Non Newtonian Fluid

Non-Newtonian fluids constitute a class of materials whose flow behaviour does not conform to Newton’s law of viscosity. Unlike Newtonian fluids, where shear stress and shear rate are linearly related through a constant coefficient of viscosity, non-Newtonian fluids exhibit a variable viscosity that changes under applied stress. This variability may arise instantaneously with changes in shear rate or gradually over time. The complexity of their behaviour means that such fluids are often better characterised using broader rheological properties and tensor-based constitutive equations within continuum mechanics.
Non-Newtonian behaviour appears in many everyday substances and industrial materials, ranging from ketchup and toothpaste to molten polymers, biological fluids and geological materials such as magma. Their wide distribution makes them central to studies in physics, chemistry, engineering and material science.

Rheological Characteristics

In Newtonian fluids, viscosity remains constant regardless of the applied shear rate. Non-Newtonian fluids, however, may vary in viscosity due to alterations in shear rate, deformation history or other environmental conditions. These fluids may also display normal stress differences or time-dependent modifications of their flow properties. Because viscosity alone cannot fully describe such behaviour, sophisticated rheological techniques are employed to measure their responses under oscillatory, shear or extensional flows using instruments such as rotational rheometers or capillary viscometers.
Mathematical descriptions often rely on tensor-valued constitutive models. For time-dependent non-Newtonian fluids, examples include the Oldroyd-B, Walters’ Liquid B and Williamson models. Analytical solutions are rare, though existence results have been derived for certain classes, such as Ladyzhenskaya-type models with nonlinear stress tensors. Time-independent non-Newtonian fluids, by contrast, possess a wider range of known analytical solutions.

Time-Independent Non-Newtonian Behaviour

Several important categories fall into the time-independent class, meaning their viscosity responds instantly to changes in shear rate without requiring prolonged application of stress.
Pseudoplastic or shear-thinning fluidsThese fluids exhibit a reduction in viscosity as shear rate increases. Many colloidal systems—including wall paint, blood and syrups—demonstrate this behaviour. Shear thinning is desirable in applications requiring easy spreading or pumping at high shear rates but stability at rest.
Dilatant or shear-thickening fluidsDilatant fluids increase in viscosity with increasing shear rate. A familiar example is a starch–water suspension such as oobleck, which behaves like a free-flowing liquid when stirred slowly yet appears solid when struck forcefully. This arises because particles within the suspension crowd and form temporary load-bearing structures under rapid deformation.
Bingham plasticsMaterials with a finite yield stress belong to this category. They behave as rigid bodies until the applied stress exceeds a threshold, after which they flow linearly with shear stress. Common examples include toothpaste, mayonnaise, drilling mud and certain chocolate formulations. Their surfaces can maintain peaks or impressions when stationary due to the yield stress.

Time-Dependent Non-Newtonian Behaviour

Time-dependent fluids modify their viscosity not only in response to shear rate but also to the duration of applied stress.
Thixotropic fluidsThixotropic materials decrease in viscosity over time when subjected to a constant shear rate. They become less resistant to flow the longer they are sheared. Many gels, clays, paints and food emulsions display thixotropy, which allows them to be dispensed easily yet remain stable when left undisturbed.
Rheopectic fluidsRheopectic fluids show the opposite behaviour, requiring increasing shear stress to maintain constant strain rate over time. They thicken gradually under continuous deformation. Although rarer, certain suspensions and industrial slurries can exhibit rheopectic tendencies.

Representative Examples

Non-Newtonian behaviour appears across a remarkable variety of natural and manufactured materials:

• Everyday substances such as soaps, cosmetics, toothpaste, mayonnaise, jam and yoghurt.
• Natural products including magma, lava, honey, plant resins and gums.
• Biological fluids such as blood, saliva, synovial fluid, semen and mucus.
• Industrial mixtures such as cement slurries, paper pulp, emulsions and dispersions.

Several iconic examples are used for science demonstrations and educational purposes. Oobleck, made from corn starch and water in ratios typically around one part water to one and a half to two parts starch, offers a clear case of shear thickening. Its properties allow demonstrations such as walking across a tub of the mixture or inducing standing waves using low-frequency sound vibrations. After rapid deformation stops, it reverts to a more fluid state.
Flubber or slime, produced from polyvinyl alcohol-based glues and borate ions, behaves as a viscoelastic Maxwell material. It flows slowly under small stresses but fractures under rapid deformation. Chilled caramel toppings containing hydrocolloids such as carrageenan exhibit shear thickening, behaving as solids when struck but flowing under gentle motion.
Silly Putty, a silicone-based polymer suspension, displays a spectrum of behaviours: it flows under its own weight when left undisturbed, bounces when dropped and breaks sharply when subjected to a rapid pull. Plant resins similarly exhibit viscoelasticity, flowing slowly but shattering under sudden force.
Quicksand, a colloidal mixture of fine sediment and water, acts as a shear-thinning non-Newtonian fluid. It appears firm at rest but liquefies under slight agitation, causing objects to sink. Conversely, ketchup undergoes shear thinning, its viscosity decreasing when the bottle is tapped correctly, allowing it to pour more readily.
Starch-based pancake mixtures, as well as granular flows modelled using I-rheology, also demonstrate non-Newtonian properties. In granular systems, apparent viscosity varies with both pressure and shear rate, reflecting the complex interactions between particles.

Applications and Broader Context

Non-Newtonian fluids appear in engineering processes, manufacturing, food production, geology and biological transport systems. Industrial mixing, coating processes, pipeline transport and pharmaceutical formulation all rely on understanding and manipulating rheological behaviour. In hazardous-waste management and radioactive waste vitrification, the behaviour of molten glass—a high-temperature non-Newtonian fluid—poses significant challenges for modelling and processing.