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Freezing of Foods: Mathematical and Experimental Aspects

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Abstract

Freezing is a widely used method to extend the shelf life of foods. However, the frozen products are subjected to temperature fluctuations during storage and shipping, which cause events such as ice recrystallization and moisture/mass migration that further damage food quality. This paper reviews the mechanisms of ice crystal formation, propagation, and glass transition and presents experimental results about the effect of freeze-thaw cycles on ice recrystallization. The mathematical models for prediction of freezing time and description of heat and mass transfer during the freezing process are also addressed. The crystal formation and moisture/mass mobility involve multiscale characteristics, while the traditional modeling can only describe single-scale averaged effects. Therefore, the hybrid mixture theory (HMT), which is based on multiscale balance laws and entropy inequality, is also discussed in the context of the freezing problem to predict phase change, crystal growth, and thermomechanical effects.

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Abbreviations

a :

Thickness/diameter (m)

B α :

Mixture viscosity of the biopolymeric matrix (Pa s)

B if :

Biot number

c app :

Apparent specific heat (J/(kg K))

c p :

Specific heat (J/ (kg K))

D w :

Coefficient of diffusivity (m2/s)

\( {}^{\beta}{\widehat{e}}^{\alpha} \) :

Net rate of mass transfer from phase β to phase α (kg/(m3 s))

E f :

Shape factor

h :

Heat transfer coefficient (W/ (m2 k))

H :

Specific enthalpy (J/Kg3)

H w :

Enthalpy of the diffusing moisture/solute (J/Kg3)

k :

Thermal conductivity (W/ (m K))

K α :

Permeability of the α phase (m2)

L f :

Latent heat of freezing (J/Kg)

\( {\dot{m}}_w \) :

Mass flux (kg/(m2 s))

m, n, A, B:

Shape factors in Eqs. (6) and (7)

p α :

Physical pressure in phase α (Pa)

P, Q:

Shape factors in Eq. (3)

t :

Time (s)

t f :

Freezing time (s)

t t :

Thawing time (s)

t plank :

Freezing time in the Plank equation(s)

T :

Temperature (K)

T a /T b :

Cooling/heating medium temperature (K)

T c :

Thermal center temperature (K)

T cr :

Initial freezing temperature (K)

T f :

Initial freezing temperature (K)

\( {\boldsymbol{v}}_l^{\alpha, s} \) :

Relative velocity of α to β phase (m/s)

W :

Concentration of the compound

ε α :

Volume fraction of α phase

μ α :

Shear viscosity of α phase (Pa s)

ρ α :

Density of phase α (kg/m3)

ƛ:

Latent heat (J/Kg)

α :

General representation of a phase

β :

General representation of a phase

s :

Solid phase

w :

Water phase

g :

Gas phase

D α/Dt :

Material time derivative with respect to velocity of α phase particle (s−1)

Dot(⋅)D s/Dt :

Material time derivative with respect to velocity of solid phase particle

∇:

Del operator

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Acknowledgements

Thanks to USDA-NIFA for providing financial support under Award No. 2015-67017-23074.

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Authors and Affiliations

  1. Agricultural and Biological Engineering, University of Illinois at Urbana-Champaign, Urbana, IL, 61801, USA

    Ying Zhao

  2. Food Science and Human Nutrition, University of Illinois at Urbana-Champaign, Urbana, IL, 61801, USA

    Pawan S. Takhar

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  1. Ying Zhao
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Correspondence to Pawan S. Takhar.

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Author has previously published as Pawan P. Singh

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Zhao, Y., Takhar, P.S. Freezing of Foods: Mathematical and Experimental Aspects. Food Eng Rev 9, 1–12 (2017). https://doi.org/10.1007/s12393-016-9157-z

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