Food Engineering Reviews

, Volume 9, Issue 1, pp 50–70 | Cite as

Mathematical Modeling and Use of Magnetic Resonance Imaging (MRI) for Oil Migration in Chocolate Confectionery Systems

Review Article


Oil migration is a common problem in chocolate confectionery products leading to quality defects, particularly fat bloom. Several factors such as contact area, ratio of the two fat phases, type of the fat, solid fat content, presence of non-fat solid particles, particle size, viscosity, structure, concentration gradient of triacylglycerols (TAGs), and storage temperature have all effect on migration rate. Mechanism of oil migration has still not been clearly understood, but possible mechanisms have been suggested and studied in the literature. Diffusion mechanism was demonstrated and modeled in many studies. Although there are so many methods to monitor and quantify migration, magnetic resonance imaging (MRI) is among the most promising techniques as being non-destructive. This review covers the literature related to basics of migration, mechanisms, and monitoring and modeling migration in chocolate through MRI and also includes a brief description about chocolate, chocolate processing, and fundamental concepts in MRI.


Oil migration Magnetic resonance imaging (MRI) Mathematical modeling 



Contact area (cm2)


Concentration (mol/cm3)


Equilibrium concentration over time (mol/cm3)


Hazelnut concentration in filter paper (kg/m3)


Diffusion coefficient or diffusivity (cm2 s−1)


Effective diffusion coefficient (cm2 s−1)


Diffusion coefficient in the liquid phase of the cocoa butter (m2/s)




Height (cm)


Equilibrium height (cm)


Molar diffusion flux of the migrating molecules (mol cm−2 s−1)


Boltzmann constant (1.38 × 10−23 J K−1)


Kinetic rate constant


Partition distribution constant


Thickness (cm)




Slab thickness expressed as a function of time


Observed pixel intensity in MRI


Total pixel liquid proton intensity in MRI


Amount of migrated oil at infinity


Amount of migrated oil at time t


Molecular radius of the diffusing material (cm)


Time (s)


Absolute temperature (K)


Longitudinal relaxation time (spin–lattice relaxation time)


Transverse relaxation time (spin–spin relaxation time)


Echo time


Repetition time


Volume (cm3)


Void volume


Volume average velocity




Aspect ratio


Angle between the capillary and a reference horizontal datum plane


Time constant


Density (g/cm3)


Contact angle between the fluid and the capillary wall


Surface tension of the fluid (units, N m−1)




Viscosity of the medium (cp)


Global tortuosity factor

Volume fraction in chocolate


Volume fraction of liquid fat in chocolate

\( {\varnothing}_{NF}^{\mathrm{T}} \)

Volume fraction of non-fat solid in chocolate

\( {\varnothing}_{SF}^{\mathrm{Fat}} \)

Volume fraction of solid fat in the cocoa butter phase


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© Springer Science+Business Media New York 2016

Authors and Affiliations

  1. 1.Department of Food Engineering|Middle East Technical UniversityAnkaraTurkey

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