Complex Fluids
Complex fluids are those that exhibit non-linear flow behaviours, unlike simple Newtonian fluids such as water or air. These systems may involve multiphase flow, non-Newtonian properties, chemical reactions or multispecies interactions. Due to their complexity, they require specialised analysis and modelling to ensure reliable and safe operation. Rheology, the study of how materials deform and flow, provides the fundamental framework for understanding and predicting the behaviour of many complex fluids.
Industries such as chemical processing, energy production, mining and water treatment frequently encounter complex fluids. Understanding complex fluids is essential for reliable equipment design, process optimisation and safe plant operation. These systems often involve challenging physics, significant economic implications and safety concerns. When not properly understood, they can result in inefficiencies, operational issues or safety risks.
At jimmylea, our complex flow consultants apply advanced CFD simulation and engineering judgement to help clients manage these risks and optimise performance. Our experience spans a wide range of industrial systems where flow behaviour cannot be simplified or assumed.
This page is part of jimmylea’s ongoing effort to share technical insights and lessons learned from real-world engineering projects involving complex fluids across Australia and Singapore.
LIQUID-BASED SYSTEMS
Liquid + Dispersed Solid = Colloid (Sol)
Description: Solid particles are uniformly dispersed within a liquid. The particles are small enough (1 nm to 1 µm) that they do not settle under gravity and often exhibit Brownian motion.
Examples: Paints, inks, milk (casein micelles), mud.
Challenges: Stability issues, particle aggregation, difficulty in separation, sensitivity to temperature and pH changes.
Liquid + Dispersed Solids (High Volume Fraction) = Suspension / Slurry
Description: High-concentration mixtures where solid particles are dispersed in a liquid, often exceeding 10% by volume. The particles are large enough to settle if not agitated.
Examples: Mineral slurries (iron ore, coal), cement paste, paper pulp suspensions, food processing slurries (chocolate, peanut butter).
Challenges: Settling, high viscosity, wear and erosion, handling difficulty.
Liquid + Gas = Bubbles, Foam
Description: Gas bubbles dispersed within a liquid. The gas phase can exist as discrete bubbles or as a continuous network forming foam.
Examples: Beer foam, shaving cream, whipped cream, aerated liquids.
Challenges: Instability, drainage, bubble coalescence, difficulty in maintaining uniform distribution.
Liquid + Immiscible Liquid = Emulsion
Description: Droplets of one immiscible liquid dispersed within another. Stability often requires emulsifiers to prevent separation.
Examples: Milk (fat droplets in water), mayonnaise, oil-water emulsions.
Challenges: Phase separation, instability without emulsifiers, viscosity variations, sensitivity to temperature and shear.
GAS-BASED SYSTEMS
Gas + Dispersed Liquid = Droplets, Sprays
Description: Liquid droplets dispersed within a continuous gas phase. Commonly formed through atomisation or aerosolisation processes.
Examples: Aerosol sprays, mist, gas scrubbers, fuel sprays in combustion systems.
Challenges: Droplet coalescence, evaporation, uneven distribution, inefficient mass transfer.
Gas + Dispersed Solids = Granular
Description: Solid particles dispersed within a gas. The particles are typically large enough to be influenced by gravity but can be suspended temporarily if agitated or fluidised.
Examples: Dust in air, powdered materials in pneumatic conveying systems.
Challenges: Segregation, dust formation, difficulty in fluidisation, wear and abrasion.
Gas + Solid + Liquid = Wet Granulates
Description: A mixture where gas is present along with solids and liquid. Typically involves wetting or coating of solid particles by the liquid phase.
Examples: Wet sand, slurry in pneumatic systems, granulation processes in pharmaceuticals.
Challenges: Inconsistent coating, particle agglomeration, drying issues, difficulty in achieving uniform mixing.
WHY COMPLEX FLUIDS BEHAVE DIFFERENTLY
The behaviour of complex fluids is governed not only by the properties of the continuous phase but also by their internal structure. Suspended particles, droplets, bubbles, polymer chains and biological material can interact with one another and with the surrounding fluid. Understanding how complex fluids respond under different operating conditions is fundamental to accurate engineering design.
These interactions may cause viscosity to vary with shear rate, time, temperature, concentration or deformation history. In some materials, an internal structure forms while the fluid is at rest and progressively breaks down when the material is mixed or pumped. In others, increasing shear promotes particle interactions that cause the material to thicken.
Consequently, the same fluid may behave differently in a storage vessel, pipeline, pump, heat exchanger or mixing tank.
APPARENT VISCOSITY
Apparent viscosity is one of the most important properties used to characterise complex fluids in engineering design and CFD simulations. For a Newtonian fluid, viscosity remains constant at a given temperature and pressure. For a non-Newtonian fluid, the ratio of shear stress to shear rate changes with the applied shear conditions. This variable quantity is commonly called apparent viscosity.
Apparent viscosity must therefore be reported together with the shear rate, temperature, solids concentration and measurement method. A single viscosity value may not adequately describe the behaviour of a complex fluid across an industrial process.
Understanding Shear Stress, Shear Rate and Viscosity
Imagine a fluid confined between two parallel plates. The lower plate is fixed while the upper plate has an area, A, and is separated from the lower plate by a fluid layer of thickness, h. A horizontal force, F, is applied to the upper plate. This force causes the plate to move at a velocity, V, dragging the adjacent fluid with it. The fluid velocity decreases progressively through the fluid layer until it reaches zero at the fixed lower plate.
The applied force divided by the plate area is the shear stress: Shear stress (τ) = F/A
For this parallel-plate example, the shear rate is given by: Shear rate (γ̇) = V/h
More generally, shear rate is the velocity gradient through the fluid: Shear rate (γ̇) = ΔV/Δy
For a Newtonian fluid, shear stress is directly proportional to shear rate: Shear stress (τ) = dynamic viscosity (μ) × shear rate (γ̇)
The proportionality constant is the dynamic viscosity. A high-viscosity fluid requires a greater shear stress to produce the same shear rate than a low-viscosity fluid. For a Newtonian fluid, viscosity remains constant regardless of shear rate.
For a non-Newtonian fluid, the relationship between shear stress and shear rate is not linear. The apparent viscosity may decrease with increasing shear rate, increase with increasing shear rate or depend on whether a yield stress has first been exceeded. The graph of shear stress (τ) versus shear rate (γ̇) is known as the flow curve.
Time-Independent Fluids
Newtonian Fluid
Description: Newtonian fluids exhibit a consistent relationship between applied force and flow rate. Their viscosity remains constant regardless of how fast they are stirred, pumped or sheared.
Key Characteristics:
- Constant viscosity at a given temperature and pressure.
- No yield stress (they flow under any applied force, however small).
- Time-independent behaviour under normal conditions.
Examples: Water, cooking oil.
Challenges: Although straightforward to model and handle, Newtonian fluids are the exception rather than the rule in the chemical, energy, resources and water process industries. Most fluids of practical interest are non-Newtonian. Designs or simulations that assume Newtonian behaviour can under-predict pressure drop, mixing requirements or settling rates when the real fluid exhibits shear-dependent viscosity or yield stress. Newtonian fluids also offer no inherent resistance to solids settling, so continuous agitation is required to maintain suspensions.
Shear-Thinning
Description: Shear-thinning fluids become less viscous as the shear rate increases. They are thick or resistant to flow when at rest, but flow more easily when stirred or pumped.
Examples: Blood, paint, yoghurt, polymer solutions.
Challenges: These fluids tend to settle or clog when idle, requiring agitation to maintain uniformity. Process equipment must be selected to handle large viscosity changes. Under low flow conditions, performance may degrade or solids may accumulate.
Shear-Thickening
Description: Shear-thickening fluids become more viscous as shear rate increases. They flow easily when undisturbed but become thick and resistant when stirred rapidly or subjected to sudden force.
Examples: Cornstarch in water, some dense slurries.
Challenges: Sudden increases in flow or agitation can cause the fluid to thicken dramatically, stressing pumps and pipes. They can cause pressure surges, vibrations or flow instability in processing equipment.
Bingham Plastic
Description: Bingham plastics behave like a solid until a minimum force (yield stress) is applied. Once that threshold is overcome, they flow like a Newtonian fluid.
Examples: Toothpaste, mayonnaise, sludges.
Challenges: Systems must be designed to overcome the yield stress to initiate flow. Inadequate pressure can cause blockages or poor flow. In low-shear areas, these fluids may not move at all, leading to sedimentation or uneven distribution.
Yield Shear-Thinning
Description: Yield-shear thinning fluids require an initial force to start flowing and then exhibit shear-thinning behaviour once in motion. They combine the characteristics of Bingham plastics and shear-thinning.
Examples: Drilling muds, tomato paste, some cosmetic creams.
Challenges: Starting flow can be difficult without sufficient force. Once flowing, they need carefully controlled agitation to maintain consistency. If left idle, they can become very thick and may block equipment or settle unevenly.
Time-dependent Fluids
Thixotropic Fluid
Description: Thixotropic fluids become less viscous over time when subjected to constant shear. They start off thick, but gradually thin out the longer they are stirred or pumped. Once the shear stops, they slowly return to their original, thicker state.
Examples: Ketchup, some clays, gel-based paints, certain drilling fluids.
Challenges: These fluids can be difficult to start flowing, but once in motion, they may become too thin if shear is prolonged. They require careful timing in mixing, transferring or applying, as flow properties change with duration. Inconsistent behaviour during stop-start operations can also lead to quality or performance issues.
Rheopectic Fluid
Description: Rheopectic fluids become more viscous over time under constant shear. They begin with low resistance to flow, but the longer they are sheared, the thicker and more resistant they become. Once shear stops, they gradually return to their original, more fluid state.
Examples: Some printer inks, high-solid suspensions, certain lubricants.
Challenges: These fluids may initially flow well but become problematic over time in continuous operations. Pumps and mixers can strain as the fluid thickens unexpectedly. If not accounted for, this behaviour can lead to equipment overload or loss of flow. Start-stop cycles must be managed carefully to avoid sudden viscosity build-up.
COMMON RHEOLOGICAL (CONSTITUTIVE) MODELS
Engineering calculations involving complex fluids require constitutive models that relate shear stress, shear rate and viscosity.
Power Law model
Used to represent shear-thinning or shear-thickening behaviour over a limited range of shear rates.
Bingham Plastic model
Represents a material with a yield stress followed by an approximately linear relationship between shear stress and shear rate.
Herschel-Bulkley model
Combines yield stress with shear-thinning or shear-thickening behaviour. It is widely used for sludges, mineral slurries, pastes and other industrial materials.
Carreau and Cross models
Represent fluids whose viscosity approaches limiting values at very low and very high shear rates. These models are often useful when rheological data cover a broad shear-rate range.
RHEOLOGY AND MULTIPHASE FLOW
Many industrial complex fluids are also multiphase systems, making rheology and phase interactions closely coupled. Suspended solids may increase viscosity or introduce yield stress, while the local viscosity influences particle settling, bubble rise, droplet breakup and phase distribution. For example:
- higher viscosity generally reduces particle settling velocity
- yield stress may support particles or bubbles against buoyancy
- shear-thinning may improve flow near an impeller while leaving remote regions poorly mobilised
- solids concentration may vary spatially, producing local changes in rheology
- gas bubbles may alter apparent density, mixing and flow resistance
For concentrated systems, treating rheology and phase distribution as independent phenomena may be inadequate.
EFFECTS OF TEMPERATURE AND CONCENTRATION
The rheology of a complex fluid may be highly sensitive to temperature, solids concentration, particle-size distribution, dissolved species and pH.
Increasing temperature commonly reduces the viscosity of liquid-based systems, although the magnitude of the change depends on the material. Increasing solids concentration can produce a non-linear rise in viscosity and may introduce yield-stress behaviour. These effects explain why rheological data for complex fluids should always be measured under representative operating conditions.
Rheological data should therefore be obtained at conditions representative of normal operation, start-up, shutdown and foreseeable upset conditions.
At jimmylea, we specialise in analysing complex fluids using advanced CFD, engineering analysis and practical process engineering experience. Whether dealing with slurries, pastes, suspensions, emulsions or other complex fluids, our objective is to deliver reliable engineering solutions that improve plant performance and reduce technical risk.
For further information on rheology, visit the Society of Rheology, an international organisation dedicated to advancing the science and application of rheology.