Mathematical modelling and optimisation of the formulation and manufacture of aggregate food products

In this PhD study, mathematical modelling and optimisation of granola production has been carried out. Granola is an aggregated food product used in breakfast cereals and cereal bars. It is a baked crispy food product typically incorporating oats, other cereals and nuts bound together with a binder, such as honey, water and oil, to form a structured unit aggregate. In this work, the design and operation of two parallel processes to produce aggregate granola products were incorporated: i) a high shear mixing granulation stage (in a designated granulator) followed by drying/toasting in an oven. ii) a continuous fluidised bed followed by drying/toasting in an oven. In addition, the particle breakage of granola during pneumatic conveying produced by both a high shear granulator (HSG) and fluidised bed granulator (FBG) process were examined. Products were pneumatically conveyed in a purpose built conveying rig designed to mimic product conveying and packaging. Three different conveying rig configurations were employed; a straight pipe, a rig consisting two 45° bends and one with 90° bend. It was observed that the least amount of breakage occurred in the straight pipe while the most breakage occurred at 90° bend pipe. Moreover, lower levels of breakage were observed in two 45° bend pipe than the 90° bend vi pipe configuration. In general, increasing the impact angle increases the degree of breakage. Additionally for the granules produced in the HSG, those produced at 300 rpm have the lowest breakage rates while the granules produced at 150 rpm have the highest breakage rates. This effect clearly the importance of shear history (during granule production) on breakage rates during subsequent processing. In terms of the FBG there was no single operating parameter that was deemed to have a significant effect on breakage during subsequent conveying. A population balance model was developed to analyse the particle breakage occurring during pneumatic conveying. The population balance equations that govern this breakage process are solved using discretization. The Markov chain method was used for the solution of PBEs for this process. This study found that increasing the air velocity (by increasing the air pressure to the rig), results in increased breakage among granola aggregates. Furthermore, the analysis carried out in this work provides that a greater degree of breakage of granola aggregates occur in line with an increase in bend angle.

The formulation, testing and stability of 16% fat cream liqueurs

Cream liqueurs manufactured by a one-step process, where alcohol was added before homogenisation, were more stable than those processed by a two -step process which involved addition of alcohol after homogenisation. Using the one-step process, it was possible to produce creaming-stable liqueurs by using one pass through a homogeniser (27.6 MPa) equipped with "liquid whirl" valves. Test procedures to characterise cream liqueurs and to predict shelf life were studied in detail. A turbidity test proved simple, rapid and sensitive for characterising particle size and homogenisation efficiency. Prediction of age thickening/gelation in cream liqueurs during incubation at 45 °C depended on the age of the sample when incubated. Samples that gelled at 45 °C may not do so at ambient temperature. Commercial cream liqueurs were similar in gross chemical composition, and unlike experimentally produced liqueurs, these did not exhibit either age-gelation at ambient or elevated temperatures. Solutions of commercial sodium caseinates from different sources varied in their calcium sensitivity. When incorporated into cream liqueurs, caseinates influenced the rate of viscosity increase, coalescence and, possibly, gelation during incubated storage. Mild heat and alcohol treatment modified the properties of caseinate used to stabilise non-alcoholic emulsions, while the presence of alcohol in emulsions was important in preventing clustering of globules. The response to added trisodium citrate varied. In many cases, addition of the recommended level (0.18%) did not prevent gelation. Addition of small amounts of NaOH with 0.18 % trisodium citrate before homogenisation was beneficial. The stage at which citrate was added during processing was critical to the degree of viscosity increase (as opposed to gelation) in the product during 45 °C incubation. The component responsible for age-gelation was present in the milk-solids non fat portion of the cream and variations in the creams used were important in the age-gelation phenomenon Results indicated that, in addition to possibly Ca++, the micellar casein portion of serum may play a role in gelation. The role of the low molecular weight surfactants, sodium stearoyl lactylate and monodiglycerides in preventing gelation, was influenced by the presence of trisodium citrate. Clustering of fat globules and age-gelation were inhibited when 0.18 % citrate was included. Inclusion of sodium stearoyl lactylate, but not monodiglycerides, reduced the extent of viscosity increase at 45 °C in citrate containing liqueurs.

On classical and other methods of discriminant analysis and estimation of log-odds

For two multinormal populations with equal covariance matrices the likelihood ratio discriminant function, an alternative allocation rule to the sample linear discriminant function when n1 ≠ n2 ,is studied analytically. With the assumption of a known covariance matrix its distribution is derived and the expectation of its actual and apparent error rates evaluated and compared with those of the sample linear discriminant function. This comparison indicates that the likelihood ratio allocation rule is robust to unequal sample sizes. The quadratic discriminant function is studied, its distribution reviewed and evaluation of its probabilities of misclassification discussed. For known covariance matrices the distribution of the sample quadratic discriminant function is derived. When the known covariance matrices are proportional exact expressions for the expectation of its actual and apparent error rates are obtained and evaluated. The effectiveness of the sample linear discriminant function for this case is also considered. Estimation of true log-odds for two multinormal populations with equal or unequal covariance matrices is studied. The estimative, Bayesian predictive and a kernel method are compared by evaluating their biases and mean square errors. Some algebraic expressions for these quantities are derived. With equal covariance matrices the predictive method is preferable. Where it derives this superiority is investigated by considering its performance for various levels of fixed true log-odds. It is also shown that the predictive method is sensitive to n1 ≠ n2. For unequal but proportional covariance matrices the unbiased estimative method is preferred. Product Normal kernel density estimates are used to give a kernel estimator of true log-odds. The effect of correlation in the variables with product kernels is considered. With equal covariance matrices the kernel and parametric estimators are compared by simulation. For moderately correlated variables and large dimension sizes the product kernel method is a good estimator of true log-odds.