Mathematical Modeling of Vegetable-Oil Crystallization

Jeppe Lindegaard Hjorth

Research output: Book/ReportPh.D. thesis

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In recent years the food sector has experienced a great boost in demand for tailor-made fats and oils to produce so-called functional foods, where ingredients have been carefully modified to yield products with specific, valuable properties. Depending on market segment and product, it may be desirable to enhance specific properties such as shelf life, viscosity, texture, sensory aspects and physical appearance.
Vegetable oils and fats constitute a considerable part of many food products such as chocolate, margarine, bread, spreads and ice cream. Several attractive properties found in these products, including flavor release, melting profile and appearance, are governed by the oils and fats added. Consequently, altering the fat phase may lead to enhanced properties of the products.
The primary focus of the present work is vegetable oils and fats originating from different sources covering the most abundant fatty-acid moieties encountered in industrial productions of food and confectionary products. The oils usually contain more than 95% triacylglycerols (TAGs), a family of molecules which is shown to govern many of the aforementioned properties of oils and fats. With few exceptions natural oils and fats comprise an abundant number of TAGs giving rise to complex chemical compositions. In this research the focus will mainly be on TAGs, disregarding minor components.
To date improvements of oils and fats have largely been based on empirical laboratory tests designed by skilled experts and specialists drawing on many years of experience and knowledge. With this in mind, the aim of the present project was to develop a transient mathematical model, describing crystallization of vegetable fats and oils, based on physicochemical phenomena. The model itself can provide the industry with a valuable tool to design and optimize products. It can also serve as a fundament for testing proposed hypotheses and facilitate realizations with respect to oil and fat crystallization.
The research carried out in this project is schematically described in Figure 2. The mathematical model is developed by combining the 5 sections. The actual work is primarily concerned with sections 2-4, while the outputs (section 5) are used as a measure of the model’s performance. Section 2 deals with the thermodynamic foundation needed to correctly understand and describe the driving force toward crystallization of TAGs from a liquid. As a consequence of the polymorphic nature of TAGs and their ability to mix non-ideally in the solid state, special measures are to be exercised to develop a versatile, predictive model describing multi-component, multi-phase solid-liquid equilibria.
With reference to research reported in literature, solid-liquid equilibria for complex systems are calculated by minimization of the Gibb’s free energy of the system. Possible phase splits are taken into account by employing the tangent-plane criterion. Non-ideal mixing leads to excess Gibb’s free energy, which can be described by an activity-coefficient model, in this case the Margules 2-suffix model. This model requires binary-interaction parameters for each pair of TAGs. Obtaining these parameters for pure binary mixtures would be extremely time-consuming, expensive and in some cases impossible due to unavailability of the pure TAGs. A new approach to simultaneously determine all interaction parameters for complex, industrial oils is developed. A series of solid-fat-content (SFC) measurements are performed for different oil blends and temperatures and the experimental SFC values are matched by the model by varying the interaction parameters. The final model with the fitted interaction parameters performs excellently and is validated against independent oil blends. This SLE model shapes the foundation needed in the following kinetic and mechanistic assessments.
Section 3 extends the developed SLE model to deal with TAG crystallization under non-isothermal conditions and deals with appropriate description of nucleation and growth phenomena. The developed model is fitted and tested against SFC curves recorded for various oil blends and temperature profiles while some necessary kinetic constants are obtained via focusedbeam-reflectance measurements (FBRM). The model includes primary and secondary nucleation and growth being governed by both integration and diffusion kinetics. Both growth constants are temperature dependent and the integration constant is allowed to change value as a function of TAG type (tri-saturated, di-saturated, etc.) due to the different degrees of conformational order needed for integration to take place. The diffusion constant is related to the viscosity of the system which in turn is a function of the solid-volume fraction. In total five adjustable parameters are indentified and fitted to experimental SFC curves. Using the fitted parameters the transient model can describe the course of crystallization for a number of oil blends and accommodates the effect of varying the cooling rate.
Section 4 refines the model behavior by introducing a population balance (PB), keeping track of the chord-length distribution (CLD) (derived from particle-size distribution (PSD)) and providing a more realistic picture of the surface area available for growth. A discretized PB, based on the moving-pivot technique, is introduced. The PSD is divided into a number of segments and this approach is numerically easy to handle and well-behaved. The method proves fast, precise and flexible with respect to mechanistic dependencies. All particles are assumed to exhibit spherical geometry and nucleation, growth and aggregation events are accommodated in the PB. Five adjustable parameters are fitted by comparing the model output with experimental CLDs recorded using FBRM. Good results are obtained taking only nucleation and growth into account and disregarding aggregation. The model describes the experimental CLDs well, not only in terms of the overall shape but also with respect to trends. The model correctly describes broader distributions as the concentration of crystallizing TAGs is increased and more narrow distributions as the cooling rate is increased.
Original languageEnglish
PublisherTechnical University of Denmark
Number of pages191
Publication statusPublished - 2014


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