Rheological Testing of Foods
Rheology is the science concerned with the deformation and flow of matter. Most rheological tests involve applying a force to a material and measuring its flow or change in shape. Rheology is important in a number of different areas of food science. Many of the textural properties that human beings perceive when they consume foods are largely rheological in nature, e.g., creaminess, juiciness, smoothness, brittleness, tenderness, hardness, etc. The stability and appearance of foods often depends on the rheological characteristics of their components, e.g., emulsions, spreads and pastes. The flow of foods through pipes or the ease at which they can be packed into containers is largely determined by their rheology.
The obvious importance of rheology in foods means that it is essential for food scientists to have analytical techniques to measure these properties. Instruments are needed for routine analysis in quality assurance laboratories, and for fundamental studies in Research and Development laboratories. Fundamental studies aim to better understand the complex relationship between the overall rheological properties of foods and the type and concentration of ingredients that they contain. This type of information enables food manufacturers to optimize the ingredients and processing conditions needed to produce high quality and reliable products.
Foods are compositionally and structurally complex systems that can exhibit a wide range of different rheological behaviors, ranging from low viscosity fluids (e.g., milk or orange juice) to hard solids (e.g., hard candy). One of the main objectives of food rheologists is to develop instrumentation and concepts that can be used to measure and describe these various types of rheological behavior. Despite the diversity and complexity of food systems it is possible to systematically characterize many of their rheological properties in terms of a few simple models: the ideal solid, the ideal liquid, and the ideal plastic. Complex systems can then be described by combining two or more of these simple models. In the following sections the concepts of the ideal solid, ideal liquid and ideal plastic will be introduced, as well as some of the deviations from these models that commonly occur in foods.
In our everyday lives we come across solid materials that exhibit quite different rheological properties. Some may be soft, others hard; some may be brittle, others rubbery; some may break easily, others may not. Despite this range of different behavior it is still possible to characterize the rheological properties of many solid foods in terms of a few simple concepts.
A material that exhibits ideal elastic behavior is referred to as a Hookean solid after the scientist (Robert Hooke) who first described it. Hooke observed experimentally that there was a linear relationship between the deformation of a solid material and the magnitude of the applied force. In fact, he found that the force per unit area (or stress) was proporitional to the relative deformation (or strain). Hookes law can be summarized by the following statement:
Stress = Modulus ´ Strain
Most elastic materials only obey Hookes law at small deformations. Equation 1 applies to a number of different types of deformation that a solid can
experience. The actual values of the stress, strain and constant used in the equation depend on the nature of the deformation. For an isotropic and homogeneous solid there are three major types of deformation that are important: simple shear, simple compression (or elongation) and bulk compression. Each of these different types of deformation can be characterized by its own stress-strain relationship.
Simple shear: Stress = t = F/A
Strain = g = DL/L = cosf
Modulus = G (shear modulus)
Simple compression: Stress = F/A
Strain = DL/L
Modulus = Y (Young’s modulus)
Bulk compression: Stress = t = F/A = Pressure, P
Strain = DV/V
Modulus = K (Bulk modulus)
Hooke’s law is only strictly applicable to elastic materials at low strains, and so most fundamental rheological studies of foods have been concerned with small deformations. Nevertheless, the rheological behavior of foods at large deformations is often more relevant to their actual use, e.g., mastication or cutting of foods. For this reason it is important to be able to systematically characterize the behavior of solids at large deformations. At strains just above the Hookes region the stress is no longer proportional to the strain, and therefore an apparent modulus is defined (just as an apparent viscosity is defined for non-Newtonian liquids). It is always necessary to stipulate the strain at which the apparent modulus of a material is measured. Even though the material does not obey Hookes law it still returns to its original shape once the force is removed. Above a certain deformation, however, a solid may not return back to its original shape once the force is removed, because it either breaks or flows. A material that breaks is referred to as brittle, whereas a material that flows is referred to as plastic (see below). The stress at which a material ruptures is often called the breaking strength. A material usually ruptures or flows because the forces that hold the atoms or molecules together are exceeded.
Liquid foods also exhibit a wide range of different rheological properties. Some have very low viscosities and flow easily, like water or milk, whilst others are very viscous, like honey or syrup. Even so, it is still possible to characterize their rheological properties using a few simple concepts.
The ideal liquid is often referred to as a Newtonian liquid after the scientist who first described it (Sir Isaac Newton). The ideal liquid has the following characteristics: it is incompressible (its volume does not change when a force is applied to it); isotropic (its properties are the same in all directions); and structureless (it is homogeneous). The rheological properties of the ideal liquid are defined by the following equation, which encapsulates the experimental finding that the rate of shear strain is proportional to the applied shear stress t.
Stress = Viscosity ´ Rate of Strain
t = hdg/dt
where, the constant of proportionality, h, is called the viscosity. The viscosity arises from the friction between the liquid layers as they slide past one another. The lower the viscosity of a liquid, the less resistance between the liquid layers, and therefore the smaller the force required to cause the top plate to move with a given velocity, or the faster the top plate moves when a given force is applied. The ideal viscous fluid differs from the ideal elastic solid because the shear stress is proportional to the rate of strain, rather than the strain. The units of shear stress t are N m-2 (or Pa), and those of shear rate are s-1, thus the viscosity h has units of N s m-2 (or Pa s) in the S.I. system. Viscosity can also be expressed in the older c.g.s. units of Poisse, where 1Pa s = 10 Poisse. Thus the viscosity of water can be quoted as 1 mPa s, 0.001 Pa s, 0.01 Poise or 1 centipoise, depending on the units used. A number of foods exhibit ideal Newtonian behavior under certain conditions, e.g., water, tea, coffee, oils, honey and milk. Nevertheless, there are many others that have non-ideal behavior and their properties cannot be described adequately by Equation 5.
Non-ideality may manifest itself in a number of different ways, e.g., the viscosity of a liquid may depend on the rate and/or the time over which the shear force is applied, or the fluid may exhibit some elastic as well as viscous properties.
Shear-Rate Dependent Non-ideal Behavior
In an ideal liquid the viscosity is independent of the shear rate. In many liquid foods the viscosity varies with the shear rate, but is independent of the length of time that the food is subjected to the shear. For example, the viscosity of a liquid food may increase or decrease as the shear rate is increased, rather than staying constant as for a Newtonian liquid. In these foods the viscosity is referred to as an apparent viscosity, because it is no longer a constant. The dependence of the apparent viscosity on shear rate, means that it is crucial to stipulate the shear rate used to carry out the measurements. The choice of shear rate to use when measuring the apparent viscosity of a non-ideal liquid is a particularly important consideration when carrying out rheological measurements in a laboratory which are supposed to mimic some process which occurs in a food naturally, e.g., flow through a pipe, the creaming of an emulsion droplet, mastication. The test in the laboratory should use a shear rate which is as close as possible to that which the food actually experiences in practice. The two most common types of shear-rate dependent non-ideal liquids are:
Time-dependent Non-Ideal Behavior
The apparent viscosity of the fluids described in the previous section depended only on the shear rate, and not on the length of time that the shear was applied. There are many foods whose rheological properties do depend on the duration of the applied shear. In some cases this change is reversible and the fluid will recover its original apparent viscosity if it is allowed to stand at rest for a sufficiently long period. In other cases the change brought about by shearing the sample is irreversible. An appreciation of the time-dependency of the flow properties of foods is of great practical importance in the food industry. The duration of pumping or mixing operations, for instance, must be carefully controlled to assure that the food sample has the most appropriate apparent viscosity. If a food is mixed or pumped for too long it may become too thick or too runny and thus loose its desirable rheological properties. Time dependent non-Newtonian behavior is classified in two different ways:
In some fluids the time dependent rheological properties are irreversible, i.e., once the shear force is removed the system does not regain its initial rheological properties. Liquids fluids that experience permanent change are called rheodestructive. This type of behavior might occur when aggregated particles are permanently disrupted and do not reform with time.
Many foods exhibit a kind of rheological behavior known as plasticity. A plastic material has elastic properties below a certain applied stress, the
Ideal Plastic Behavior
The ideal plastic material is referred to as a Bingham Plastic after the scientist who first proposed this type of rheological behavior (Sherman 1970). Two equations are needed to describe the rheological behavior of a Bingham plastic, one below the yield stress and one above it:
t = Gg (for t < t0)
t - t0 = hdg/dt (for t ³ t0)
where G is the shear modulus, h is the viscosity and t0 is the yield stress. Foods that exhibit plastic behavior usually consist of a network of aggregated molecules or particles dispersed in a liquid matrix. For example, margarine and butter consist of a network of tiny fat crystals dispersed in a liquid oil phase. Below a certain applied stress there is a small deformation of the sample, but the weak bonds between the crystals are not disrupted. When the critical yield stress is exceeded the weak bonds are broken and the crystals slide past one another leading to flow of the sample. Once the force is removed the flow stops. A similar type of behavior can be observed in emulsions containing three-dimensional networks of aggregated droplets.
Above the yield stress the fluid flow may exhibit non-Newtonian behavior similar to that described earlier for liquids, e.g. psuedoplastic, dilatant, thixotropic, rheopectic. The material may also exhibit non-ideal elastic behavior below the yield stress, e.g., the yield point may not be sharply defined, instead, the stress may increase dramatically, but non instantaneously, as the shear rate is increased.
Most food materials are not pure liquids, or pure solids, but have rheological properties that are partly viscous and partly elastic. Plastic materials exhibit elastic behavior below the yield stress, and viscous behavior above the yield stress. In contrast, viscoelastic materials exhibit both viscous and elastic behavior simultaneously. When a force is applied to a viscoelastic material it does not instantaneously take-up its new dimensions (as a purely elastic material would), it takes some finite time. In addition, when the force is removed the material does not return instantaneously back to its non-deformed state, and it may even remain permanently deformed.
Two types of experimental tests are used by food scientists to characterize the viscoelastic properties of foods: transient and dynamic measurements. Both types of tests can be carried out using simple shear, simple compression or bulk compression of foods, depending on how the instruments are designed. Since shear tests are the most commonly used in the food industry at present only these will be considered. Nevertheless, simple and bulk compression tests can also be carried out in a similar manner.
In a transient experiment a constant force is applied to a material and the resulting strain is measured as a function of time, or vice versa.
· Creep. In a creep experiment a constant stress is applied to a sample and the corresponding strain is followed as a function of time. Results are expressed in terms of a parameter called the compliance J = strain/stress, because the stress remains constant. The change in strain of a material can also be measured when the stress is removed, i.e. creep recovery. Viscoelastic materials can often be characterized by a modulus and a relaxation time, which can be determined by an analysis of the strain curves with time. A distinction is usually made between a viscoelastic solid and a viscoelastic liquid. When a constant force is applied to a viscoelastic solid the creep compliance reaches a finite equilibrium value (JE) at long times. When the force is removed the compliance tends to zero. On the other hand, when a constant force is applied to a viscoelastic liquid the compliance continues to increase at a steady rate, and when the force is removed the material does not return to its initial shape.
· Stress relaxation. Instead of applying a constant force and measuring the change in the strain with time, it is also possible to apply a constant strain and measure the change in the stress with time. These types of experiments are referred to as stress relaxation. The same types of information can be obtained from either creep or stress relaxation experiments, and the method used usually depends on the instrument available.
In a dynamic experiment a sinusoidal stress is applied to a material and the resulting sinusoidal strain is measured, or vice versa. In a dynamic experiment, a sinusoidal stress is applied to a material and the resulting sinusoidal strain is measured, or vice versa. In this section, we will only consider the case where a stress is applied to the sample and the resultant strain is measured. The applied stress is characterized by its maximum amplitude (t0) and its angular frequency (w). The resulting strain has the same frequency as the applied stress, but its phase is different because of relaxation mechanisms associated with the material. Information about the viscoelastic properties of the material can therefore be obtained by measuring the maximum amplitude (g0) and phase shift (d) of the strain. The amplitude of the applied stress used in this type of test is usually so small that the material is in the linear viscoelastic region, i.e., the stress is proportional to the strain, and the properties of the material are unaffected by the experiment. The dynamic shear rheological properties of a material can be described by the complex shear modulus G = G’ + iG”, where the parameters G' and G" are referred to as the storage modulus and loss modulus, respectively. This is because G' is the measure of the energy stored in the material per cycle, whereas G" is a measure of the energy dissipated as heat (and therefore lost) per cycle. For a perfectly elastic material the stress and strain are completely in phase, and for a perfectly viscous material all the energy is lost as heat and the stress and strain are 90o out-of-phase. The phase angle that the stress lags behind the strain is given by the symbol d. The phase angle of a material provides a useful insight into its viscoelastic properties: d = 0o for a perfectly elastic solid; d = 90o for a perfectly viscous fluid; and, 0 < d < 90o for a viscoelastic material. The more elastic a material (at a particular frequency), the smaller the phase angle, and the lower the amount of energy dissipated per cycle.
Measurement of Rheological Properties
Foods are diverse and complex materials which exhibit a wide range of different rheological properties, e.g., solids, liquids, plastics and viscoelastic behaviour. Consequently, a variety of different instruments have been developed for characterizing their rheological properties. Instruments vary according to the type of deformation they apply to the sample (shear, compression, elongation or some combination), the property measured, the cost, the ease of operation etc.
In many industrial applications it is necessary to have instruments which make measurements that are rapid, low-cost, simple to carry-out and reproducible, rather than giving absolute fundamental data. Thus simple empirical instruments are often used, rather than the sophisticated and expensive instruments often used in research and development. The information obtained from these instruments is difficult to relate to the fundamental rheological properties of a material because the stresses and strains applied are not easily defined. Rather than having a simple elongation, shear or compression, different types of forces may be applied simultaneously. For example, when a blade cuts through a meat sample, 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 for and the measurement temperature.
For food scientists involved in research and development it is often more important to use instruments that 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 interpreted using suitable mathematical analysis. Rheological properties determined using these techniques can be compared with measurements made by other workers in the literature or in other laboratories. In addition, measured rheological properties can be compared with predictions made using various mathematical theories that have been developed to relate the structure and composition of materials to their fundamental rheological properties. There is an increasing trend in the food industry to use instruments that provide more fundamental data where ever possible.
Instruments can be conveniently categorized 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 foods.
Simple compression and elongation
These types of measurements are most frequently carried out on solid or semi-solid foods that are capable of supporting their own weight. Fundamental measurements are usually 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. The probe can have many different designs depending on the type of information required. Some of the most commonly used designs include: a flat plate, a blade, a cylindrical spike and a set of teeth! The type of probe used may also depend on whether or not the analyst is trying to mimic some actual process, e.g., chewing, biting or cutting. The probe can be moved vertically, either upwards or downwards, at a controlled speed (e.g., 10 mm per minute). The lower plate usually contains a pressure sensor that measures the force exerted on the sample when it is deformed by the probe. Thus the instrument measures both the stress and strain on the sample as it is compressed. Some of the common tests carried out using Universal Testing Machines are:
By using different fixtures the same instruments can be used to carry out elongation experiments. A sample is clamped at both ends, then the upper clamp is moved upwards at a controlled speed and the force required to elongate the sample is measured by the pressure sensor. Again the elastic modulus and breaking strength can be determined. Universal Testing Machines can also be adapted to perform various other types of experiments, e.g., 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. As well as carrying out standard compression measurements, they can also be used to carry out transient or dynamic compression measurements on viscoelastic materials. These instruments are usually expensive ($40,000 - $80,000), and are therefore only available to large food companies and some Research laboratories. Nevertheless they are extremely powerful tools for carrying out fundamental studies on food materials. 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.
Some complications can arise when carrying out simple compression experiments. There may be friction between the compressing plates and the sample that can lead to the generation of shear as well as compression forces. 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 deformation, thus the data depends on the rate of sample deformation.
Instruments that measure shear are used to characterize the rheological properties of liquids, viscoelastic materials, plastics and solids. The instrument and test-method used depends on the nature of the sample to be analyzed. Some instruments are only useful for low viscosity ideal liquids, others for solids, and others can be used for a wide range of different materials. Some instruments are capable of measuring the viscosity over a wide range of shear rates, whereas others make the determination at a single shear rate (and are therefore only suitable for analyzing Newtonian liquids). Some instruments are only capable of carrying out transient measurements, whereas more sophisticated instruments are also capable of carrying out dynamic measurements. 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 the Ostwald viscometer. This 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. The viscosity of the liquid is measured by sucking up liquid into one of the arms of the tube using a slight vacuum and then measuring the time taken for it to flow back through a capillary of known radius and length. The time t taken to travel through the capillary is related to the viscosity by the following equation:
t = C´h/r
where, r 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:
hS = h0 (tSrS/ t0r0)
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. 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 that can be analyzed.
Mechanical Viscometers and Dynamic Rheometers
A number of analytical instruments have been designed that can measure the shear properties of liquids, viscoelastic materials, plastics and solids. These instruments are usually computer controlled and can carry out sophisticated test procedures as a function of time, temperature, shear rate or frequency. Most of these instruments can be adapted to carry out tests using either the concentric cylinder, cone-and-plate or parallel plate arrangements discussed below. All of these arrangements can be used to measure the viscosity of liquids, the viscoelasticity of semi-solid foods or the elasticity of solids. The instruments can be divided into two different types: constant stress instruments apply a constant torque to the sample and measure the strain or rate of strain generated, whereas constant strain instruments apply a constant strain or rate of strain and measure the torque generated in the sample. For convenience, we will just mention constant stress instruments below.
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 them can also be used for more expensive applications such as the transient and dynamic rheological tests mentioned earlier. Typically the rheological properties of samples are measured as a function of time or temperature.
Many of the techniques mentioned above are unsuitable for application in the food industry because the instrumentation is too expensive, requires highly skilled operators or measurements take too long to carry out. For this reason a large number of highly empirical techniques have been developed by food scientists. Many of these empirical techniques have become widely accepted for analyzing specific food types. Typical examples may be penotrometers to measure the hardness of fats, specially designed guillotines for analyzing meat samples, devices for measuring the flow of sauces when release from a cup etc. It is difficult to analyze the data from these devices using fundamental concepts because it is difficult to define the stresses and strains involved. Nevertheless, these devices are extremely useful where rapid empirical information is required.
Gels. Gels are good systems for fundamental rheological studies because they are usually isotropic and homogeneous and can be prepared in many different shapes. Consequently, a huge amount of work has been carried out on characterizing the rheological properties of food gels. Both simple compression and shear measurements are used routinely. Typical experiments might be:
· Prepare a solution of the protein or polysaccharide to be analyzed. Place it in a dynamic rheological device which measures the shear modulus of samples. Heat or cool the sample at a controlled rate so that it gels and measure the temperature at which gelation occurs, the rigidity of the gel (shear modulus) and possibly the breaking strength of the final gel.
· Make a gel sample of standard shape and dimensions. Place the gel in a Universal Testing Machine and compress it at a known speed (typically 10 mm min-1). The variation of the stress with strain is recorded. From this graph it is possible to determine the Youngs modulus of the gel and its breaking strength.
The aim of these types of study is to determine the relationship between the structure and interactions of the various ingredients in foods and the final rheological properties of the gel. This is important when developing functional ingredients that act as gelling agents in foods, or to determine the best processing conditions.
Cheese. Most cheeses are also homogeneous and isotropic materials and are therefore amenable to fundamental studies using standard compression or shear tests. It is often important to find out the relationship between the rigidity or breaking strength of a cheese and variations in its composition or the processing conditions used to manufacture it. Thus it is possible to determine the optimal ingredients or processing conditions required to produce a high quality product. This has become increasingly important recently with the attempts of many manufacturers to develop low-fat cheeses that have properties that mimic their full-fat analogs. Attempts are often made to relate rheological measurements to sensory characteristics such as firmness, chewiness and crumbliness.
Mayonaisse. It is important that mayonnaise products have thick and creamy textures, but that they are not so viscous that they will not flow out of the bottle. In addition, it is often necessary for them to have a small yield stress so that they do not collapse under their own weight once they have been poured onto a plate or salad. The rheological properties depend on their composition, e.g., the concentration of oil droplets present, or the concentration of thickening agents. Rheological equipment is needed to characterize the properties of mayonnaise products, and to elucidate the contribution of the various ingredients which they contain. Typically the deformation of the product may be measured as a function of shear rate in order to determine the yield stress.
Margarines and Spreads. As mentioned earlier it is important that spreadable products such as margarines and low-fat spreads retain their shape when they are removed from the refrigerator, but that they spread easily when a knife is applied. Thus they must exhibit plastic properties: i.e., have yield stresses below which they are elastic and above which they are viscous. It is usually necessary for these products to exhibit their properties over a relatively wide range of temperatures. Rheological instruments are therefore needed to characterize the properties of these systems to ensure that they do exhibit the appropriate plastic behavior. Just as with mayonnaise the deformation of a product with increasing shear stress might be measured to determine the yield stress of a product.
Meat. Meat is a complex biological material, which is heterogeneous and non-isotropic. It is therefore difficult to carry out fundamental rheological measurements on this type of product. In addition, food scientists are often interested in properties such as the tenderness or chewiness of a meat product that are complex sensory properties, consisting of both shear and compression, and usually involving large deformations. For this reason tests on meat are often carried out using empirical instruments. For example, a device has been developed which measures the force required for a blade to slice through a piece of meat.