(39b) Classification and Regression Modelling for Investigating the Effect of Particle Size and Morphology on the Functionality of Industrial Spray Dried Milk Powder

The rehydration of instant whole milk powder (IWMP) is a complex process and is quantified using a a variety of offline tests, all of which have poor repeatability, are labour intensive, and can only be carried out post production. Consequently the ability to infer the rehydration properties of the powder whilst manufacturing would be an invaluable tool, potentially enabling corrective measures to be taken during production. However, the evaluation of alternative measurement techniques, and their subsequent correlation with subjective rehydration tests forms a considerable challenge. This work compares partial least squares regression (PLS) and classification trees, a classification technique, for determining if particle size and morphology can predict two IWMP functional rehydration tests; namely dispersibility and slowly dissolving particles (SDPs).

Dispersibility measures how quickly IWMP breaks up into individual particles and is measured by dissolving a specific amount of powder in water for a short amount of time, before being passed through a mesh, with more residue (or total solids of the reconstituted milk) indicating poor performance. SDPs on the other hand are measured by rehydrating milk, pouring it in and out of a test tube and monitoring the amount of undissolved white particles on the surface of the tube. Although the particle size is implicated in both, both tests are subjective and are sensitive to the measurement conditions, such as the stirring speed, time and temperature. Both tests infer important characteristics of bulk powder behaviour.

Particle morphology on the other hand measures individual particle characteristics, and it is proposed that morphology can be used as a proxy variable for the dispersibility and SDPs. Particle morphology includes circularity, convexity, solidity, minimum and maximum Feret diameters and elongation. Different particle morphology distributions characteristics assumed to be determined by the drying conditions and agglomeration in the dryer. For example, it is hypothesised that convexity and solidity would be an indicator for the ‘looseness’ of the agglomerate shape, and hence how quickly it can disperse in the water.

In order to investigate the effect of morphology on dispersibility and SDPs, 35 milk powder samples were collected in-situ from a large scale industrial spray dryer. The dispersibility and SDPs were measured at the industry laboratory, and the particle morphology was measured using light microscopy and image processing. The morphology characteristics were extracted for all particles larger than 100 μm, as these particles were considered to be best indicator of the agglomeration state of the powder. The distribution for each parameter was characterised using the mean, median, standard deviation, spread, and the 10^th and 90^th percentiles.

As every particle is slightly different, the result of each morphological characteristic measurement is a distribution, as opposed to a single value. This makes the elucidation of any relationship with dispersibility or SDPs more complex. The first method treated the problem by assuming that the distribution data can be treated similarly to spectral data, such as from a near infra-red (NIR) instrument, and then correlating it against the quality parameters using PLS. However, given the nature of the tests the data for SDPs and dispersibility are highly discretised. Therefore, random forests, a classification technique was also investigated for modelling the data, to determine if this is a more appropriate method. Because there were 35 total samples compared with 36 morphological predictor variables, bootstrapping was chosen to validate whether the models had predictive ability. The models were re-run multiple times with a random re-selection of testing data to determine their robustness.

For SDPs, the mean square error (MSE) varied significantly for PLS, between 15-50 % using the validation data set and 10 principal components. On the other hand, random forest classification modelling was more consistent, with re-runs reducing the root mean square error going down to 15 % within 10 trees. Dispersibility models showed slightly worse performance, with higher MSE for both PLS and random forests. However, random forest again produced more consistent models with multiple model re-runs.

PLS is a linear regression technique, often applied for spectral absorbance data. For quality parameters such as concentration of a substance, an increase in absorbance at particular wavelengths with an increase in concentration is often reasonable. However, there is no clear reason to assume that a worsening in dispersibility would change linearly with particular morphology characteristics. The physical parameters that influence the functional tests are not fully understood, and it is possible that the mechanisms that give good, moderate and poor dispersibility or SDP results are entirely different in their nature. Given that classification trees does not require this assumptions, they were chosen for interpretation. They also gave more consistent model results.

The size and morphological distribution characteristics that came up with the most importance to the model for dispersibility were mass of particles smaller than 125 µm, the solidity distribution standard deviation and 90^th percentile, and the 90^th percentiles of circularity. It is known that the amount of fine particles affects the dispersibility of the powder, as they aggregate and prevent further water from penetrating into the solid. It was hypothesised that the solidity and circularity would be representative of the agglomeration state of the dryer, and would thus be predictive variables. They are a measure of how open the agglomerate is, and the distribution describes how many open agglomerates there are. Therefore, it may be possible to use this to assess where in the spray dryer the agglomeration is occurring.

The morphological distribution characteristics that were found to be the most important for SDPs were similar to those of dispersibility, with fraction of fine particles being important, but also coarse ones, larger than 450 µm. The fraction of coarse particles may be important as they dissolve more slowly simply due to size. Both solidity and circularity were important, similar to for dispersibility, the solidity and circularity could be indicative of drying history and agglomeration conditions.

The standard functional tests being studied are complex, thus it is important to select the appropriate modelling technique to extract useful information, as certain assumptions regarding linearity may not be valid. This is especially true when the range of functional performance narrow, with only a small number of the samples being off-specification. Classification trees were investigated for their ability to model discretised outputs where linearity cannot be assumed, as required for standard PLS regression. Solidity, circularity and size were found to be correlated with SDPs and dispersibility, and are expected to indicate the agglomeration happening in the spray dryer. This data shows that morphology and size distributions have strong potential for inferring powder functionality and spray dryer operation.