound water
Prediction/validation
Cracker
Interpretation Reduction to volume
average parameters
Esveld, van der Sman, van Dalen, van Duynhoven, Meinders (2012) Effect of morphology on water sorption in cellular solid foods Part1: Network based model. Part 2: Sorption in cereal crackers. Journal of Food Engineering. 109 (301-320).
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Cell based network model
Macroscopic flux only via gas phase Constricted by pore connections Lumped sorption in lamellae
aw1 aw2
aw3
av1 av2
av3
I12
I23
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ODE’s for avapor and awater
Water balance per cell
Local sorption from vapor to solid Geometric pore constant
Diffusion time
f(d2, Dw(aw) Visco-elastic relaxation time
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Constitutive relation for cell-cell conductance
Proportional to pore area
The effective diffusion distance is less than the centre-pore distance dcp and the pore radius rp
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distance centre-poreef
fect
ive
diffu
sion
dista
nce
to p
ore
FEM intersecting spheresdistance centre porepore radiuscombination
dcp
r p
i, jpi, j
i, j j,i
Ag =
δ + δ
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X-ray micro-Tomography (XRT) of crackers
Proofing time 115 min (coarse morphology) Proofing time 10 min (fine morphology)
420×420×311 voxels with a resolution of 7.8 µm
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Segmetation to convex domains
Binary map Euclidean distance map Watershed
Labeled solid space Labeled air space Classification of cell shell
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Decomposition into cells
Fine structured cracker 2 500 cells
Coarse structured cracker 400 cells
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Identification of flow connections
Fine structured cracker 10 000 connections
Coarse structured cracker 1500 connections
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Activity in gas and condensed phase
The solid potential rises up to the gas potential and together it continues like normal diffusion.
Lines show 1D continuous model based on the volume averaged properties (φ, γ, τ)
3 cubes = 10mm Fine structured
Coarse structured
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Relative vapor conductivity
Fine Coarse Relative vapor conductivity (γ) 33 ± 1% 64 ±11% Porosity (φ) 65.6 % 78.1 % Sauter diameter air cells 0.33 mm 0.75 mm Lamellae thickness 54 μm 93 μm Open surface fraction 18 % 28 %
Relative vapor conductivity is double for coarse structure Not because of double cell size, but double open surface area
And because a few large cells carry a large part of the flux
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SPI NMR profiles and simulation
Fine structure: 25 mm sample Almost classical diffusion profile Good agreement with simulation
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SPI NMR profiles and simulation
Coarse structure: 25 mm sample Faster, More flattened profiles
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Total water increase in 132 hr
Fine structured cracker Limited local sorption rate has no influence, Could as well use effective diffusivity model
Coarse structured cracker Anomalies in SPI amplitude Slight difference between simulation
directions Effect of limited local sorption only
visible in first hours
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/m)
PT25 SPI
PT10 XRD(8X)
PT10 XRD(8Y)
PT10 XRD(11Z)
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tau = 0
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PT130 SPI
PT115 XRD(8X)
PT115 XRD(8Y)
PT115 XRD(11Z)
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tau = 0
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What for small samples (3.3mm) ?
Limited local sorption rate cannot be ignored for small samples Effective diffusivity (local equillibrrium) valid for
samples > 1 cm At initial water contents > 10%
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pt10 (1X)
with tau = 0, d_ext = 0
with Dv = inf
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pt115 (1X)
with tau = 0, d_ext = 0
with Dv = inf
τ=0
Dv=∞
τ=0
Dv=∞
Actual Actual
Fine structured Coarse structured
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Application to bread curst
fractured crust punctured crust to release moisture
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Conclusions
Cellular network model Based on actual structure Provide structure statistics Allows volume averaging Validated with experimental SPI/MRI profiles
Morphology effect on transport
Vapor transport is determined by fraction open surface area Local sorption rate influenced by lamellae thickness
Effective diffusivity not related with rate of moisture sorption in solid. can not be applied for small samples
( )v vsat
weff
sdry
DD dw1da
γ ρ=
−ϕ ρ
Thank you And my co-authors: Magda Witek, Carel Windt (SPI-NMR) Gerard van Dalen (XRT) John van Duynhoven, Unilever Vlaardingen Ruud van der Sman, Marcel Meinders , WUR