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Figure 6. Effect of temperature on consistency coefficient for liquid egg yolk and salted yolk.

Figure 7. Arrhenius-type plot of viscosity for 40% w/w sucrose solutions between 0 and 80°C.

Figure 7. Arrhenius-type plot of viscosity for 40% w/w sucrose solutions between 0 and 80°C.

tic, that is, they exhibit viscous flow behavior (as discussed), but also behave somewhat as elastic solids. The viscoelastic aspect of rheological behavior is particularly relevant to material response in situations of unsteady motion, that is, when stresses or strains are changing with time. Examples of this are cutting, mashing, chewing, and swallowing of solid materials, and mixing, pouring, spreading, or pumping of fluid systems.

Elasticity can be defined as that property of a food by virtue of which, after deformation and on removal of stress, it tends to recover part or all of its original size, shape, or both (18). Clearly many products, such as cheese, are elastic if the stresses are small, but if the stress is high so that the product is crushed to only a fraction of its original height, for example, then there will be little recovery. The limit of stress, beyond which a food loses its elasticity, is called the elastic limit. On mastication the elastic limit of any food will be exceeded, but the elasticity of many foods (such as Mozzarella cheese, marshmallows, gelatin desserts) is an important sensory aspect of the food. Products, such as margarines, which tend to flow when the elastic limit is exceeded are viscoelastic in their rheological behavior. A food's viscoelasticity can be measured and expressed in terms of its storage and loss moduli. The storage modulus G' is a measure of elasticity, or energy stored, and the loss modulus G" is a measure of viscosity, or energy lost, by a food when it is subjected to stress and strain (19). The ratio of the loss and storage moduli is called the loss tangent.

Viscoelastic parameters depend on food composition and temperature, so, as with other rheological measurements, the sample and test conditions must be described in detail (8).

Principles of Measuring Viscoelastic Properties

There are different techniques for measuring viscoelastic properties of foods, but probably the most commonly used is dynamic testing wherein linear viscoelastic response to very small oscillatory shear is observed. Idealized dynamic responses of elastic, viscous, and viscoelastic systems to sinusoidal oscillatory shear are shown in Figure 8. In such tests, the strain y is a sinusoidal function of time t:

where co is the oscillatory frequency and y0 is the maximum strain amplitude. The strain rate, or shear rate, will be the first derivative of strain with respect to time:

If the food behaves as an ideal elastic (Hookean) solid, stress is directly proportional to strain:

but in an ideal viscous (Newtonian) fluid, the stress is directly proportional to shear rate:

Figure 8. Idealized dynamic response of elastic, viscous, and viscoelastic systems to sinusoidal oscillatory shear.

Most foods exhibit both viscous and elastic properties at the same time and will have a viscoelastic stress response that combines the features of equations 7 and 8:

where the moduli G' and G" are as defined previously. On softening a food (increasing the temperature of a cheese or increasing the water content of a dough, for example) the food will become more liquidlike and less solidlike and its loss tangent (G"/G', eq. 4) will increase. Such objective characterization, putting numbers on what is observed sensorily, can be very valuable in product development and in quality control.

Texture Profile Analysis

Dynamic testing, as described in the preceding paragraph, can give a rigorously correct rheological characterization of a food, and it may be possible to correlate viscoelastic parameters with fundamental, molecular-level properties. The analysis of dynamic testing data becomes highly complex if the elastic limit of the product is exceeded. As indicated earlier, mastication almost always exceeds the elastic limit of solid or semisolid foods, and so do many food processing operations. A rheological method was needed to imitate the mastication (chewing) process and still provide objective data; therefore, texture profile analysis (TPA) was developed in response to this need.

In a TPA measurement, a food sample of specific dimensions is compressed, the compressive force is removed and the sample is compressed again. This two-bite sequence is imitative of the chewing process. During the test, the amount of compression (distance) and compressive force are recorded. The resultant force vs distance plot (sometimes compressive stress, force per unit area, is used instead of force) is called a TPA curve. An Instron TPA curve for Cheddar cheese is shown in Figure 9. In that measurement, a cylinder of cheese 25 mm high and 21 mm in diameter was compressed 20 mm (80%) until it was only 5 mm high. Then the platen was lifted off the cheese and lowered again to the same point. Several TPA parameters may be derived from the TPA curve: the maximum force H, which occurs at the end of the first compression, is called the hardness; the force of the first maximum F is called the fracturability (not every food shows a fractura-bility peak); the work done to compress the sample on the "first bite" is given as the area Aj, and on the second bite, A2, and the ratio A2/A1 is called the cohesiveness C; the distance S is called the springiness; the negative or tensile area A0 is the adhesion or stickiness; gumminess G is the product of hardness times cohesiveness; and chewiness is the product of hardness times cohesiveness times springiness. One advantage of the TPA method is that the parameters derived from it have been shown to correlate with sensory perception; it really is a way to replace or supplement subjective evaluation of foods with numbers and so has proven invaluable in product characterization and development.

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