1 Definition and basic concepts

A non-Newtonian fluid is any fluid whose resistance to flow is not constant under changing conditions. In such materials, viscosity may vary with applied force, deformation history, elapsed time, or the rate at which the fluid is moved. This behavior contrasts with that of ideal Newtonian fluids, which maintain a nearly fixed viscosity at a given temperature and pressure.

Non-Newtonian behavior is seen in many complex liquids and soft materials. Some become easier to pour when stirred, while others stiffen under sudden impact or gradually change texture when left undisturbed. These effects arise from suspended particles, long molecular chains, internal structure, or reversible interactions within the material.

1.1 Newtonian versus non-Newtonian behavior

Newtonian fluids obey a linear relationship between shear stress and shear rate. In practical terms, if the force applied to the fluid doubles, the rate of flow changes proportionally. Water and air are common examples of this simplified behavior under ordinary conditions.

Non-Newtonian fluids do not follow this linear pattern. Their flow response may accelerate, slow down, or shift into a semi-solid state depending on how they are handled. This difference is important in both theory and applications, because it means that the same material can behave very differently in a spoon, a pipe, or a machine mixer.

1.2 Viscosity and shear stress

Viscosity is a measure of a fluid’s internal resistance to motion. Shear stress is the tangential force per unit area that causes layers of fluid to slide past one another. In Newtonian fluids, viscosity is constant for a given temperature, so shear stress and shear rate rise together in a predictable way.

In non-Newtonian fluids, viscosity is often described as apparent viscosity, since the value depends on the testing conditions. A material may seem thick at rest but flow readily when agitated, or it may become more resistant as the rate of deformation increases. These changing responses are central to rheological analysis.

1.3 Rheology as a field of study

Rheology is the study of deformation and flow in matter. It covers both liquids and soft solids, especially materials whose properties cannot be captured by simple viscosity alone. The field combines concepts from physics, chemistry, materials science, and engineering.

Researchers use rheology to understand how substances move, spread, settle, or recover their shape. The discipline is especially useful for formulating foods, cosmetics, polymers, paints, biomedical gels, and industrial suspensions, where texture and flow are closely linked.

1.4 Elastic and time-dependent effects

Many non-Newtonian fluids show elastic effects as well as viscous ones. Elasticity means that the material can store some of the energy from deformation and release it later. This gives rise to behaviors such as recoil, delayed recovery, and shape memory-like responses.

Time dependence is another key feature. Some materials change their flow properties while a force is maintained, while others gradually return to their original state after the force is removed. These effects make the behavior of complex fluids dependent not only on the current stress, but also on their recent mechanical history.

2 Classification of non-Newtonian fluids

Non-Newtonian fluids are commonly grouped according to how their viscosity or flow response changes under stress. The major classes include shear-thinning, shear-thickening, Bingham plastic, viscoelastic, thixotropic, and rheopectic materials. A single substance may display more than one type of behavior under different conditions.

2.1 Shear-thinning fluids

Shear-thinning fluids become less viscous as the shear rate increases. They are often easy to stir, spread, or pump once motion begins, yet may appear thicker when left still. This property is also called pseudoplastic behavior.

2.1.1 Common examples

Common examples include paint, ketchup, shampoo, syrupy polymer solutions, and some food emulsions. Blood also exhibits shear-thinning over a range of flow conditions. In daily use, this property helps products spread smoothly while remaining stable in the container.

2.1.2 Mechanism of viscosity decrease

The decrease in viscosity usually results from internal structure aligning with the direction of flow. Long-chain molecules, colloidal particles, or weakly connected networks can organize under stress, reducing resistance to motion. In some cases, weak bonds are partially broken as shear increases, which also lowers resistance.

2.2 Shear-thickening fluids

Shear-thickening fluids increase in viscosity as the shear rate rises. Under gentle movement they may flow normally, but under sudden force they can resist motion strongly or momentarily behave like a solid. This response is often dramatic in concentrated suspensions.

2.2.1 Common examples

Examples include mixtures of cornstarch and water, dense silica suspensions, and some particulate slurries. These materials are often used in demonstrations because they can be stirred slowly but feel firm when struck.

2.2.2 Mechanism of viscosity increase

Thickening can occur when particles crowd together and temporarily jam under rapid deformation. The fluid between particles is then unable to move aside quickly enough, producing a sharp rise in resistance. In some systems, hydrodynamic interactions and frictional contacts contribute to the effect.

2.3 Bingham plastics

Bingham plastics resist flow until a minimum stress, called the yield stress, is exceeded. Below this threshold, the material behaves like a soft solid; above it, the substance begins to move. After yielding, the relation between stress and flow may become more regular.

2.3.1 Yield stress behavior

Yield stress is the critical force needed to initiate motion. This feature allows a material to hold its shape under small loads while still being spreadable or pumpable when enough force is applied. The concept is important in understanding pastes, slurries, and mud-like systems.

2.3.2 Everyday examples

Examples include toothpaste, some drilling muds, and certain cosmetic creams. These products are designed to remain in place until squeezed, pressed, or mixed, which makes yield stress useful in packaging and handling.

2.4 Viscoelastic fluids

Viscoelastic fluids combine liquid-like flow with solid-like elasticity. Their response depends on both the rate of deformation and the ability of internal structures to store and release energy. Many polymer melts and solutions show this behavior.

2.4.1 Combined fluid and elastic response

When deformed, viscoelastic materials may stretch, recoil, or form transient shapes before fully flowing. This dual character distinguishes them from simple liquids. The material may resist sudden changes more strongly than slow ones, producing unusual effects such as stringiness or die swell.

2.4.2 Stress relaxation and creep

Stress relaxation occurs when the internal stress decreases over time while the material is held at a fixed deformation. Creep is the gradual change in shape under a constant load. Together, these processes reveal how internal molecular or structural arrangements adjust over time.

2.5 Thixotropic fluids

Thixotropic fluids thin gradually when subjected to continued shear and recover their thickness when allowed to rest. The change is time-dependent rather than immediate, so the same applied force can produce different results depending on duration.

2.5.1 Time-dependent thinning

Under prolonged agitation, internal bonds or particle networks weaken, causing the viscosity to fall. This is different from ordinary shear-thinning, which depends mainly on the rate of shear. Thixotropy involves a delayed structural breakdown.

2.5.2 Recovery after rest

When the force is removed, the internal structure slowly rebuilds. The fluid can then regain much of its original thickness. This property is useful in products that should spread easily during use but remain stable afterward.

2.6 Rheopectic fluids

Rheopectic fluids show the opposite time-dependent trend: viscosity increases with sustained shear. This behavior is less common than thixotropy and is often observed in certain concentrated dispersions or lubricating materials.

2.6.1 Time-dependent thickening

Under continued agitation, the material gradually becomes more resistant to flow. The buildup may arise from slow structural formation, particle aggregation, or other changes that develop during deformation. The effect is usually progressive rather than abrupt.

2.6.2 Comparison with thixotropy

Thixotropy and rheopexy are both time-dependent, but they differ in direction. Thixotropic fluids weaken with ongoing motion and recover at rest, whereas rheopectic fluids strengthen during continued motion. These opposite patterns help classify materials with delayed structural responses.

3 Physical behavior

The behavior of non-Newtonian fluids depends on how their internal structures react to mechanical forces. These reactions may be reversible or permanent, immediate or delayed, and they often vary with temperature and deformation history.

3.1 Response to shear

Shear is one of the most important ways to probe complex fluids. By changing the rate or duration of applied shear, scientists can observe whether the material thins, thickens, yields, or develops elastic effects.

3.1.1 Flow under increasing stress

As stress increases, a non-Newtonian fluid may pass through several regimes. It may start as a near-solid, then begin to flow gradually, or show a sudden transition at a yield point. In some materials, the increase in stress produces a non-linear rise in flow rate.

3.1.2 Reversible and irreversible changes

Some structural changes reverse quickly when the force is removed. Others persist, especially if particle networks are broken, aligned, or rearranged in a lasting way. The distinction between reversible and irreversible behavior matters in processing and storage.

3.2 Response to pressure and deformation

Non-Newtonian fluids can react not only to shear but also to compression, extension, and other forms of deformation. These responses often reveal hidden structural asymmetries or internal stresses.

3.2.1 Normal stress effects

Normal stress effects arise when forces perpendicular to a surface influence flow behavior. They can cause phenomena such as climbing up a rotating rod or pulling inward on curved surfaces. These effects are especially noticeable in viscoelastic fluids.

3.2.2 Memory and hysteresis

Many complex fluids display hysteresis, meaning their response depends on whether stress is increasing or decreasing. A material may follow one path when being loaded and a different path when being unloaded. This “memory” of prior conditions is typical of structured fluids.

3.3 Temperature dependence

Temperature strongly affects the motion of molecules and the strength of interactions between them. As a result, it can alter viscosity, elasticity, and the balance between solid-like and liquid-like behavior.

3.3.1 Thermal effects on viscosity

For many fluids, higher temperature lowers viscosity by increasing molecular mobility. In some non-Newtonian systems, however, the response is more complicated because temperature can also alter aggregation, hydration, or phase structure. This makes temperature control important in experiments and applications.

3.3.2 Phase and structural changes

Heating or cooling may shift a material between different internal states. A gel can soften, a suspension can stabilize or separate, or a polymer solution can change from fluid to more solid-like behavior. Such transitions may be gradual or abrupt, depending on composition.

4 Mathematical models

Mathematical models describe non-Newtonian behavior using equations that relate stress, strain rate, and material parameters. These models are simplifications, but they are useful for comparing substances and predicting how they will behave in processing systems.

4.1 Power-law model

The power-law model represents fluids whose viscosity changes with shear rate according to a nonlinear exponent. It is widely used for shear-thinning and shear-thickening materials over limited ranges of flow. Although simple, it does not describe all conditions equally well.

4.2 Bingham model

The Bingham model applies to materials with a yield stress followed by approximately linear flow. It treats the substance as rigid below the yield point and as viscous above it. This approach is useful for pastes and suspensions that retain shape until sufficient force is applied.

4.3 Herschel–Bulkley model

The Herschel–Bulkley model combines yield stress with power-law flow. It is more flexible than the basic Bingham form and can represent many real materials more accurately. Because it can capture both a threshold for movement and non-linear post-yield behavior, it is widely used in rheology.

4.4 Casson model

The Casson model is often used for materials that show a gradual transition from solid-like resistance to flow. It has been applied to products such as printing inks, chocolate, and certain biological fluids. The model is valued for describing flow onset in structured liquids.

4.5 Maxwell and Kelvin–Voigt models

The Maxwell model represents viscoelastic behavior by combining elastic and viscous elements in series, making it useful for stress relaxation. The Kelvin–Voigt model combines them in parallel and is often used to describe creep. Both are idealized mechanical analogies that help explain time-dependent deformation.

5 Measurement and characterization

Non-Newtonian fluids are studied with instruments that apply controlled forces and record the resulting flow or deformation. Accurate measurement is essential because results may depend on time, geometry, and the way the sample was prepared.

5.1 Viscometry and rheometry

Viscometry measures viscosity, while rheometry examines broader mechanical behavior, including elasticity and time dependence. Rheometers are especially valuable for complex fluids because they can impose different types of stress and strain.

5.1.1 Rotational rheometers

Rotational rheometers apply shear through rotating plates, cylinders, or cones. They are widely used because they can measure flow curves over a range of conditions. These devices help determine whether a fluid is shear-thinning, shear-thickening, yield-stress based, or viscoelastic.

5.1.2 Capillary and oscillatory methods

Capillary methods measure how a fluid passes through a narrow tube, which is useful for high-shear conditions. Oscillatory methods apply small periodic deformations and are especially helpful for studying elastic response. Together, these techniques provide complementary information.

5.2 Flow curve analysis

Flow curves summarize the relation between applied stress and resulting shear rate. They are among the most important tools for classifying complex fluids and comparing formulations.

5.2.1 Shear stress versus shear rate

The shape of the stress-versus-rate curve reveals whether a material has a linear, curved, thresholded, or time-dependent response. By examining these trends, researchers can estimate parameters such as yield stress, consistency, and flow index.

5.2.2 Apparent viscosity

Apparent viscosity is calculated from measured stress and shear rate. It is not a fixed material constant in non-Newtonian fluids, but rather a value that changes with test conditions. This makes it useful for practical descriptions of how a substance behaves in use.

5.3 Experimental challenges

Measuring complex fluids can be difficult because their structure may change during testing. Errors may arise from sample preparation, instrument geometry, temperature variation, or chemical instability.

5.3.1 Wall slip

Wall slip occurs when the fluid moves near the container surface more easily than expected. This can make the measured viscosity appear lower than it really is. It is a common problem in suspensions, gels, and pastes.

5.3.2 Sample history and aging

The prior treatment of a sample can strongly influence results. Mixing, resting, heating, storage time, and repeated testing may all alter the structure of the fluid. Aging effects are especially important in thixotropic and particulate systems.

6 Examples and applications

Non-Newtonian fluids are widespread in everyday life and modern industry. Their unusual flow properties are often desirable because they improve spreading, stability, transport, or controlled release.

6.1 Everyday substances

Many household materials display complex rheology. These products are often formulated to behave one way in the package and another way during use.

6.1.1 Food products

Foods such as ketchup, yogurt, custard, mayonnaise, honey, and dough often show non-Newtonian behavior. Their texture depends on ingredients, mixing, temperature, and water content. In cooking and food processing, these properties affect pouring, spooning, and mouthfeel.

6.1.2 Personal care products

Toothpaste, lotions, shampoos, and gels are designed to remain stable in containers while flowing readily when squeezed or rubbed. Controlled viscosity helps these products stay on the skin or hair long enough to be useful without becoming runny.

6.2 Industrial uses

Industry relies on non-Newtonian fluids in products that must coat surfaces, reduce wear, carry particles, or maintain stable suspensions. Their behavior is often tailored through additives and formulation design.

6.2.1 Coatings and inks

Paints, varnishes, and printing inks frequently need to thin during brushing, spraying, or rolling, then regain body afterward. This allows smooth application while reducing sagging, dripping, or spreading beyond the intended area.

6.2.2 Lubricants and greases

Greases are often structured, yield-stress materials that stay in place yet flow under mechanical load. Some lubricants also show shear-dependent viscosity, which can improve performance in moving parts by reducing friction under operating conditions.

6.2.3 Polymers and suspensions

Polymer melts, filled resins, slurries, and particle dispersions are major examples in manufacturing. Their rheology affects mixing, extrusion, molding, pumping, and storage stability. Proper control of these properties is essential to product quality.

6.3 Biological and medical relevance

Living systems contain fluids and soft materials with complex flow properties. These characteristics help biological tissues function under mechanical stress and influence how medical materials are designed.

6.3.1 Blood flow

Blood is a suspension of cells in plasma and therefore does not behave like a simple liquid. Its effective viscosity varies with flow conditions, vessel size, and cell interactions. This has practical importance for circulation and clinical measurement.

6.3.2 Biomaterials and gels

Hydrogels, tissue scaffolds, wound dressings, and drug-delivery systems often rely on viscoelastic or shear-sensitive behavior. Their mechanical response can affect comfort, placement, and release of active compounds. Such materials are also studied for compatibility with biological tissues.

7 Factors influencing non-Newtonian behavior

Several physical and chemical factors shape how a non-Newtonian fluid behaves. Small changes in formulation or environment may produce large differences in flow response.

7.1 Particle concentration

As the amount of suspended material increases, particles interact more strongly and can form networks or clusters. Higher concentration often leads to greater viscosity, stronger yield behavior, or more pronounced thickening under shear. Dilute systems usually show weaker effects.

7.2 Molecular structure

Long, flexible molecules tend to produce viscoelasticity and shear-thinning. Branched polymers, entangled chains, and associative compounds can create especially complex responses. The architecture of the molecules often determines whether the fluid is stable, elastic, or time dependent.

7.3 Temperature and pH

Temperature can change mobility, bonding, and phase state, while pH may alter charge, solubility, or aggregation in materials containing acids, bases, or ionizable groups. These factors can strengthen or weaken structure, sometimes in a highly sensitive manner.

7.4 Additives and solvents

Thickeners, salts, surfactants, plasticizers, and solvents can all modify flow behavior. Additives may promote stability, increase body, or reduce friction between particles and chains. Solvent choice also influences molecular interactions and the balance between dispersed and continuous phases.

8 Scientific and engineering significance

Non-Newtonian fluids are important because they require specialized models, instruments, and design strategies. Understanding them improves control over manufacturing, product quality, and material performance.

8.1 Process design considerations

In pipes, mixers, reactors, and pumps, flow resistance may change as operating conditions change. Engineers must account for shear-dependent viscosity, yield stress, and possible time effects when selecting equipment and setting operating parameters. Ignoring these factors can lead to poor mixing or unexpected pressure losses.

8.2 Product stability and performance

Many commercial products are designed around specific rheological targets. A sauce may need to pour easily yet stay on food, while a cream may need to spread without separating. Stability, shelf life, texture, and user experience all depend on carefully controlled non-Newtonian properties.

Current work focuses on more precise measurement, predictive modeling, and the design of responsive materials. Researchers study complex fluids for soft robotics, biomedical devices, advanced coatings, and sustainable formulations. As understanding improves, new materials are being developed that adapt their flow in useful and sometimes highly selective ways.

</INTERNAL_LINK_CANDIDATES> Rheology (the study of deformation and flow in matter) Newtonian fluid (a fluid with constant viscosity under a given temperature) Viscosity (a measure of resistance to flow) Shear stress (the tangential force causing layers of fluid to slide) Shear rate (the rate at which adjacent fluid layers move relative to each other) Apparent viscosity (the measured viscosity under specific flow conditions) Shear-thinning (decrease in viscosity with increasing shear rate) Shear-thickening (increase in viscosity with increasing shear rate) Bingham plastic (a material that flows only after yield stress is exceeded) Yield stress (the minimum stress required to initiate flow) Viscoelasticity (combined viscous and elastic response) Stress relaxation (decrease of stress over time at fixed deformation) Creep (gradual deformation under constant stress) Thixotropy (time-dependent thinning under sustained shear) Rheopexy (time-dependent thickening under sustained shear) Power-law model (an equation describing non-linear viscosity behavior) Herschel–Bulkley model (a model combining yield stress and power-law flow) Rotational rheometer (an instrument that measures flow under controlled rotation) Wall slip (sliding at the boundary that distorts viscosity measurements) Hydrogel (a water-rich gel with soft, polymeric structure)