Digital Prototyping of Milk Products

Digital prototyping has revolutionised the automotive industry by providing designers and engineers with digital models of their products that enable virtual product design, visualisation, and simulation [1]. However, digital prototyping does not exist in the food industry as the colloidal nature of most foods make them much more challenging to visualise and simulate realistically.

We present models and methods that take steps toward digital prototyping of milk products and other food colloids. To simulate the dynamics of liquid products that only exist digitally, we use deformable simplicial complexes with an optimisation-based, linear finite element method [2,3]. Visualisation of products that only exist digitally requires a model for predicting the optical properties of the product materials.

The optical properties (absorption coefficient, scattering coefficients, and phase function or asymmetry parameter) are the input needed for a Monte Carlo based graphical rendering. We have developed a model for predicting the optical properties of milk as a function of its fat and protein contents [4].

However, the model has only been validated to a limited extent. We suggest that diffuse reflectance measurements can be used for more extensive validation and for gathering data that can be used to extend our current model such that it can also predict how the optical properties develop during fermentation or acidification of milk to yogurt.

A well-established way of measuring optical properties is by static light scattering measurements. This, however, is an invasive procedure where a sample must be placed in a relatively small container (like a cuvette) and scanned by a photon detector orbiting the sample. The container must be small enough to ensure that the sample enters the single scattering regime.

Diffuse reflectance measurements have the advantage of being noninvasive. However, the analysis becomes more complex as such measurements include multiple scattering effects. To measure optical properties using diffuse reflectance, we capture high dynamic range images of laser at different wavelengths incident on a sample in situ.

The wavelength of the laser is easily adjustable as we use an NKT Photonics SuperK laser [5]. This enables us to retrieve spatially and spectrally resolved diffuse reflectance images. We also acquire images with the laser at several angles of incidence to enable oblique-incidence reflectometry. This enables us to use existing techniques [6,7] for retrieving the apparent optical properties of a sample.

The validation consists in comparison of measured optical properties with predicted optical properties. One of our goals is to extend our model for digital prototyping of milk products such that it can also predict how the optical properties develop during gelation of milk to yogurt. The influence of the colloidal aggregation on the optical properties is described by the static structure factor.

As our method is noninvasive, we can use our setup for monitoring an acidification process over time. The challenge is to investigate whether we can use the resulting diffuse reflectance images to measure the static structure factor or similar optical properties of gels. We can see some correlation between measured diffuse reflectance and the rheology of the gel.

This indicates that some quantity similar to the static structure factor is measurable using spatially resolved diffuse reflectance. There are ways of predicting the static structure factor for different types of colloids [8]. Thus if we succeed in measuring a similar quantity, we can extend our model and validate the extension.

This work was (in part) financed by the Centre for Imaging Food Quality project which is funded by the Danish Council for Strategic Research (contract no 09-067039) within the Programme Commission on Health, Food and Welfare. This work was also in part financed by the Digital Prototypes project funded by the Danish Council for Technology and Innovation (Resultatkontrakt).