Food emulsions can exhibit a wide range of different types of rheological behavior, including liquid, solid, plastic, and viscoelastic (Dickinson and Stainsby 1982, Dickinson 1992). Consequently, a variety of instrumental methods have been developed to characterize their rheological properties. Instruments vary according to the type of deformation they apply to the sample (shear, compression, elongation, or some combination), the property they measure, their cost, their sophistication, and their ease of operation (Whorlow 1992).
In many industrial applications, it is necessary to have instruments that make measurements which are rapid, low cost, simple to carry out, and reproducible, rather than give absolute fundamental data (Sherman 1970, Rao 1995). Thus simple empirical instruments are often used in quality assurance laboratories, rather than the more sophisticated and expensive instruments used in research and development. The information obtained from these empirical instruments is often difficult to relate to the fundamental rheological constants of a material because the applied stresses and strains are not easily measured or defined. Rather than a simple elongation, shear, or compression, different types of forces may be applied simultaneously. For example, when a blade cuts through a meat product, both shear and compression forces are applied together, and the sample is deformed beyond the limit where Hooke's law is applicable. To compare data from different laboratories, it is necessary to carefully follow standardized test procedures. These procedures may define experimental parameters such as the sample size and preparation procedure, the magnitude of the force or deformation, the design of the device used, the speed of the probe, the length of time the force is applied, and the measurement temperature.
For food scientists involved in research and development, it is usually necessary to use instruments which provide information about the fundamental rheological constants of the material being tested. These instruments are designed to apply well-defined stresses and strains to a material in a controlled manner so that stress-strain relationships can be measured and interpreted using available mathematical theories. Rheological properties determined using these techniques can be compared with measurements made by other workers or in other laboratories. In addition, measured rheological properties can be compared with predictions made using various mathematical theories which have been developed to relate the structure and composition of materials to their fundamental rheologi-cal properties.
It is convenient to categorize rheological instruments according to whether they utilize simple compression (or elongation) or shear forces.*
* At present, few instruments utilize bulk compression to analyze the rheological properties of food emulsions.
8.3.1. Simple Compression and Elongation
This type of test is most frequently carried out on solid or semisolid foods that are capable of supporting their own weight (e.g., butter, margarine, and frozen ice cream) (Bourne 1982, Rao et al. 1995). Measurements are often carried out using instruments referred to as Universal Testing Machines. The solid sample to be analyzed is placed between a fixed plate and a moving probe (Figure 8.12). The probe can have many different designs depending on the type of information required, including a flat plate, a blade, a cylindrical spike, and even a set of teeth!
The probe can be moved vertically, either upward or downward, at a controlled speed. Either the probe or the plate contains a pressure sensor which measures the force exerted on the sample when it is deformed by the probe. The instrument also records the distance that the probe moves through the sample. The stress and strain experienced by a material can therefore be calculated from a knowledge of its dimensions and the force and deformation recorded by the instrument.
Some of the common tests carried out using Universal Testing Machines are:
1. Stress-strain curve. The stress on a sample is measured as a function of strain as it is compressed at a fixed rate (Figure 8.1). The resulting stress-strain curve is used to characterize the rheological properties of the material being tested. The slope of stress versus strain at small deformations is often a straight line, with a gradient equal to the elastic modulus (Table 8.1). At intermediate deformations, the stress may no longer be proportional to the strain and some flow may occur, so that when the stress is removed the sample does not return to its original shape. At larger deformations, the sample may rupture and the breaking stress, strain, and modulus can be determined. The operator must decide the distance and speed at which the probe will move through the sample. For viscoelastic materials, the shape of the upward and downward curves may be different and depends on the speed at which the probe moves. This type of test is used commonly to test solid samples and gels, such as margarine, butters, spreads, and desserts.
2. Repeated deformation. The sample to be analyzed is placed between the plate and the probe, and then the probe is lowered and raised a number of times at a fixed speed so that the sample experiences a number of compression cycles (Rao et al. 1995). An ideal elastic solid would show the same stress-strain curve for each cycle. However, the properties of many materials are altered by compression (e.g., due to rupture or flow), and therefore successive compression cycles give different stress-strain curves. This type of test is often used to give some indication of the processes that occur when a food is chewed in the mouth (i.e., the breakdown of food structure).
3. Transient experiments. The sample is placed between the plate and the probe and then compressed to a known deformation, and the relaxation of the stress with time is measured (stress relaxation). Alternatively, a constant stress could be applied to the sample, and the variation of the strain is measured over time (creep). This type of experiment is particularly useful for characterizing the rheological properties of viscoelastic food emulsions (see Section 8.2.4).
By using different fixtures, the same type of instrument can be used to carry out elongation experiments. A sample is clamped at both ends, and then the upper clamp is moved upward at a controlled speed and the force required to elongate the sample is measured by the pressure sensor as a function of sample deformation. Again, the elastic modulus and breaking strength of the material can be determined by analyzing the resulting stress-strain relationship. Universal Testing Machines can also be adapted to perform various other types of experiments, such as bending or slicing.
Recently, a number of more sophisticated instruments, based on dynamic rheological measurements, have been developed to characterize the rheological properties of solids, plastics, and viscoelastic materials (Harwalker and Ma 1990, Wunderlich 1990, Whorlow 1992). In addition to carrying out the standard compression measurements mentioned above, they can also be used to carry out dynamic compression measurements on viscoelastic materials. The sample to be analyzed is placed between a plate and a probe, and an oscillatory shear stress of known amplitude and frequency is applied to it. The amplitude and phase of the resulting strain are measured and converted into a storage and loss modulus using suitable equations (Section 126.96.36.199). The amplitude of the applied stress must be small enough to be in the linear viscoelastic region of the material. These instruments are relatively expensive to purchase and therefore only tend to be used by research laboratories in large food companies, government institutions, and universities. Nevertheless, they are extremely powerful tools for carrying out fundamental studies of food emulsions. The rheological properties of a sample can be measured as a function of time or temperature, and thus processes such as gelation, aggregation, crystallization, melting, and glass transitions can be monitored. The measurement frequency can also be varied, which provides valuable information about relaxation processes within a sample.
Some complications can arise when carrying out simple compression experiments. There may be friction between the compressing plates and the sample, which can lead to the generation of shear as well as compressional forces (Whorlow 1992). For this reason, it is often necessary to lubricate the sample with oil to reduce the effects of friction. In addition, the cross-sectional area of the sample may change during the course of the experiment, which would have to be taken into account when converting the measured forces into stresses. Finally, for viscoelastic materials, some stress relaxation may occur during the compression or expansion, and so the results depend on the rate of sample deformation.
Instruments which utilize shear measurements are used to characterize the rheological properties of liquids, viscoelastic materials, plastics, and solids (Whorlow 1992, Rao 1995). The type of instrument and test method used in a particular situation depend on physicochemi-cal characteristics of the sample being analyzed, as well as the kind of information required. Some instruments can be used to characterize the rheological properties of both solids and liquids, whereas others can only be used for either solids or liquids. Certain types of viscom-
eters are capable of measuring the viscosity of fluids over a wide range of shear rates and can therefore be used to analyze both ideal and nonideal liquids, whereas the shear rate cannot be controlled in others and so they are only suitable for analyzing ideal liquids. A number of instruments can be used to characterize the rheological behavior of viscoelastic materials using both transient and dynamic tests, whereas others can only use either one or the other type of test. To make accurate and reliable measurements, it is important to select the most appropriate instrument and test method and to be aware of possible sources of experimental error.
The simplest and most commonly used capillary viscometer is called the Ostwald viscometer (Hunter 1986, Whorlow 1992). This device consists of a glass U-tube into which the sample to be analyzed is poured. The whole arrangement is placed in a thermostated water bath to reach the measurement temperature (Figure 8.13). The viscosity of the liquid is measured by sucking it into one arm of the tube using a slight vacuum and then measuring the time it takes to flow back through a capillary of fixed radius and length. The time it takes to travel through the capillary is related to the viscosity by the following equation:
where p is the density of the fluid, t is the measured flow time, and C is a constant which depends on the precise size and dimensions of the U-tube. The higher the viscosity of the fluid, the longer it takes to flow through the tube. The simplest method for determining the viscosity of a liquid is to measure its flow time and compare it with that of a liquid of known viscosity, such as distilled water:
where the subscripts s and 0 refer to the sample being analyzed and the reference fluid, respectively. This type of viscometer is used principally to measure the viscosity of Newtonian liquids. It is unsuitable for analyzing non-Newtonian liquids because the sample does not experience a uniform and controllable shear rate (Hunter 1986). U-tubes with capillaries of various diameters are available to analyze liquids with different viscosities: the larger the diameter, the higher the viscosity of the sample which can be analyzed.
188.8.131.52. Mechanical Viscometers and Dynamic Rheometers
A number of mechanical rheological instruments have been designed to measure the shear properties of liquids, viscoelastic materials, plastics, and solids (Whorlow 1992, Macosko 1994). These instruments are usually computer controlled and can carry out sophisticated test procedures as a function of time, temperature, shear rate, or frequency (Figure 8.14). Basically, the sample to be analyzed is placed in a thermostated measurement cell, where it is subjected to a controlled shear stress (or strain). The resulting strain (or stress) is measured by the instrument, and so the rheological properties of the sample can be determined from the stress-strain relationship. The type of rheological test carried out depends on whether the sample is liquid, solid, or viscoelastic. The instruments can be divided into two different types: constant stress instruments, which apply a constant torque to the sample and measure the resultant strain or rate of strain, and constant strain instruments, which apply a constant strain or rate of strain and measure the torque generated in the sample. For convenience, only constant stress instruments are discussed here, although both types are commonly used in the food industry.
A number of different types of measurement cells can be used to contain the sample during an experiment (Pal et al. 1992):
1. Concentric cylinder. The sample is placed in the narrow gap between two concentric cylinders. The inner cylinder is driven at a constant torque (angular force) and the resultant strain (angular deflection) or rate of strain (speed at which the cylinder rotates) is measured, depending on whether one is analyzing a predominantly solid or liquid sample.* For a solid, the angular deflection of the inner cylinder from its rest position is an indication of its elasticity: the larger the deflection, the smaller the shear modulus. For a liquid, the speed at which the inner cylinder rotates is governed by the viscosity of the fluid between the plates: the
* In some instruments, the outer cylinder rotates and the torque on the inner cylinder is measured.
faster it spins at a given torque, the lower the viscosity of the liquid being analyzed. The torque can be varied in a controlled manner so that the (apparent) elastic modulus or viscosity can be measured as a function of shear stress. This instrument can be used for measuring the viscosity of non-Newtonian liquids, the viscoelas-ticity of semisolids, and the elasticity of solids.
2. Parallel plate. In this type of measurement cell, the sample is placed between two parallel plates. The lower plate is stationary, while the upper one can rotate. A constant torque is applied to the upper plate, and the resultant strain or rate of strain is measured, depending on whether one is analyzing a predominantly solid or liquid sample. The main problem with this type of experimental arrangement is that the shear strain varies across the sample: the shear strain in the middle of the sample is less than that at the edges. The parallel plate arrangement is therefore only suitable for analyzing samples which have rheological properties that are independent of shear rate, and it is therefore unsuitable for analyzing nonideal liquids or solids.
3. Cone and plate. This is essentially the same design as the parallel plate instrument, except that the upper plate is replaced by a cone. The cone has a slight angle which is designed to ensure that a more uniform shear stress acts across the sample. The cone and plate arrangement can therefore be used to analyze nonideal materials.
Any of these arrangements can be used to carry out simple viscosity measurements on fluids, by measuring the variation of shear stress with shear rate. However, some of the more sophisticated ones can also be used to carry out transient and dynamic rheological tests. Typically, the rheological properties of samples are measured as a function of time or temperature.
A number of possible sources of experimental error are associated with rheological measurements carried out using shear viscometers and rheometers (Sherman 1970, Hunter 1989, Pal et al. 1992). First, the gap between the cylinders or plates should be at least 20 times greater than the diameter of the droplets, so that the emulsion appears as a homogeneous material within the device (Pal et al. 1992). On the other hand, the gap must be narrow enough to ensure a fairly uniform shear stress across the whole of the sample. Second, a phenomenon known as wall slip may occur within a viscometer or rheometer, which can cause serious errors in the measurements if not properly taken into account (Sherman 1970). It is normally assumed that the liquid in direct contact with the surfaces of the cylinders (or plates) moves with them at the same velocity (Hunter 1986). This assumption is usually valid for simple liquids because the small molecules are caught within the surface irregularities on the cylinder and are therefore dragged along with it. For an emulsion, this assumption may not hold because the droplets or flocs are greater in size than the surface irregularities. Under these circumstances, a phase separation occurs at the cylinder surface where a thin layer of continuous phase acts as a lubricant and slip occurs. Wall slip effects can be taken into account by roughening the surfaces of the cylinders or by using a range of different gap widths (Hunter 1986, Pal et al. 1992). Third, the rheological properties of many samples depend on their previous thermal and shear history, and so this must be carefully controlled in order to obtain reproducible measurements. For example, the viscosity of many foods decreases substantially upon shearing due to disruption of an aggregated network of particles or molecules, and the recovery of the initial viscosity takes a certain length of time to achieve after the shear stress is removed. Fourth, many emulsions may be susceptible to creaming or sedimentation during the course of an experiment, which should be avoided if accurate rheological measurements are required.
Many of the techniques mentioned above are unsuitable for application in the food industry because the instrumentation is too expensive, it requires skilled operators, or measurements take too long to carry out (Sherman 1970, Rao et al. 1995). For these reasons, a large number of empirical techniques have been developed by food scientists that provide simple and rapid determinations of the rheological properties of a sample. Many of these empirical techniques have become widely accepted for analyzing specific food types. Typical examples include penetrometers to measure the hardness of butters, margarines, and spreads (Sherman 1970); devices for measuring the time it takes for liquids to flow through a funnel (Liu and Masliyah 1996); or devices that measure the time it takes for a spherical ball to fall through a sample contained within a glass tube (Becher 1957). It is difficult to analyze the data from these devices using fundamental rheological concepts because it is difficult to define the stresses and strains involved. Nevertheless, these devices are extremely useful when rapid empirical information is more important than fundamental understanding.
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