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Validation of a Difussion Model Using Moisture Profiles Measured by Means of TD-NMR in Apples (Malus domestica)

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Abstract

Time domain nuclear magnetic resonance has been used to obtain experimental moisture profiles of apples during convective drying. The drying curves obtained at temperatures of 50 °C, 60 °C, 70 °C, 80 °C and 90 °C during convective drying have been modelled using a diffusion model, solved by a finite elements method. The parametric identification was carried out by comparing the experimental and simulated drying curves, and the validation of the model was conducted by comparing the experimental and the simulated moisture profiles. The proposed diffusion model including solid shrinkage and temperature influence on the diffusion coefficient allowed an adequate prediction of not only the drying curves (MRE = 5.4 ± 0.8%) but also the moisture profiles (MRE = 11.0 ± 1.7%). These results support the hypotheses admitted to formulate the mathematical equations of the model and demonstrate the usefulness of this methodology to validate the proposed model.

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Abbreviations

A r :

Rectangular face area (m2; Eq. 2)

A s :

Square face area (m2; Eq. 1)

a w :

Water activity (Eq. 8)

C 0 :

Entropic accommodation factor (Eq. 9) dimensionless

C g :

Guggenheim constant (Eq. 8)

D 0 :

Pre-exponential factor (m2/s; Eq. 4)

D e :

Effective diffusion coefficient (m2/s; Eq. 3)

e 1 :

Short thickness (m; Eq. 1)

e 2 :

Long thickness (m; Eq. 2)

e 02 :

Initial long thickness (m; Eq. 7)

E a :

Activation energy (J/mol; Eq. 4)

ΔH 1 :

Difference between the heats of sorption of the monolayer and the multilayer of water (J/mol; Eq. 9)

ΔH 2 :

Difference between the vaporisation heat of water and the sorption heat of the multilayer of water (J/mol; Eq. 10)

K 0 :

Entropic accommodation factor (Eq.10)

K g :

Constant in the GAB model (Eq. 8)

L :

Half length of the parallelepiped (m)

MRE :

Mean relative error (%)

M :

Moisture content (kg water/kg wm)

N :

Number of samples (Eq. 6)

R :

Universal gas constant (J/mol K; Eq. 4)

RH :

Relative humidity (%)

RMSE :

Root mean square error

r 2 :

Correlation coefficient

SE :

Standard error

S y :

Standard deviation (sample; Eq. 5)

S yx :

Standard deviation (estimation; Eq. 5)

T :

Temperature (°C)

t :

Time (s)

V c :

Calculated value (Eq. 6)

V e :

Experimental value (Eq. 6)

var :

Explained variance (%)

W :

Average moisture content (kg water/kg dm)

W e :

Equilibrium moisture content (kg water/kg dm)

W m :

Monolayer moisture content (kg water/kg dm; Eq. 8)

W l :

Local moisture content (kg water/kg dm) (Eq. 3)

x :

Distance (m)

δ :

Nominal length dimensionless

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Acknowledgements

The authors would like to acknowledge the financial support from the MICINN (DPI2009-14549-C04-02) and the Research Fellowship of the Conselleria d'Innovació, Interior i Justícia (Govern de les Illes Balears).

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Authors and Affiliations

  1. Department of Chemistry, Universitat de les Illes Balears, Cra. Valldemossa km 7.5, 07122, Palma de Mallorca, Spain

    Óscar Rodríguez, Valeria S. Eim, Susana Simal, Antoni Femenia & Carmen Rosselló

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  1. Óscar Rodríguez
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  2. Valeria S. Eim
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  3. Susana Simal
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  4. Antoni Femenia
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  5. Carmen Rosselló
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Correspondence to Susana Simal.

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Rodríguez, Ó., Eim, V.S., Simal, S. et al. Validation of a Difussion Model Using Moisture Profiles Measured by Means of TD-NMR in Apples (Malus domestica). Food Bioprocess Technol 6, 542–552 (2013). https://doi.org/10.1007/s11947-011-0711-7

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  • DOI: https://doi.org/10.1007/s11947-011-0711-7

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