Determination of the diffusion coefficients of small solutes in cheese: A review | Dairy Science and Technology

EDPS Account

Volume 90 / No 5 (September–October 2010)

Dairy Sci. Technol., 90 5 (2010) 477-508

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Review

Table I.

Principles, advantages and drawbacks of existing methods for the determination of effective diffusion properties in cheese-like matrices.

Technique	Principle	Model	Advantages	Drawbacks	Refs.
Infinite cylinder in contact with a perfectly mixed solution	A semi-infinite cylinder of the matrix, initially free from the diffusing solute, is in contact: either with a well-stirred solution containing a constant concentration C _s of the solute at the interface or with another semi-infinite cylinder of matrix containing a concentration C _s of the solute	One-dimensional diffusion macroscopic scale measurement of the concentration profiles of the migrating solutes along the x axis as a function of time effective diffusion coefficient with Fick’s second law of diffusion Maxwell-Stefan diffusivities with the Maxwell-Stefan multicomponent approach	Can be adapted for various small molecules easy to implement	Destructive and low resolution: thin slicing of the sample gives spatial resolution of > 1 mm slow: several days of diffusion a lot of analyses are required to obtain concentration profiles as a function of the distance and the time a large number of assumptions are required when using the Maxwell-Stefan multicomponent approach lack of physical interpretation of the Maxwell-Stefan diffusivities	[29] [61] [85] [23]

Touching semi-infinite cylinders
Diffusion cell	A slab of matrix is placed in between two compartments of perfectly mixed solutions A and B of different solute concentrations	One-dimensional diffusion macroscopic scale evaluation of the solute quantity having migrated through the product slab in a given time effective diffusion coefficient with Fick’s second law of diffusion	Quite inexpensive can be adapted to a large range of products can be adapted to a multicomponent system (simultaneous diffusion of several components)	Slow: several days of diffusion accurate determination of solute concentrations is required in both compartments	[20] [89] [90] [88]
SL-NVRK	Based on the on-line monitoring of release kinetics of NaCl from a matrix containing a salt concentration C _s into water a conductivity probe, immersed in the well-stirred aqueous solution, continuously measured the electrolytes released until thermodynamic equilibrium	One-dimensional diffusion macroscopic scale effective diffusion coefficient with Fick’s second law of diffusion	Non-destructive non-invasive easy and fast (no analytical technique to quantify concentrations)	Lack of specificity of the measure with the conductivity probe modelling difficulties because of the two unknown parameters: the effective diffusion coefficients of salt and of the other electrolytes of the product can be applied to ionic solutes only	[46] [47]
PFG-NMR	Based on the attenuation of individual proton resonances under the influence of linear field gradients the amplitude of the signal is directly related to the self-diffusion coefficient of the molecule	Microscopic scale measurement of the self-diffusion coefficient of small molecules (random translational motion of molecules driven by internal kinetic energy)	No initial gradient of concentration non-destructive non-invasive promising approach for characterizing the structural modifications during the coagulation process	High cost difficulty to sample the product in the thin NMR tubes high complexity of the spectral data obtained with real food products difficulty to establish the physical link between the self-diffusion coefficient and the effective diffusivity estimated with classical methods	[13] [55] [56] [16] [22]
NMR imaging	Imaging technique used primarily in medical settings to produce high-quality images of the inside of the human body MRI is based on the principles of NMR MRI primarily images the NMR signal from the hydrogen nuclei. ²³Na-MRI is based on the paramagnetic properties of the naturally occurring ²³Na isotope	Microscopic scale measurement of the self-diffusion coefficient of water or Na or visualization of water or Na distribution	No initial gradient of concentration non-destructive non-invasive	High cost complex calibration and data handling work insensitive technique to molecules with low mobility difficulty to establish the physical link between self-diffusion coefficient and effective diffusivity	[79] [78] [45]
FRAP technique	A certain region within a fluorescently labelled sample is irreversibly photobleached with a short intense light pulse measurement of the fluorescence recovery inside the bleached area as a result of diffusional exchange of bleached fluorophores by unbleached molecules	Microscopic scale analysis of the fluorescence recovery inside the bleached area with Fick’s law of diffusion effective diffusion coefficient and fraction of mobile species	No initial gradient of concentration simple non-destructive and slightly invasive	High cost: a CLSM is necessary the migrating molecule has to be fluorescent or it must be marked by a fluorescent probe not adapted to complex and opaque media like cheese	[57] [14] [43]