4.2 Shear-thinning and shear-thickening fluids

Non-Newtonian fluid behavior

Non-Newtonian fluids are fluids whose viscosity changes depending on the applied shear stress or shear rate. Unlike Newtonian fluids (like water), where viscosity stays constant regardless of how hard you push, non-Newtonian fluids respond dynamically to mechanical force. This makes them central to colloid science, where you're constantly dealing with suspensions, emulsions, and polymer solutions during formulation, processing, and quality control.

Non-Newtonian fluids fall into two main categories based on how they respond to shear:

• Shear-thinning (pseudoplastic) fluids get less viscous as shear rate increases
• Shear-thickening (dilatant) fluids get more viscous as shear rate increases

Shear-thinning fluids

Characteristics of shear-thinning fluids

Shear-thinning fluids decrease in viscosity as the applied shear rate or shear stress increases. At rest or low shear rates, the apparent viscosity is high. As you increase the shear rate, the fluid flows more easily and the apparent viscosity drops.

This behavior shows up in complex fluids containing long-chain molecules, elongated particles, or loosely aggregated structures that can rearrange under shear.

Examples of shear-thinning fluids

• Polymer solutions: polyethylene oxide, xanthan gum solutions
• Concentrated suspensions: ketchup, toothpaste
• Emulsions: mayonnaise, salad dressings
• Biological fluids: blood (red blood cells deform and align under shear, reducing viscosity in smaller vessels)

Mechanisms of shear-thinning behavior

Three main mechanisms drive shear-thinning:

1. Particle/molecule alignment: Elongated particles or polymer chains orient in the flow direction at higher shear rates, reducing resistance to flow.
2. Chain disentanglement: In polymer solutions, overlapping chains become entangled at rest. Shear pulls them apart, allowing easier flow.
3. Aggregate breakdown: In flocculated suspensions, weak attractive forces hold particles in loose networks. Shear breaks these structures apart, releasing trapped solvent and lowering viscosity.

Applications of shear-thinning fluids

• Pipeline transport: Lower viscosity at high shear rates means less energy needed for pumping
• Paints and coatings: The fluid thins during brushing or spraying for easy application, then thickens at rest to prevent dripping
• Pharmaceuticals: Controlled-release formulations can exploit shear-thinning to flow through a syringe needle but remain viscous at the injection site
• Food processing: Easier mixing and pumping during manufacturing, while maintaining thick texture on the shelf

Shear-thickening fluids

Characteristics of shear-thickening fluids

Shear-thickening fluids increase in viscosity as the applied shear rate or shear stress increases. At low shear rates, they flow relatively easily. Push them harder, and they resist flow more strongly.

Shear-thickening is less common than shear-thinning and typically occurs in concentrated suspensions of rigid particles. The onset of thickening often happens abruptly above a critical shear rate.

Examples of shear-thickening fluids

• Cornstarch suspensions: the classic demonstration where the fluid solidifies under impact
• Silica nanoparticle suspensions: used in protective material research
• Certain polymer solutions: such as concentrated polyvinyl alcohol
• Electrorheological and magnetorheological fluids: viscosity can be tuned with external electric or magnetic fields

Mechanisms of shear-thickening behavior

1. Hydrocluster formation: At high shear rates, particles are forced close together and hydrodynamic lubrication forces push them into transient clusters. These clusters jam the flow and increase viscosity.
2. Lubricated-to-frictional transition: At low shear, thin fluid films lubricate particle contacts. Above a critical stress, those films break down and direct frictional contact between particles takes over, dramatically increasing resistance.
3. Flow-resisting structures: In some polymer systems, chains can entangle or particles can arrange into configurations that resist further deformation.

Applications of shear-thickening fluids

• Body armor and impact protection: Shear-thickening fluid impregnated into fabrics stiffens on impact, absorbing energy
• Vibration damping: Shock absorbers and dampers that stiffen under sudden loads
• Controllable hydraulic systems: Fluids whose resistance can be tuned for advanced machinery
• Enhanced oil recovery: Rheological additives that modify flow behavior in porous rock formations

Rheological models

Power-law model

The simplest model for non-Newtonian flow relates shear stress ($\tau$) to shear rate ($\dot{\gamma}$):

$\tau = K \dot{\gamma}^n$

• $K$ is the consistency index (units depend on $n$), reflecting the overall "thickness" of the fluid
• $n$ is the flow behavior index, a dimensionless number that captures the type of non-Newtonian behavior

How to interpret $n$:

• $n < 1$: shear-thinning
• $n = 1$: Newtonian (reduces to Newton's law of viscosity, with $K$ equal to the viscosity)
• $n > 1$: shear-thickening

The power-law model is useful for quick engineering estimates, but it breaks down at very low and very high shear rates. It predicts infinite viscosity as $\dot{\gamma} \to 0$ for shear-thinning fluids, which isn't physically realistic.

Carreau model

The Carreau model fixes the power-law's limitations by capturing the plateau viscosities at both extremes of shear rate:

$\eta = \eta_\infty + (\eta_0 - \eta_\infty)[1 + (\lambda \dot{\gamma})^2]^{(n-1)/2}$

• $\eta_0$: zero-shear viscosity (the plateau at very low shear rates)
• $\eta_\infty$: infinite-shear viscosity (the plateau at very high shear rates)
• $\lambda$: relaxation time, which sets the shear rate at which the transition from Newtonian to power-law behavior begins
• $n$: power-law index in the intermediate region

This model gives a more complete picture of the flow curve but requires four parameters, meaning you need more experimental data to fit it.

Cross model

The Cross model serves a similar purpose to the Carreau model with a slightly different mathematical form:

$\eta = \eta_\infty + \frac{\eta_0 - \eta_\infty}{1 + (K \dot{\gamma})^m}$

• $K$: a time constant (analogous to $\lambda$ in the Carreau model)
• $m$: a dimensionless exponent related to the power-law index

The Cross model is particularly well-suited for describing polymer solutions and melts. In practice, the Carreau and Cross models often fit the same data comparably well; the choice between them is often a matter of convention in your field.

Comparison of rheological models

For fluids that also have a yield stress (a minimum stress needed before flow begins), the Herschel-Bulkley model is more appropriate: $\tau = \tau_y + K\dot{\gamma}^n$, where $\tau_y$ is the yield stress.

Measurement techniques

Rotational rheometry

Rotational rheometers are the workhorse instruments for characterizing non-Newtonian fluids. The sample sits between a rotating element and a stationary surface, and the instrument measures torque and angular velocity.

Common geometries include:

• Cone-and-plate: Provides uniform shear rate across the sample; good for most fluids
• Parallel plates: Adjustable gap; useful for samples with large particles or for temperature sweeps
• Concentric cylinders (Couette): Good for low-viscosity fluids that would flow off a plate

Rotational rheometers can run steady-shear tests (viscosity vs. shear rate), oscillatory tests, and creep tests, making them versatile for full rheological characterization.

Capillary rheometry

Capillary rheometers force fluid through a narrow tube at controlled flow rates or pressures. The pressure drop across the capillary and the volumetric flow rate give you the shear stress and shear rate.

These instruments are well-suited for high-viscosity materials and can reach much higher shear rates than rotational rheometers, making them valuable for simulating processing conditions like extrusion or injection molding.

Oscillatory rheometry

Oscillatory tests apply a small sinusoidal strain to the sample and measure the resulting stress. From the amplitude ratio and phase angle between stress and strain, you get the complex modulus $G^*$, which splits into:

• Storage modulus $G'$: the elastic (solid-like) component
• Loss modulus $G''$: the viscous (liquid-like) component

When $G' > G''$, the material behaves more like a solid; when $G'' > G'$, it behaves more like a liquid. These tests are run at small strains within the linear viscoelastic region so you don't disturb the sample's microstructure.

Challenges in measuring non-Newtonian fluids

• Time-dependent behavior: Thixotropic fluids (viscosity decreases over time at constant shear) and rheopectic fluids (viscosity increases over time) make results sensitive to shear history. You need consistent pre-shear protocols.
• Wall slip: Some fluids slip at the instrument surface rather than shearing uniformly, giving artificially low viscosity readings. Roughened or serrated geometries can help.
• Shear banding: The fluid may split into bands of different shear rates rather than deforming uniformly, complicating interpretation.
• Sample sensitivity: Gels, emulsions, and other structured fluids can be disrupted during loading. Gentle sample preparation and rest periods before measurement are critical.

Factors affecting non-Newtonian behavior

Influence of particle size and shape

Particle size and shape strongly influence rheology. Smaller particles have greater surface area per unit volume, leading to more particle-particle interactions and generally higher viscosities at the same volume fraction.

Anisotropic particles (rods, plates, fibers) can align in the flow direction under shear, which is a primary driver of shear-thinning in many suspensions. Spherical particles, by contrast, are more likely to form hydroclusters and exhibit shear-thickening at high concentrations.

Effect of particle concentration

Increasing the volume fraction of particles raises viscosity, but the relationship is nonlinear. At low concentrations, the fluid may behave nearly Newtonian. As concentration increases, particle-particle interactions become dominant and non-Newtonian behavior emerges.

Two critical thresholds matter:

• Percolation threshold: the concentration at which particles form a continuous network, often leading to a yield stress
• Maximum packing fraction ($\phi_m$): the theoretical limit of particle loading, where viscosity diverges toward infinity

Role of particle-particle interactions

The balance between attractive and repulsive interparticle forces determines the microstructure and therefore the rheology:

• Attractive forces (van der Waals, depletion): promote flocculation and network formation, increasing viscosity and often creating yield stress behavior
• Repulsive forces (electrostatic, steric stabilization): keep particles dispersed, reducing viscosity and suppressing aggregation

Tuning surface chemistry, adding surfactants, or adjusting pH and ionic strength are all practical ways to control these interactions and tailor rheological behavior.

Impact of temperature on rheology

Temperature affects viscosity through two routes. First, higher temperature increases molecular thermal motion, weakening intermolecular interactions and generally lowering viscosity. Second, temperature can alter the microstructure itself.

Thermoresponsive polymers (like poly(N-isopropylacrylamide)) undergo dramatic conformational changes at specific temperatures, causing sharp transitions in viscosity. For any non-Newtonian fluid, reporting the measurement temperature is essential since even a few degrees can shift the flow curve significantly.

Industrial applications

Food and beverage processing

• Controlling texture, mouthfeel, and shelf stability of products like sauces, yogurts, and dressings
• Optimizing pumping, mixing, and filling operations by matching equipment to the fluid's rheological profile
• Developing new formulations where, for example, a dressing needs to pour easily but cling to salad leaves (shear-thinning behavior)

Pharmaceuticals and cosmetics

• Formulating stable drug delivery systems (suspensions, emulsions, gels) that maintain uniform dosing
• Controlling how topical products spread on skin, absorb, and stay in place after application
• Designing injectable formulations with low viscosity during injection (high shear through the needle) but high viscosity at the injection site (low shear) for sustained release

Paints and coatings

• Achieving good flow and leveling during application while preventing sagging and dripping afterward
• Controlling brushing and rolling characteristics so the coating feels smooth to apply
• Formulating high-solids and water-based coatings that meet both application and environmental requirements

Enhanced oil recovery

• Injecting polymer solutions that shear-thin during pumping but maintain viscosity in the reservoir to push oil more effectively
• Controlling the mobility ratio between the injected fluid and oil to improve sweep efficiency through porous rock
• Designing viscoelastic surfactant solutions that combine viscosity modification with interfacial tension reduction

Future research directions

Development of novel non-Newtonian fluids

• Smart fluids with stimuli-responsive rheology, switchable by pH, temperature, or electric/magnetic fields
• Bio-based and sustainable non-Newtonian fluids derived from renewable feedstocks
• Nanoparticle-based fluids with tunable rheological properties for specialized applications

Optimization of rheological properties

• Systematic tailoring of particle size, shape, and surface chemistry to achieve target flow behavior
• Multi-component formulations where synergistic interactions between components produce rheological properties unattainable by individual components alone
• Machine learning approaches for navigating large formulation spaces and predicting optimal compositions

Modeling and simulation of non-Newtonian flow

• Advanced constitutive models that capture complex behaviors like thixotropy, viscoelasticity, and yield stress simultaneously
• Multiscale modeling linking molecular dynamics to mesoscale (e.g., dissipative particle dynamics) to continuum-level CFD simulations
• Computational fluid dynamics of non-Newtonian flow in realistic industrial geometries (extruders, mixers, porous media)

Emerging applications of non-Newtonian fluids

• 3D printing: Non-Newtonian inks that flow through the nozzle but hold their shape immediately after deposition
• Biomedical engineering: Injectable hydrogels for tissue engineering that are fluid during injection but gel in situ
• Functional coatings: Adhesives and coatings with rheology tunable to specific application methods
• Energy devices: Non-Newtonian electrolytes and redox-active fluids for flow batteries and other energy storage systems