This article discusses a study focusing on developing a mathematical model for creating and modifying the structure of chocolates. In the experimental study at the University of Birmingham's Centre for Formulation Engineering, researchers cooled and heated chocolate through rapid programmed temperature changes and then studied what happened using differential scanning calorimetry. The data was fitted to six kinetic processes. To make the modeling easier, the system of six polymorphs and liquid chocolate was simplified to model only three materials: stable solids, unstable solids, and melt. Then equations were developed to describe the nucleation of crystals, growth of stable and unstable phases, and the melting of the stable and unstable solids. The model developed simplifies the number of crystal forms, but this simplification makes it possible to model differential scanning calorimetry data. Once fitted to differential scanning calorimetry data over a range of cooling rates, the model can then be used both to predict behavior and to explain what is happening in the process. The model can be used to show how ‘frozen cone’ methods work.

## Article

Chocolate is not only a delectable treat all around the world, but a good example of an engineered food that has been designed and built industrially. Food scientists and engineers have learned to control the taste and flavor of chocolate, as well as its structure and thermal properties, so it has just the right texture and melts at just the right speed when we bite into it.

Industrially, the structure of chocolate is the result of a series of complex process operations, based on the trials and errors of thousands of cooks over hundreds of years. Today, we would like to be able to model how to create and modify that structure without so many trials and errors.

This represents a significant challenge, since molten chocolate is a complex non-Newtonian fluid, a material whose viscosity changes with the applied shear force. So are mayonnaise, peanut butter, egg whites, and also multigrade lubricants, molten polymers, and industrial slurries.

These liquids are much more difficult to model than Newtonian fluids like water. Nevertheless, some of the methods developed by engineers to model solidification processes can be used in the food industry.

Understanding the mechanics and chemistry of chocolate production helps us design manufacturing processes and new types of products. It also makes it possible to find better ways to reduce fat and sugar content while retaining chocolate as an experience that people crave. Many of the lessons learned by working with chocolate can be applied to other foods to improve their taste and nutritional qualities to make better use of natural food resources in an increasingly hungry world.

## Making Microstructured Foods

The food industry has to produce products that people want to eat at a price they can afford. Foods are often physically complex fluids and soft solids, with rheological and material properties that are time- and process-dependent, and which have a natural variation. The microstructure of the material, at micrometer to millimeter scales, is critical to taste as well as nutrition. Creation of microstructure is very difficult to describe in engineering terms, but uses a combination of mechanical process such as mixing, heating, and cooling that act on the chemistry of the components of the food.

For example, in the baking of bread, the material starts as flour and water, which is mixed to create a rheologically complex multiphase mixture of air and dough. The viscosity of the dough changes by several orders of magnitude over about one minute, and the structure then becomes a solid. Building a model of this is very difficult, and there is still no efficient model that describes the creation of bread's structure; but as bread has been made efficiently for several thousand years, clearly the experiment has proven easier than theory.

Many emulsion-based foods share these same non-Newtonian properties and offer similar challenges to modeling. Margarines and spreads, for example, are made by combining shear and temperature. First shear creates the droplet structure, and then chilling produces a continuous phase which is solid enough to prevent droplet ripening. (Droplets ripen when their size changes over time, and this eventually causes the emulsion to break down.)

To manufacture foods to meet consumer demands it is thus important to understand how structure develops. The breakdown of any structure is also critical as:

• Breakdown in the mouth determines the taste, texture, and eating pleasure of each product.

• Breakdown in the stomach and gastrointestinal tract determines what nutrients are transferred to the body and at what rate.

To control breakdown, so that the food is optimal in the mouth and in digestion, requires a combined understanding of food chemistry and material science, together with knowledge of how processing affects food structure, chemistry, and attractiveness. This understanding can be exploited to make, for example, low-fat products whose microstructure produces a mouth feel similar to the original.

## Heat Transfer in Chocolate

Chocolate is a complex structured product, a mixture of a dispersed hydrophilic phase made of sugar and cocoa solids in a continuous fat matrix rich in cocoa butter. The fat crystal structure determines both the macroscopic and sensory properties of chocolate.

The manufacture of chocolate involves a series of controlled thermal processes. The engineering problem is that there are many different crystalline states of cocoa butter, which is reported to exist as five or six different polymorphs identified using X-ray diffraction (XRD) and differential scanning calorimetry (DSC). These polymorphs (traditionally numbered using Roman numerals I-VI) have different crystal structures and melting points between 14 and 32 °C (57-90 °F).

The form that is attractive to the consumer, and is thus desired by the manufacturer, is form V, which melts rapidly in the mouth. Form V also has attractive mechanical and optical properties, giving chocolate a glossy surface and the ability to fracture. In addition, this form is easy to manufacture, as the chocolate sets in such a way that it readily demolds at the end of the process.

But it is not the thermodynamically stable form—which can be seen when chocolate is heated and then cooled. As it cools, it “blooms,” that is, the cocoa butter separates from the rest of the material to yield a mottled, phase-separated form. This is not only unattractive in appearance, but it forms crystals that do not melt at body temperature. This makes the chocolate taste gritty.

Chocolate sold commercially is thus kinetically trapped. To make form V efficiently requires either the addition of seed crystals or a complex series of heating and shear processes that temper chocolate so it will solidify into the correct form.

Tempering is central to chocolate making. Shear and temperature are applied to the chocolate to create nuclei of the right form.

The liquid chocolate is then either poured into molds or poured in a curtain to cover the centers of chocolate bars. Conventional processing methods use slow cooling tunnels, reducing temperatures by 1-2 °C per minute, which allows correctly tempered chocolate to set into the form required by the consumer.

Conventional solidification of chocolate has been extensively studied using differential scanning calorimetry, which involves measuring the heat flow required to melt or solidify the material. The combination of shear and time causes the polymorphic form to change from one which will result in untempered chocolate to one which gives the correct form.

For instance, data show that below some shear rate the material switches from a form that melts at 21 °C, which will result in stable tempered chocolate in the final product, to one that melts at 13 °C, which will result in unstable and untempered chocolate. This type of process can be modeled relatively simply using conventional computational heat transfer programs if data for the variation of effective specific heat capacity, Cp , measured by differential scanning calorimetry as a function of cooling rate, are used in the thermal conduction equation

$ρCpeff∇T∇t=∇k∇T.$

For conventional cooling rates of 1-3 °C /min., this approach is sufficient to model cooling rates and does not require kinetic data for the rate of crystallization. But what happens if we want to cool our chocolate at faster rates? This approach fails at higher cooling rates, and we require both kinetic and thermal data.

## ‘Frozen Cone’ Processing

Yet there is at least one exception to the rule that chocolate must cool slowly. Recently, processes have been developed that use cooling rates of tens of degrees per second for short times. Such processes include the manufacturing of thin hollow shapes, such as Easter eggs, which are often filled later. Known as the frozen cone process, it involves the short application (typically 3 seconds) of a cold plunger (held at about -20 °C) to shape the product to the required geometry, followed by traditional cooling tunnels. Conventional theory suggests that this should not produce a tempered product. Since the products are widely sold, the theory clearly needs modifying.

To explain how this can happen it is necessary to develop some kinetic understanding of the processes. At the University of Birmingham's Centre for Formulation Engineering, we cooled and heated chocolate through rapid programmed temperature changes and then studied what happened using differential scanning calorimetry.

We fitted the data to six kinetic processes. To make the modeling easier, the system of six polymorphs and liquid chocolate was simplified to model only three materials: stable solids, unstable solids, and melt. The stable solids are chocolate polymorphs that will lead to the correct final product, while the unstable solids are polymorphs that will lead to untempered chocolate. We then developed equations to describe the nucleation of crystals, growth of stable and unstable phases, and the melting of the stable and unstable solids.

The model simplifies the number of crystal forms, but this simplification makes it possible to model differential scanning calorimetry data. Once fitted to differential scanning calorimetry data over a range of cooling rates, the model can then be used both to predict behaviour and to explain what is happening in the process.

The model can be used to show how ‘frozen cone’ methods work. The thermal conductivity of chocolate is so low that the layer of chocolate affected by the short cooling stage—and cooled into the untempered form—is only a few hundred micrometers thick. Most of the material cools at the slow rates required to make conventionally tempered product. Much of the untempered material in that thin, flash-frozen layer transforms into a tempered structure after it is reheated by heat transfer from the rest of the chocolate, which was not affected by the frozen cone.

For chocolate processors, this is valuable information because it enables them to predict the processing time required for different chocolate products. Using the validated numerical model, we could estimate the time required to solidify the chocolate for different processing geometries and temperatures.

## Research Challenges

Overall, food processes are commonplace, but not well understood. They involve a large number of engineering processes. Improving the efficiency of these processes will create safer, healthier, and more sustainable foods. The challenge for the scientist and engineer is to understand the interaction between processing and structure, so we can control the taste and nutrient delivery of our products.

We have described work on chocolate that can be used to explain industrial processes, but we also could have discussed the design of baking or margarine processes. The engineering model makes it easier to understand existing processes and to design new ones.

The structure of the product is important both in enhancing consumer response (as taste and mouth feel) and in providing nutrition (by delivery to the stomach and GI tract). Little is known about the processes of digestion and the best way to deliver food to the body. Eating and digestion constitute a complex mixing and reaction problem that has not been widely studied by engineers. Yet this type of understanding is needed to enable rational design of better foods, and to design materials that deliver the right molecule at the right time.

Work at University of Birmingham described here was carried out as part of projects funded by the Engineering and Physical Sciences Research Council, the Biotechnology and Biological Sciences Research Council, and the Technology Strategy Board of the U.K. The research received industrial support from Cadbury, Magna Ltd., Campden BRI, Heineken, Unilever, and others. This article is based on a keynote speech delivered at the August 2010 International Heat Transfer Conference (IHTC14) in Washington, D.C. Further information on the conference is available at www.asmeconferences.org/IHTC14.