Dairy Science & Technology · Dairy Processing & Product Technology · also Food Rheology, Rheology of Dairy Foods
Flow and deformation of milk, cream, yoghurt, cheese, butter and ice cream, and how instruments measure texture.
In the exams: ICAR AICE subject 37 Unit 5 and subject 38 Unit 1
Rheology is the study of how materials flow and deform when a force acts on them. Milk flows through a pipe, cream pours, yoghurt holds a spoon and then slumps, cheese bends, fractures or stretches, butter spreads and ice cream melts down on a plate. Each of these behaviours can be measured, described with a small set of equations, and linked to what the product is made of and how it was processed. Texture is the sensory side of the same story: what a consumer feels in the hand and the mouth. A dairy technologist needs both, because a plant designs pumps, heat exchangers and fillers around flow properties, and sells products on texture.
This manual starts with the basic quantities (stress, strain, strain rate) and the classification of materials into fluids, solids and viscoelastic materials in between. It then covers the flow models used for dairy fluids (Newtonian, power-law, Bingham, Herschel-Bulkley and Casson), the instruments that measure them, viscoelasticity in creep and stress relaxation, the mechanical models of Maxwell, Kelvin-Voigt and Burgers, and dynamic oscillatory testing. Later chapters deal with large deformation and fracture, texture profile analysis, the rheology of the main dairy products, the effect of processing and stabilisers, and how instrumental measurements are related to sensory panels.
General rheological theory for all foods is written in the food-technology subject food-physical-properties-rheology, and the fluid mechanics of pumping and pipe flow in this track's dairy-fluid-flow-thermodynamics. This manual gives short reminders of that theory and spends its words on dairy foods: milk and cream, set and stirred yoghurt, cheese, butter and ice cream. Product manufacture itself is covered in fermented-milks-technology, cheese-science-technology, fat-rich-dairy-products and frozen-dairy-desserts; the colloid science behind gels and emulsions in dairy-colloids-emulsions-gels; and the design of sensory panels in sensory-evaluation-dairy.
In examinations this subject appears in national agricultural research entrance and fellowship examinations in dairy technology and dairy engineering, where rheology and fluid mechanics form a unit of their own, and in the food engineering sections of postgraduate engineering and food technology entrance tests. Questions ask for definitions, model equations, the meaning of parameters such as the flow behaviour index or the loss tangent, and short calculations of apparent viscosity, shear rate, stress decay and texture parameters.
The physical properties of milk itself (density, viscosity, surface tension and their dependence on composition) are set out in milk-composition-physical-properties; this manual builds on them rather than repeating them. Pumps, heat exchangers, homogenisers and fillers, whose selection and sizing depend on the flow behaviour described here, are covered in dairy-processing-equipment.
Rheology describes a material by the relation between the force applied to it and the deformation that results. Force alone is not enough, because the same force spread over a larger area deforms a sample less. The quantity used is stress, force per unit area, measured in pascals (1 Pa = 1 N/m²). When the force acts perpendicular to a surface, as when a cheese cylinder is compressed between two plates, the stress is a normal stress (tensile or compressive). When the force acts parallel to the surface, as when one layer of milk slides over another in a pipe or between the plates of a rheometer, it is a shear stress, written τ (tau).
Deformation is described by strain, a dimensionless ratio. In compression or tension, the engineering (Cauchy) strain is the change in length divided by the original length. In shear, the shear strain γ (gamma) is the displacement of the top of a layer divided by its thickness. For fluids that keep deforming as long as the stress acts, what matters is how fast the strain changes: the shear rate γ̇ (gamma dot), in reciprocal seconds (s⁻¹). In a thin gap of thickness h between a stationary plate and a plate moving at velocity v, the shear rate is v/h. Typical shear rates differ by process: pouring from a carton is of the order of tens per second, stirring and pumping hundreds, and spraying through an atomiser far higher. A viscosity measured at one shear rate may therefore mislead a designer working at another.
Two idealised materials anchor the classification. An ideal (Hookean) elastic solid deforms instantly when loaded, holds the deformation while the load stays constant, and recovers fully and instantly when the load is removed; stress is proportional to strain, and the constant is a modulus. In shear, τ = Gγ, where G is the shear modulus; in tension or compression, σ = Eε, where E is Young's modulus. An ideal (Newtonian) viscous fluid flows as long as a stress acts and does not recover when it is removed; stress is proportional to shear rate, τ = ηγ̇, where η (eta) is the dynamic viscosity in pascal-seconds (Pa·s). Water at room temperature has a viscosity of about 1 mPa·s.
Most dairy foods lie between these extremes. They are viscoelastic: part of the energy put into deforming them is stored and recovered (elastic behaviour) and part is lost as heat (viscous behaviour). A yoghurt gel recovers a little after a light touch but flows when stirred; a young cheese springs back when pressed gently but flows slowly under its own weight on a warm day. Whether a material looks more solid or more liquid depends on the time scale of the test compared with the material's own relaxation time, an idea expressed by the Deborah number (relaxation time divided by observation time). A high Deborah number means solid-like behaviour over the test; a low one means liquid-like behaviour.
A practical classification therefore runs: Newtonian fluids (milk, skim milk, whey at ordinary concentrations); non-Newtonian time-independent fluids (concentrated milks, cream, ice cream mix); time-dependent fluids (stirred yoghurt, some concentrates); viscoelastic soft solids (set yoghurt, fresh cheese, butter); and viscoelastic solids that fracture (hard cheese).
A Newtonian fluid has one viscosity at a given temperature, whatever the shear rate. Whole milk, skim milk and whey behave as Newtonian fluids at ordinary temperatures and concentrations, which is why a single viscosity value is quoted for them. The viscosity of milk depends mainly on its casein micelles and fat globules, the two dispersed phases that take up the most volume; dissolved lactose and salts contribute a smaller amount. Viscosity rises with total solids and fat content and falls with temperature. Values for whole milk are of the order of 2 mPa·s at 20 °C, but they vary with composition, temperature and measurement method, so a designer should use measured values for the actual product.
Cold raw milk can show slight non-Newtonian behaviour, because fat globules cluster at low temperature (cold agglutination); homogenisation and warming remove most of this effect. Concentrating milk, for example by evaporation or ultrafiltration, raises viscosity steeply once the volume fraction of micelles becomes large, and concentrated products move away from Newtonian behaviour.
For fluids whose viscosity changes with shear rate but not with time of shearing, the ratio τ/γ̇ at a given shear rate is called the apparent viscosity, η_app. Several models describe the flow curve (τ against γ̇).
The power-law (Ostwald-de Waele) model is τ = Kγ̇ⁿ, where K is the consistency coefficient (Pa·sⁿ) and n the flow behaviour index (dimensionless). The apparent viscosity is then η_app = Kγ̇ⁿ⁻¹. When n < 1 the fluid is shear-thinning (pseudoplastic): its apparent viscosity falls as shear rate rises. Cream, concentrated milk, ice cream mix and stirred yoghurt are shear-thinning. When n > 1 the fluid is shear-thickening (dilatant), which is rare in dairy foods. When n = 1 the model reduces to Newtonian with K = η.
Some materials need a minimum stress, the yield stress τ₀, before they flow. A Bingham plastic flows linearly above the yield stress: τ = τ₀ + η_pl γ̇, where η_pl is the plastic viscosity. The Herschel-Bulkley model combines a yield stress with power-law behaviour: τ = τ₀ + Kγ̇ⁿ. It is widely used for stirred yoghurt, quark-type products and thick cream, which hold their shape on a spoon (yield stress) and thin as they are stirred (n < 1). The Casson model, √τ = √τ₀ + √(η_c γ̇), is another yield-stress model, best known from chocolate and used for some dairy desserts; when it is used, the form of the equation should always be stated, because several variants exist.
These models are curve fits, not laws of nature. Parameters depend on the shear-rate range fitted, temperature and sample history, so reported values should always carry the conditions under which they were measured.
Some fluids change viscosity while being sheared at constant rate. A thixotropic fluid becomes thinner with time of shearing and recovers, at least partly, when left at rest; the structure broken by shear rebuilds slowly. Stirred yoghurt is the classic dairy example: its viscosity falls during pumping and filling and partly recovers in the cup during cold storage. A loop test, in which shear rate is raised and then lowered, shows thixotropy as a hysteresis loop, the down-curve lying below the up-curve; the area between them is a rough index of structural breakdown. A rheopectic fluid does the opposite, thickening with time of shearing; it is uncommon in dairy foods.
Thixotropy must be distinguished from irreversible breakdown. If a yoghurt gel is over-sheared during manufacture, much of the lost viscosity never returns. That is why plants handle stirred yoghurt with low-shear pumps and gentle smoothing, and why sample preparation for measurement must be standardised: a sample stirred differently before testing gives a different result.
Viscometers measure flow properties; rheometers also measure solid-like and viscoelastic properties. The simplest instrument for Newtonian fluids is a glass capillary viscometer such as the Ostwald or Ubbelohde type, in which the time for a fixed volume to flow through a capillary under gravity is proportional to the kinematic viscosity (dynamic viscosity divided by density, in m²/s or centistokes). It is accurate for milk and whey but unsuitable for non-Newtonian products, because the shear rate varies across the tube and is not controlled.
Pressure-driven tube viscometers apply the Hagen-Poiseuille relation for laminar Newtonian flow in a tube: Q = πΔPR⁴/(8ηL), where Q is the volumetric flow rate, ΔP the pressure drop over length L, and R the tube radius. The shear stress at the wall is τ_w = ΔPR/(2L), and for a Newtonian fluid the wall shear rate is 4Q/(πR³). For a non-Newtonian fluid this 'apparent' wall shear rate must be corrected, because the velocity profile is no longer parabolic; the Rabinowitsch-Mooney correction does this, and for a power-law fluid it multiplies the apparent wall shear rate by (3n + 1)/(4n). Tube and in-line viscometers are attractive for process monitoring because they measure the product as it flows in the plant.
Rotational instruments shear the sample between a rotating and a stationary surface and measure torque. In a concentric (coaxial) cylinder geometry, sometimes called a cup-and-bob or Couette geometry, the sample fills a narrow annular gap; when the gap is small compared with the radius, the shear rate is nearly uniform and is approximately the bob surface speed divided by the gap. This geometry suits low-viscosity fluids such as milk and cream because the large wetted area gives a measurable torque. In a cone-and-plate geometry, a cone with a small angle (commonly a few degrees) rotates above a flat plate; because the gap widens in proportion to the radius, the shear rate is the same everywhere in the sample and equals the angular velocity divided by the cone angle in radians. This is the preferred geometry for accurate flow curves of homogeneous fluids, but it needs particle sizes much smaller than the gap at the cone tip. Parallel-plate geometry allows a chosen gap and suits soft solids such as cheese discs and set yoghurt, though shear rate varies with radius.
Simple single-point rotational viscometers, in which a spindle rotates in a large container of sample, are widely used for quality control of yoghurt and dairy desserts. They give a reproducible number for comparing batches but not a true shear rate, so their readings are reported as apparent viscosity at stated spindle, speed, temperature and time, and cannot be compared across instrument types.
Rheological results depend strongly on handling. Temperature must be controlled tightly, because viscosity of dairy products changes markedly with temperature. Samples should be loaded the same way each time and allowed a defined rest period so structure can recover from loading. Wall slip, where a thin layer of serum forms at a smooth surface and the sample slides rather than shears, is common with yoghurt, cheese and fat-rich products; roughened or serrated geometries reduce it. Evaporation at the sample edge during long tests is prevented with a solvent trap or a thin oil layer. Every reported value should state instrument, geometry, gap, temperature, shear rate or frequency, and sample history.
Viscoelastic materials are usually characterised by tests in which either stress or strain is held constant and the other is followed with time. In a creep test, a constant stress is applied suddenly and the strain is recorded; after a set time the stress is removed and the recovery of strain is followed. In a stress relaxation test, a constant strain is applied suddenly and the stress needed to hold it is recorded as it decays. Both tests are run at small deformations, inside the linear viscoelastic region where the response is proportional to the load, so that the results describe the material and not damage to it.
A creep result is often expressed as creep compliance, J(t) = γ(t)/σ₀, the strain per unit applied stress, in Pa⁻¹. Compliance curves from tests at different stresses superimpose if the test is linear, which is a useful check. A typical creep curve for a dairy gel shows an instantaneous elastic jump, a curved region of retarded (delayed) elastic deformation, and finally a straight region of steady viscous flow. On removal of the stress, the instantaneous and retarded parts recover, while the viscous flow is permanent. The proportion recovered is a measure of how solid-like the material is.
In stress relaxation the stress falls with time while the strain is held. A purely elastic solid would hold its stress indefinitely; a purely viscous fluid would relax immediately. Real dairy foods fall between: a hard cheese relaxes slowly, a soft cheese or yoghurt faster. The time taken for stress to fall to a given fraction of its initial value is a convenient index, and the relaxation modulus G(t) = σ(t)/γ₀ describes the curve. Relaxation data are often fitted with one or more exponential terms, each with its own relaxation time, or with simple empirical models such as the Peleg normalised relaxation equation, in which the normalised decay is expressed as a function of two constants.
Relaxation and creep describe the same underlying behaviour from two sides. Relaxation is the natural test for materials that will be held at a fixed deformation, such as a cheese block pressed into a mould; creep suits materials that carry a constant load, such as a cheese wheel sagging under its own weight in a store or a yoghurt gel holding up fruit. Both are used in research on how age, fat content, moisture and salt alter cheese body.
Mechanical models build viscoelastic behaviour from two ideal elements: a spring, which obeys Hooke's law (σ = Gγ), and a dashpot, a piston in a viscous oil, which obeys Newton's law (σ = ηγ̇). Connecting them in series or in parallel gives the classic models. The models are not pictures of the molecular structure of cheese or yoghurt; they are a compact way of describing measured curves with a few constants, each of which can be compared between samples.
The Maxwell model places a spring and a dashpot in series. The same stress passes through both, and the strains add. Under constant strain the stress relaxes exponentially: σ(t) = σ₀ e^(−t/λ), where λ = η/G is the relaxation time. After one relaxation time the stress has fallen to about 37% (1/e) of its initial value. Under constant stress the Maxwell element jumps elastically and then flows at a steady rate for ever, so it describes a viscoelastic liquid. A generalised Maxwell model, several Maxwell elements in parallel, fits the multi-stage relaxation of real cheeses better than a single element.
The Kelvin-Voigt model places a spring and a dashpot in parallel. Both share the same strain, and the stresses add. Under a constant stress σ₀ the strain rises gradually towards the spring's value: γ(t) = (σ₀/G)(1 − e^(−t/λ)), with retardation time λ = η/G. After one retardation time the strain has reached about 63% of its final value. On removal of the stress, the strain decays back to zero. The Kelvin-Voigt element therefore describes delayed elasticity in a viscoelastic solid; it cannot show instantaneous elasticity or permanent flow.
The four-element Burgers model joins a Maxwell element and a Kelvin-Voigt element in series. Its creep compliance has three parts: an instantaneous compliance J₀ = 1/G₀ from the free spring; a retarded compliance J₁(1 − e^(−t/λ₁)) from the Kelvin-Voigt element, with λ₁ = η₁/G₁; and a steady viscous term t/η₀ from the free dashpot. Written in full, J(t) = J₀ + J₁(1 − e^(−t/λ₁)) + t/η₀. This reproduces the typical creep curve of yoghurt, cheese and butter, and its constants are widely reported in dairy research: J₀ reflects the stiffness of the network bonds, J₁ and λ₁ the rearrangement of the network, and η₀ the slow flow of the whole structure.
When a creep curve needs more than one retarded region, extra Kelvin-Voigt elements are added in series; each brings its own compliance and retardation time. As with all such fitting, the constants depend on stress, temperature and test duration, so comparisons are meaningful only between samples tested under the same conditions.
In an oscillatory test, a small sinusoidal strain γ = γ₀ sin(ωt) is applied at angular frequency ω (rad/s, equal to 2π times the frequency in hertz), and the resulting stress is measured. For a purely elastic solid the stress is in phase with the strain; for a purely viscous fluid it is 90° out of phase, because stress follows the rate of strain. For a viscoelastic material the stress leads the strain by a phase angle δ between 0° and 90°.
The stress can be split into a part in phase with strain and a part 90° out of phase. Dividing each by the strain amplitude gives the storage modulus G′ (elastic, energy stored and recovered each cycle) and the loss modulus G″ (viscous, energy dissipated as heat each cycle). The loss tangent tan δ = G″/G′ summarises the balance: below 1 the material is more solid-like, above 1 more liquid-like. The complex modulus is |G*| = √(G′² + G″²), and the complex viscosity is |η*| = |G*|/ω. Set yoghurt and cheese typically have G′ greater than G″ across ordinary frequencies, with tan δ well below 1; ice cream mix and cream at low fat have G″ greater than G′.
Several standard sweeps are used. A strain (or stress) amplitude sweep at fixed frequency finds the linear viscoelastic region (LVR), where G′ and G″ are independent of amplitude; the end of the LVR, where G′ starts to fall, marks the onset of structural breakdown and gives a critical strain. All other small-amplitude tests must be run inside the LVR. A frequency sweep at fixed amplitude shows how the material responds over different time scales: a strong gel has G′ almost independent of frequency, while a weak or particle gel shows G′ rising with frequency. A time sweep at fixed amplitude and frequency follows gel formation, for example acid gelation of milk during yoghurt fermentation or rennet coagulation in cheesemaking. A temperature sweep follows melting of fat or of a cheese network.
Gelation is commonly located at the point where G′ rises above G″, the G′ = G″ crossover, although the true gel point is defined more strictly as the point where tan δ becomes independent of frequency (the Winter-Chambon criterion). For rennet coagulation, the time at which G′ exceeds a small threshold value is also used as a practical gelation time. These small-strain methods are attractive because they do not break the gel being studied.
The Cox-Merz rule states that, for many polymer solutions, the steady-shear viscosity at shear rate γ̇ equals the complex viscosity at angular frequency ω when the two numbers are equal. It is useful for estimating flow behaviour from oscillatory data, but structured dairy gels often fail it, because steady shear breaks the structure while small oscillations do not.
Small-amplitude tests describe the intact structure, but processing and eating involve large strains. Two further approaches are used in research. Large-amplitude oscillatory shear (LAOS) continues an oscillatory test well past the linear region and analyses the distorted stress waveform, giving information on how a yoghurt or cheese network yields within each cycle. Extensional rheology measures resistance to stretching rather than shearing; it matters for the stretch of molten pasta-filata cheese, for the formation of filaments when a spoon is lifted from a thick dessert, and for breakup of jets in filling and atomisation. Both methods need specialised instruments and careful interpretation, and their results are not yet standardised across laboratories, so they are mainly research tools rather than routine quality tests.
Small-strain tests describe the intact structure, but eating, slicing, grating and shredding break that structure. Large-deformation tests, usually uniaxial compression of a cylinder between flat plates on a universal testing machine, measure how the material yields and fractures. The force-deformation curve is converted to stress and strain. Because a cylinder widens as it is compressed, true stress is calculated on the current cross-sectional area; assuming constant volume, the current area equals the original area multiplied by the original height divided by the current height.
Two strain measures are used. Engineering strain is the change in height divided by original height, ε_E = ΔH/H₀. True (Hencky) strain integrates small increments and equals ε_H = ln(H₀/H), the natural logarithm of original over current height. At small deformation the two are almost equal, but they diverge at large compression: a sample compressed to half its height has an engineering strain of 0.5 but a Hencky strain of about 0.69. Reports must state which strain is used. Friction between sample and plates causes barrelling; lubricated plates reduce it.
The point at which the sample breaks gives the fracture stress and fracture strain. Together with the initial slope (an apparent modulus), these describe the material in terms closely linked to sensory words. A short-bodied, crumbly cheese such as a well-aged hard cheese fractures at small strain; a young, elastic cheese deforms to a large strain before fracturing; a pasta-filata cheese stretches. Fracture strain is sensitive to pH, calcium and moisture: low pH and calcium loss give a shorter, more crumbly body, while higher moisture and intact protein give a longer, more elastic body. Proteolysis during ripening cuts the casein network and reduces fracture stress.
Other large-deformation tests include cutting with a wire or blade, penetration with a probe (common for yoghurt gel firmness and butter hardness), and extrusion through an orifice. These empirical tests give numbers that depend on probe size, speed and sample geometry, so they are useful for comparing products within one laboratory under fixed conditions rather than as material constants.
Texture profile analysis (TPA) imitates two bites. A cylinder of sample is compressed twice to a set fraction of its height by a flat probe, with a pause between, and the force-time curve is analysed. TPA grew from the General Foods texture profile work and was adapted to universal testing machines; the conditions used (sample size, compression level, crosshead speed and pause) strongly affect the values and must always be reported.
The standard parameters are read from the curve as follows. Hardness is the peak force in the first compression. Adhesiveness is the negative area after the first compression, the work needed to pull the probe away from a sticky sample. Springiness (elasticity) is the ratio of the time or distance to the peak in the second compression to that in the first, a measure of how far the sample recovers between bites. Cohesiveness is the ratio of the positive area of the second compression to that of the first (A₂/A₁), showing how well the structure survives the first bite. Gumminess is hardness multiplied by cohesiveness and applies to semi-solid foods. Chewiness is gumminess multiplied by springiness and applies to solid foods; gumminess and chewiness should not both be reported for the same product, because a food is either semi-solid or solid. Resilience, the ratio of the upstroke to downstroke area within the first compression, is sometimes added.
TPA is widely used for cheese (including processed cheese and paneer-type products), set yoghurt, cream cheese and some traditional products. It is quick and ties directly to sensory language, but it has known weaknesses. High compression levels destroy fragile gels so that the second bite measures debris; low levels may miss fracture altogether. Results are instrument- and setting-specific, so values from different laboratories cannot be pooled unless conditions match. Units must be stated: hardness in newtons, adhesiveness in newton-seconds or joules, while springiness and cohesiveness are dimensionless ratios. In a cheese ripening trial, hardness and chewiness typically fall and cohesiveness changes as proteolysis proceeds, but the direction and size of change depend on the variety and conditions.
Yoghurt is an acid gel: as lactic acid bacteria lower the pH towards the isoelectric point of casein, colloidal calcium phosphate dissolves and casein micelles aggregate into a particle network. Set yoghurt is a continuous gel tested by penetration, small-amplitude oscillation or TPA; its firmness and resistance to whey separation (syneresis) increase with protein content and with heat treatment of the milk, because denatured whey proteins attach to micelles and join the network. Stirred yoghurt is the same gel broken into a smooth, thick, shear-thinning and thixotropic fluid; its viscosity depends on the gel before stirring, the intensity of stirring and pumping, and storage. Exopolysaccharide-producing cultures raise viscosity and reduce syneresis, although their effect depends on the type and amount of polysaccharide and its interaction with protein. Details of manufacture are in fermented-milks-technology.
Cheese rheology is governed by the para-casein network, its degree of hydration and mineralisation, fat content and state, and proteolysis. At low temperature fat is largely solid and stiffens the cheese; on warming, fat melts and the protein network softens. Meltability (how far a cheese flows when heated) and stretchability (how far molten cheese draws into strings) matter for pizza and cooking cheese. Meltability is often assessed by the Schreiber test, in which a disc of cheese is heated in an oven and the spread is measured, or by the Arnott test, which records the drop in height of a cylinder; both are empirical and condition-specific. Rheometer temperature sweeps give G′ falling and tan δ rising on heating, and the temperature at which tan δ passes 1 is sometimes used as an index of melting. Moderate proteolysis and partial calcium loss improve melt; excessive proteolysis gives a soft, over-flowing melt and poor stretch. Pasta-filata cheeses owe their stretch to a calcium-reduced, aligned protein network formed during hot stretching. Manufacture is covered in cheese-science-technology.
Butter is a plastic fat: a network of fat crystals holding liquid fat and water droplets. It has a yield stress and spreads only once that stress is exceeded. Its hardness and spreadability depend strongly on temperature, on the solid fat content of the milk fat (which varies with season and feeding) and on crystallisation conditions, including cream tempering programmes. Butter softens when worked and partly regains firmness on standing, a behaviour known as work softening that is linked to breaking and reforming crystal bonds. Hardness is commonly measured by cone penetration or by wire cutting at a stated temperature. See fat-rich-dairy-products for processing.
Fluid milk and cream are the simplest dairy fluids rheologically but the most important for plant design, because they are pumped, heated and filled in the largest volumes. Milk is close to Newtonian, so pump and heat-exchanger calculations can use a single viscosity at the process temperature. Cream becomes increasingly shear-thinning as fat content rises, and very high-fat cream can show a small yield stress, especially when cold, when fat globules are partly crystalline and can form clusters. Ageing cream at low temperature before whipping or churning is partly a rheological step: it allows fat to crystallise so that globules collide and partially coalesce in the way the product needs.
Concentrated milks show the steepest changes. As evaporation or membrane filtration raises solids, the volume fraction of casein micelles and fat globules approaches the point where particles crowd each other, and viscosity rises sharply rather than in proportion. Concentrates for spray drying are therefore held at limits set by the atomiser, because high viscosity gives larger droplets and poorer powder; heat treatment before evaporation and storage time of the concentrate both change its viscosity. Sweetened condensed milk can thicken during storage (age thickening), which is followed by viscosity measurement at a fixed temperature. In all these cases a measured flow curve at the process temperature is worth more than any handbook value, because composition and history vary from plant to plant.
Ice cream mix is a shear-thinning fluid whose viscosity is raised by stabilisers, protein, sugars and fat; mix viscosity affects whipping, air incorporation and the smoothness of the frozen product. Frozen ice cream is a complex foam containing ice crystals, air cells, partly coalesced fat and an unfrozen concentrated serum. Its hardness rises steeply as temperature falls, because more water freezes. Meltdown, the rate and shape of melting on a mesh at controlled temperature, depends on the partly coalesced fat network and the serum viscosity; a strong fat network holds shape after the ice has melted. Frozen-dairy-desserts covers manufacture.
Processing changes rheology mainly through the dispersed phases. Homogenisation reduces fat globule size and coats the new surfaces with casein and whey protein, so the globules behave like protein particles; in yoghurt they join the gel network and increase firmness, and in cream they can raise viscosity by forming clusters, especially when homogenised at low pressure or high fat (homogenisation clusters). Heat treatment of milk at temperatures that denature whey proteins (for yoghurt typically well above pasteurisation, held for several minutes) greatly increases acid-gel firmness and water holding, because β-lactoglobulin binds to micelles and increases the number of particles taking part in the network. Concentrating solids by evaporation, ultrafiltration or added milk powder raises viscosity and firmness. Cooling rate and tempering govern fat crystallisation and therefore the firmness of cream and butter. Mechanical shear after gel formation reduces viscosity, partly reversibly.
Hydrocolloids are added to control viscosity, prevent separation and improve texture; their use is regulated and permitted levels differ by product and country, so labels and national standards must be checked. Carrageenans are sulphated galactans from red seaweed; κ-carrageenan reacts with κ-casein at very low concentration and is used to prevent whey separation in ice cream mixes and to suspend cocoa in chocolate milk. High-methoxyl pectin adsorbs to casein micelles at low pH and prevents them aggregating, which is why it stabilises acidified milk drinks and drinking yoghurts against sedimentation. Gelatin forms a thermoreversible gel and gives body to yoghurt and desserts. Locust bean gum and guar gum are galactomannans that raise viscosity; locust bean gum is used in ice cream mixes, where it slows ice crystal growth during temperature fluctuation, but neutral polysaccharides can cause phase separation with milk proteins (depletion flocculation), so they are often combined with carrageenan. Xanthan gum gives highly shear-thinning, yield-stress solutions. Starches, including modified starches, thicken desserts and yoghurts. Each changes the flow curve differently, so the choice depends on the texture wanted and on interactions with protein.
Sensory texture is what trained or consumer panels perceive: firmness, thickness, smoothness, creaminess, stickiness, spreadability, mouth-coating. Descriptive panels are trained with reference samples and scales, as set out in sensory-evaluation-dairy; consumer panels report liking. Instrumental tests are used because they are faster, cheaper and more repeatable, but they are only useful if their numbers track what people perceive. Establishing that link is called instrumental-sensory correlation.
The link is strongest when the instrument imitates the action in the mouth or hand. Spoon-thickness of yoghurt correlates better with apparent viscosity at shear rates of the order of tens per second (the range usually associated with oral processing of fluids) than with values at very low or very high rates, although the exact shear rate in the mouth varies with product and person. Cheese firmness perceived on the first bite correlates with compression hardness or fracture stress; cheese crumbliness correlates with low fracture strain. Creaminess is complex: it depends on viscosity, fat content and droplet size, and on lubrication between tongue and palate, so tribology (the study of friction and lubrication between soft surfaces) is increasingly used alongside rheology for low-fat products.
A correlation study measures the same set of samples, covering a deliberately wide range of texture, with both an instrument and a trained panel. Simple correlation coefficients show which instrumental parameters move with which sensory attributes; multivariate methods such as principal component analysis and partial least squares regression handle many correlated variables at once. A high correlation within a narrow set of samples can be misleading, and a relation built for one product type rarely transfers to another. Once validated, an instrumental test can replace part of routine sensory checking, for example a yoghurt viscosity specification or a cheese hardness window at release, but periodic panel checks remain necessary because ingredients and processes drift.
For students, the practical message is to measure what matters at the conditions that matter: the right test, at the right temperature, deformation and rate, and with a stated method, so that results can be compared across batches and over time.
A student uses this subject to read and draw flow curves, recognise which model fits a dairy product, and carry out the calculations that recur in exams: apparent viscosity from a power-law fit, shear rate in a cone-and-plate, stress decay in a Maxwell element, tan δ and complex modulus from oscillatory data, and TPA parameters from a two-bite curve. In the laboratory, the student learns to control temperature, sample loading and rest time, to check the linear viscoelastic region before a frequency sweep, and to report every condition with each value. These habits are the difference between a number that can be compared and one that cannot.
A process or quality technologist five years in uses rheology to set and defend specifications: yoghurt viscosity at a stated spindle, speed and temperature; cheese hardness and melt for a pizza customer; butter spreadability at refrigerator temperature. The same person troubleshoots: thin stirred yoghurt traced to over-shearing in a pump or a change in milk protein; whey separation traced to low heat treatment or a stabiliser change; poor cheese melt traced to pH or calcium. They choose pumps and heat exchangers with the product's non-Newtonian behaviour in mind and work with suppliers on stabiliser systems.
A plant head or technical director with twenty-five years uses rheology at the level of product and process strategy. Reformulations for lower fat, sugar or additives change texture, and the senior manager must judge which instrumental and sensory tests prove the new product is acceptable before launch. Capacity changes, new pumps and longer pipelines all alter shear history, so rheological data enter project decisions. Senior staff also settle disputes with customers over texture complaints, which needs agreed, documented test methods rather than single readings.
A researcher or professor with a PhD and long experience uses rheology to study structure: how casein networks form and break, how fat crystal networks give butter its plasticity, how proteolysis changes cheese fracture, how polysaccharides interact with proteins. They design experiments across small and large deformation, combine rheology with microscopy and scattering, and teach the careful interpretation of models that are often over-fitted. They also review papers and set examination questions, and must insist that reported values carry their measuring conditions.
This manual gives no typical numerical values for the viscosity, consistency coefficient, flow behaviour index, moduli or TPA parameters of particular dairy products, because published values vary widely with composition, temperature, method and instrument; students should consult measured data for the product at hand. It describes extensional rheology, tribology and large-amplitude oscillatory shear only briefly, and does not cover rheology of powders and bulk flow, which belongs with dairy powders and handling. Stabiliser permitted levels are not given because they are set by national law and change.
Original practice questions written to the syllabus and pattern of the exams named in each question's examTags. They are not past papers and do not reproduce any board's questions. Parameter values in numerical questions are illustrative, stated in the question, and are not typical values for any named product.
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