X-ray Computer Tomography

Transcription

1 X-ray Computer Tomography 1 Effect of morphology on water sorption in cellular solid foods Erik Esveld

2 2 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!

3 3 Model based on material and structure 53% Material ESEM + isotherm Sorption data 80% 89% 99% Structure XRT Cracker Prediction/validation SPI-MRI water content profiles Suitable for bound water 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 ( ).

4 4 Cell based network model a w3 a v3 I 23 I 12 a v1 a v2 a w1 a w2 Macroscopic flux only via gas phase Constricted by pore connections Lumped sorption in lamellae

5 5 ODE s for a vapor and a water Water balance per cell Local sorption from vapor to solid Geometric pore constant Diffusion time f(d 2, D w (a w ) Visco-elastic relaxation time

6 6 Constitutive relation for cell-cell conductance A i,j i,j p g = δ i, j +δ j,i d cp rp Proportional to pore area The effective diffusion distance is less than the centre-pore distance d cp and the pore radius r p 0 effective diffusion distance to pore FEM intersecting spheres distance centre pore pore radius combination distance centre-pore

7 7 X-ray micro-tomography (XRT) of crackers Proofing time 10 min (fine morphology) Proofing time 115 min (coarse morphology) voxels with a resolution of 7.8 µm

8 8 Segmetation to convex domains Binary map Euclidean distance map Watershed Labeled solid space Labeled air space Classification of cell shell

9 9 Decomposition into cells Fine structured cracker cells Coarse structured cracker 400 cells

10 10 Identification of flow connections Fine structured cracker connections Coarse structured cracker 1500 connections

11 11 Activity in gas and condensed phase 3 cubes = 10mm Fine structured Coarse structured 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)

12 12 Relative vapor conductivity Relative vapor conductivity is double for coarse structure Not because of double cell size, but double open surface area 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 % And because a few large cells carry a large part of the flux

13 13 SPI NMR profiles and simulation Fine structure: 25 mm sample Almost classical diffusion profile Good agreement with simulation

14 14 SPI NMR profiles and simulation Coarse structure: 25 mm sample Faster, More flattened profiles

15 15 Total water increase in 132 hr 20% 20% 18% 16% 4% 3% tau = 0 18% 16% PT130 SPI PT115 XRD(8X) PT115 XRD(8Y) Water content (m/m) 14% 12% 10% 8% 6% 2% 1% 0% PT25 SPI Water content (m/m) 14% 12% 10% 8% 6% PT115 XRD(11Z) 4% 3% 2% PT10 XRD(8X) 4% PT10 XRD(8Y) 2% PT10 XRD(11Z) 0% % 1% tau = 0 2% 0% % Time ( s) Time ( s) 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

16 16 What for small samples (3.3mm)? 20% 20% 18% 18% Water content (m/m) 16% 14% D v = τ=0 12% 10% 8% 6% 4% 2% Actual pt10 (1X) with tau = 0, d_ext = 0 with Dv = inf Water content (m/m) τ=0 16% D14% v = 12% 10% 8% 6% 4% 2% Actual pt115 (1X) with tau = 0, d_ext = 0 with Dv = inf 0% Time ( s) 0% Time ( s) Fine structured Coarse structured Limited local sorption rate cannot be ignored for small samples Effective diffusivity (local equillibrrium) valid for samples > 1 cm At initial water contents > 10%

17 17 Application to bread curst fractured crust punctured crust to release moisture

18 18 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 D weff = γd ρ ( 1 ) v ϕ ρ vsat sdry dw da

19 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