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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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0 0.2 0.4 0.6 0.8 1

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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0 100 200 300 400 500 600 700

Time (√s)

Wat

er c

onte

nt (m

/m)

PT25 SPI

PT10 XRD(8X)

PT10 XRD(8Y)

PT10 XRD(11Z)

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tau = 0

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Time (√s)

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er c

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nt (m

/m)

PT130 SPI

PT115 XRD(8X)

PT115 XRD(8Y)

PT115 XRD(11Z)

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0 30 60 90 120

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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0 50 100 150 200Time (√s)

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er c

onte

nt (m

/m)

pt10 (1X)

with tau = 0, d_ext = 0

with Dv = inf

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0 50 100 150 200

Time (√s)

Wat

er c

onte

nt (m

/m)

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