Definition and basic concept of rheology
Rheology is the science of the flow and deformation of materials under the action of external forces, which studies the viscous flow and elastic deformation behavior and internal laws of materials in response to external forces. In essence, rheology reveals the relationship between material structure and mechanical behavior, and is an important bridge connecting the microstructure and macroscopic properties of materials. Rheology covers the entire range from ideal Newtonian fluids to ideal elastic solids, and most actual materials such as polymer melts, solutions, suspensions, emulsions, gels, soft substances, etc. exhibit complex rheological behavior. The description of rheological properties requires a series of parameters, including viscosity, modulus, flexibility, relaxation time, yield stress, etc., which change with shear rate, time, temperature and other factors, which constitute the basic content of rheology research.
Physics of rheology
The physical basis of rheology is based on the intersection of continuous medium mechanics and polymer physics, and the relationship between stress and strain and its rate is described through constitutive equations. According to the different responses of materials to external forces, the rheological behavior can be divided into three categories: ideal viscosity, ideal elasticity and viscoelasticity.
The ideal viscosity behavior follows Newton's law of friction, that is, the shear stress is directly proportional to the shear rate, and the proportional constant is the dynamic viscosity. The constitutive equation of Newtonian fluids can be expressed as:
τ = η·γ̇
where τ represents shear stress, η represents dynamic viscosity, and γ̇ represents shear rate. Fluids that meet this relationship are called Newtonian fluids, such as water, glycerin, low molecular weight liquids, etc. The viscosity of Newtonian fluids is constant at a given temperature and pressure and does not change with shear conditions.
The ideal elastic behavior follows Hooke's law, that is, the shear stress and the shear stress become directly proportional, and the proportional constant is the shear modulus. The constitutive equation of an ideal elastic solid can be expressed as:
τ = G·γ
where G represents the shear modulus and γ represents the shear strain. Solids that meet this relationship are called Hook elastomers, such as ideal springs, metals under low strain, etc. The deformation of the elastomer occurs instantaneously, and after unloading, it is fully restored instantaneously, and the energy is stored during the deformation process and can be completely released.
Viscoelastic behavior is the complex behavior of most actual materials, which is characterized by both viscous flow and elastic deformation. The response of viscoelastic materials under the action of external forces is time-dependent, manifested as creep, stress relaxation, dynamic mechanical behavior and other phenomena. Viscoelasticity can be roughly described by the mechanical model, and the simple Maxwell model is composed of a spring and a sticky pot in series, and its constitutive equation is:
γ̇ = τ̇/G + τ/η
where τ̇ represents the rate of change in stress. This model describes stress relaxation, but not creep. The Kelvin-Voigt model consists of a spring and a sticky pot connected in parallel, and its constitutive equations are:
τ = G·γ + η·γ̇
This model describes creep behavior, but not stress relaxation. More complex four-element models or multi-parameter models can more accurately describe the viscoelastic behavior of actual materials.
From the molecular level, the rheological behavior of polymer materials stems from the movement and conformational changes of molecular chains. In the resting state, the polymer chain is conformed in a random linear group, and the entropy value is the largest. When subjected to external force, the molecular chain is oriented in the direction of the external force, the conformation changes, the entropy value decreases, and the elastic recovery force is generated. At the same time, the process of entanglement and untangling between molecular chains and the slippage of chain segments leads to irreversible viscous flow. Factors such as molecular weight, molecular weight distribution, branching structure, and cross-linking directly affect the kinetic ability of molecular chains, thereby determining the rheological properties of materials.
Rheometry uses precision instruments to measure the response of materials under various stress or strain conditions, and obtains rheological parameters and their changes with conditions. Rotary rheometers obtain viscosity and modulus by measuring torque and angular displacement, oscillatory rheometers measure energy storage modulus and loss modulus by applying sinusoidal alternating strain, and capillary rheometers obtain viscosity at high shear rates by measuring pressure and flow rate. These measurements provide basic data for material processing and applications.
Measurement method of rheology
Laboratory measurement of rheology selects appropriate measurement methods and instruments according to the test purpose and material properties, mainly including rotational rheological test, oscillatory rheological test, capillary rheological test and falling ball viscosity test.
Rotational rheological testing is a commonly used rheological measurement method for determining parameters such as viscosity and yield stress of fluids. The test was carried out on a rotary rheometer, which mainly consists of a measuring fixture, a drive motor, a torque sensor and a temperature control system. According to the geometric configuration of the measurement system, it can be divided into three basic forms: coaxial cylinder type, tapered plate type, and parallel plate type. The coaxial cylinder type is suitable for low-viscosity fluids, where the sample is injected into the annular gap between the inner and outer cylinders during measurement, and the outer cylinder rotates or the inner cylinder rotates to produce shear flow. The cone plate type consists of a flat plate and a slightly angled cone, the sample is placed between the cone plates, and the cone rotates to produce a uniform shear rate, suitable for medium to high viscosity fluids and small amounts of samples. The parallel plate consists of two parallel round plates with the sample placed between the plates and the upper plate rotating to create a shear flow, suitable for high-viscosity fluids and suspensions.
During the steady-state rotation test, a constant shear rate is set, the shear stress when the steady state is reached, and the viscosity is calculated. By changing the shear rate, the flow curve of viscosity with the shear rate can be obtained to determine the type of fluid and the shear thinning behavior. Yield stress can be determined by stress scan or creep recovery test.
Oscillatory rheological testing is used to determine the viscoelastic parameters of materials, and is suitable for studying the structural properties and dynamic mechanical behavior of materials. The rheometer is subjected to sinusoidal alternating strain or stress and the corresponding stress or strain response is measured. For ideal elastomers, stress and strain are in phase; For ideal viscous bodies, the stress and strain phase are different, and the phase difference is 90 degrees. For viscoelastomers, the phase difference is between 0 and 90 degrees. The measurement results are expressed as energy storage modulus G', loss modulus G" and loss tangent tanδ:
G' = (τ₀/γ₀)·cosδ
G" = (τ₀/γ₀)·sinδ
tanδ = G"/G'
where τ₀ and γ₀ are the amplitudes of stress and strain respectively, δ are the phase differences. The energy storage modulus reflects the elastic composition of the material, representing the energy stored and released per cycle; The loss modulus reflects the viscous composition of the material and represents the energy dissipated per cycle. Through frequency scanning, strain scanning, temperature scanning, etc., the dynamic mechanical spectrum of the material can be obtained, and the information such as structural relaxation, vitrification transition, and cross-linking network can be analyzed.
Capillary rheological testing is suitable for determining viscosity at high shear rates and simulating flow behavior during polymer processing. The test is carried out on a capillary rheometer, after the material is heated and melted, the melt is extruded from the capillary tube with a piston at a constant speed or pressure, the pressure difference and extrusion rate at both ends of the capillary tube are measured, and the apparent viscosity is calculated. Through capillaries with different length-to-diameter ratios, Bagley correction can be performed to eliminate inlet pressure loss; Rabinowitsch correction corrects non-Newtonian behavior by measuring at different shear rates. Capillary rheological testing can obtain a complete curve of viscosity with shear rate, providing data support for extrusion, injection molding and other processing processes.
The Falling Ball Viscometer is suitable for measuring the viscosity of transparent Newtonian fluids, and calculates the viscosity according to Stokes' Law by measuring the speed at which the spheres fall at a uniform rate in the liquid. When measuring, select the appropriate diameter and density of the sphere, measure the time when the sphere falls through a certain distance under constant temperature conditions, and substitute the Stokes formula to calculate the viscosity. This method is simple and intuitive, but it is limited to Newtonian fluids and is not suitable for opaque samples.
Regardless of the method, sample preparation and the choice of measurement conditions are critical. The sample should be homogeneous, free of bubbles and impurities; The measured temperature needs to be accurately controlled and stable within a certain range; Before measurement, the instrument needs to be calibrated for inertia, zero gap and temperature control. During the measurement process, it is necessary to ensure that the sample is in full contact with the fixture and there is no wall slippage; For structural fluids, the impact of pre-test shear history and resting time on results is also considered.
Key factors affecting rheological measurement results
The accuracy and repeatability of rheological measurement results are influenced by a combination of factors, from sample characteristics to instrument setup, each of which can have a significant impact on the measured value.
The chemical structure and composition of the material itself are intrinsic factors that affect rheological properties. For polymer materials, the molecular weight and its distribution directly determine the zero shear viscosity and shear thinning behavior, and the higher the molecular weight, the higher the zero shear viscosity, and the more obvious the shear thinning. The branching structure of the molecular chain affects the relaxation behavior, and the long chain branching can enhance strain hardening and tensile viscosity. The composition and sequence distribution of copolymers affect the interaction and compatibility of the chains, which in turn affects the rheological response. The type, content, shape and surface properties of the packing material determine the rheological behavior of the packing system, and yield stress and thixotropy can occur at high filling volume.
The preparation process and state of the sample have an important impact on the measurement results. Differences in thermal history will lead to different structures and morphology of polymer materials, such as crystallinity and phase separation morphology, which in turn will affect rheological behavior. Air bubbles in the sample are a common source of problems, and the bubbles can deform and move under shear, interfering with stress transfer and making the measured values abnormal. The residual solvent or moisture in the sample will volatilize during high-temperature testing, forming bubbles at the interface between the sample and the fixture, which seriously affects the reliability of the data. Degradation or cross-linking of samples can occur during testing, especially at high temperatures and for long periods of time, as a change in viscosity over time.
The selection and setup of measurement fixtures directly impact the accuracy and scope of application. Fixtures with different geometries are suitable for samples with different viscosities and characteristics, and the cone plate type is suitable for medium and high viscosity fluids, but it is important to note that particles in the sample may damage the cone tip. The parallel plate type is suitable for high viscosity fluids and suspensions, but the shear rate varies radially; Coaxial cylindrical models are suitable for low-viscosity fluids but require correction for end effects. Fixture size selection takes into account torque range and sample volume, and small size fixtures can improve stress resolution at the expense of signal-to-noise ratio. The fixture clearance needs to be set accurately, too large or too small will change the calculation of the shear rate and the actual shear state of the sample.
The selection of measurement parameters should be in line with the characteristics of the sample and the purpose of the study. The range of shear rates in steady-state testing should cover the region of interest, too low may exceed the lower limit of torque measurement, and too high may cause flow instability or sample throwout. The selection of strain amplitude in oscillation test should ensure that the linear viscoelastic zone is linear, and the linear range is predetermined by strain scanning. The choice of frequency range should cover the target relaxation process. Controlling the rate of ramp-up in temperature scanning requires balancing temperature uniformity and measurement time, which can lead to uneven internal sample temperatures.
Wall slip is a common source of error in rheological measurements, especially for highly packed systems, gels, and polymer melts. When the adhesion of the sample to the fixture interface is insufficient, the flow may occur at the interface between the sample and the wall, rather than inside the sample, resulting in low viscosity measurements. Wall slip can be suppressed by using rough surface fixtures, increasing normal pressure, or employing serrated grippers. For samples with severe slippage, different clearance test methods can be used to judge and correct the slip effect.
The thermal effect cannot be ignored under the condition of high-speed shear or high-frequency oscillation. The heat generated by viscosity dissipation increases the temperature of the sample and decreases the viscosity, resulting in measurement errors. For high-viscosity samples, low thermal conductivity makes heat less likely to be lost, and the thermal effect is more pronounced. Measures such as small clearances, controlled test time, and the use of preheated fixtures can reduce the effects of thermal effects.
The calibration status and routine maintenance of the instrument directly affect measurement accuracy. Torque transducers need to be calibrated regularly with standard viscosity oil; The accuracy of the temperature control system needs to be verified by a precision thermometer; The effects of bearing friction and air resistance require inertia correction and friction correction. The cleanliness of the fixture is critical, and residue can change the surface properties and effective clearance of the fixture. The flexibility of the test system can cause phase correction errors in high-modulus sample measurements that need to be compensated for by appropriate procedures.
The technical level of the operator is also a factor that cannot be ignored. The consistency of sample loading, the exclusion of bubbles, the judgment of thermal balance, and the identification of abnormal curves all require experience accumulation and technical judgment. For structural fluids such as thixotropic materials, the shear history of the loading process affects the initial state, and standardized operating procedures need to be developed to ensure comparable results.
Application of rheology in the industrial field
Rheological testing has a wide range of application value in many industrial fields, and is an important technical support for material research and development, process optimization, quality control and product design.
In the field of polymer material processing, rheology is closely related to processing technology and product performance. During the extrusion process, the viscosity of the polymer melt with the shear rate determines the extrusion pressure and yield, and the melt strength affects the out-of-mold expansion and traction stability of the extrusion. In injection molding, melt fluidity and mold filling behavior are controlled by viscosity and modulus, and rheological data optimizes injection temperature, injection speed, and holding pressure to reduce warping and sink marks. In blow molded films, the strain hardening behavior of the melt in tensile flow determines the stability of the bubble tube and the uniformity of film thickness. The rheological data provided by the material supplier provides a basis for customers to select materials and optimize the process, and the processing company adjusts the process parameters in real time through online rheological monitoring.
In the coatings and inks industry, rheology directly determines the workability and final appearance of a product. The coating needs to have a high enough low shear viscosity to prevent settling during storage, an appropriate viscosity at a moderate shear rate to achieve good atomization and spreading when painting or spraying, a high enough zero shear viscosity to prevent sagging under the action of gravity after coating, and good leveling to obtain a flat surface. The thixotropic properties of the coating are adjusted by adding rheological additives, so that its shear is thinned and the structure is controllable, meeting the requirements of each stage of construction. The rheology of inks affects transfer performance and dot clarity during the printing process, ensuring consistent print quality through optimization of viscosity, yield values, and thixotropy.
In the food industry, rheology is the scientific basis for evaluating food quality and taste. The melting properties and smoothness of chocolate in the mouth are closely related to its rheological behavior, and plastic viscosity and yield stress are indicators of chocolate quality control. The viscoelasticity and thixotropic properties of semi-solid foods such as yogurt and cream affect scooping, spreadability, and mouthfeel. The rheological properties of the dough reflect the gluten network structure and processing adaptability, and the baking quality of bread is predicted by tensile rheology and dynamic oscillation tests. The viscosity of the beverage affects the taste and stability, and the rheological behavior is regulated by adding thickeners. Food rheology research provides quantitative tools for product formulation optimization, process design, and quality evaluation.
In the petroleum industry, rheology is directly related to the efficiency of oil and gas extraction and transportation. The rheological characteristics of drilling fluid determine its ability to carry rock chips, suspension weighting materials and clean the wellbore, and optimize the rock-carrying effect and circulating pressure by adjusting yield stress and thixotropy. The rheological behavior of crude oil affects the energy consumption and safety of pipeline transportation, and high-condensation crude oil and heavy oil need to be heated or added to improve the flow of decondensants. The rheological characteristics of fracturing fluid affect the sand carrying capacity and fracture propagation, and improve the fracturing effect by controlling viscoelasticity and drag reduction properties. The rheology of the polymer solution in tertiary oil recovery determines the displacement efficiency and spillover coefficient, which is the key factor to improve oil recovery.
In the field of daily chemical products, rheology affects the appearance, usability and stability of products. The fluidity of liquid products such as shampoos and body washes affects pouring and pumping performance, controlling consistency and foam stability by adjusting zero shear viscosity and thixotropy. The appendicity and absorption of creams and lotions are related to their rheological behavior, and the change of viscosity during the spreading process determines the user experience. The yield stress of the toothpaste ensures that it does not drip on the brush head, the shear thinning ensures that it is easy to disperse when brushing, and the structural recovery ensures that the extruded strips maintain their shape. The rheological properties of makeup products such as liquid foundation and lipstick affect the uniformity and durability of makeup. Daily chemical companies optimize formulas and processes through rheological testing to ensure stable product quality and consistent user experience.
In the field of biomedicine, rheology plays a significant role in physiological research and drug development. The rheological properties of blood affect blood circulation and microcirculation perfusion, and changes in the ability of red blood cells to aggregate and deform are associated with a variety of diseases. The viscoelasticity of joint synovial fluid is essential for joint lubrication and cushioning, and the deterioration of its rheological properties is associated with the development of arthritis. The rheological properties of biomaterials such as tissue engineering scaffolds, drug sustained-release carriers, and medical adhesives affect their function and in vivo behavior. The rheology of topical preparations such as ointments and gels affects drug release and skin penetration. Rheological testing evaluates the performance of biomaterials and pharmaceutical preparations to provide quality assurance for clinical applications.
In the field of building materials, rheology guides the optimization of construction processes and formulation design. The rheological characteristics of freshly mixed concrete affect the pumping, pouring and vibrating compaction effect, and optimize the workability by adjusting the yield stress and plastic viscosity, while ensuring the segregation stability. The rheology of mortar and putty affects plastering and surface flatness, with thixotropy and water retention being key parameters. The rheological behavior of asphalt determines the rutting resistance of the pavement at high temperature and the crack resistance at low temperature, and the PG grade is evaluated by dynamic shear rheology test. The rheology of architectural coatings, sealants, and waterproof materials also affects construction performance and service life. Rheological testing has become an important means of quality control and research and development of building materials.
Summary and outlook
Rheology, as the science of studying the flow and deformation of matter, reveals the intrinsic link between material structure and mechanical response in a complete lineage from ideal Newtonian fluids to complex viscoelastomers. Through standardized measurement methods such as rotational rheology, oscillatory rheology, and capillary rheology, rheological parameters such as viscosity, modulus, relaxation time, and yield stress can be quantified, providing a scientific basis for understanding material behavior and optimizing the process. The combined influence of many factors, from molecular structure and composition to test conditions and instrument status, requires rheology testers to have a deep theoretical foundation and rigorous practical skills. In a wide range of fields such as polymer processing, coating inks, food, petroleum, daily chemicals, biomedicine, and building materials, rheological methods have become an important technical support for material research and development, process optimization, quality control, and product innovation.
Looking ahead, rheological detection technology is developing in the direction of high precision, multi-mode, microscale and online. The new generation of rheometers uses magnetic levitation bearing technology to greatly reduce friction noise and achieve accurate measurements at ultra-low torque and ultra-low frequency, expanding the boundaries of rheological testing. By combining rheometers with microscopes, light scattering, spectrometers, etc., optical-rheological combined technology can observe the shear-induced structural evolution on the line, providing direct experimental evidence for understanding the flow-structure relationship. The development of interface rheological testing technology has made it possible to study the two-dimensional rheological behavior of liquid-liquid interface and gas-liquid interface, providing a deeper understanding of emulsion stability and foam properties.
As an emerging branch, microrheology uses the micron-level thermal motion or active drive of tracer particles to invert the viscoelasticity of materials by tracking their motion trajectories, and realizes the rheological properties of tracer samples and local areas. Techniques such as diffusion spectroscopy, optical tweezers, and magnetic rotation provide diversified means for microrheological measurement. Microrheology has shown unique advantages in the study of biological macromolecular solutions, gelation processes, and intracellular mechanical environment, promoting the intersection of soft matter physics and biomechanics.
The continuous emergence of complex fluids and soft matter materials poses new challenges to rheology. The rheological behavior of heterogeneous systems such as high-fill composites, multiphase polymer blends, liquid crystal polymers, etc. is more complex, and more refined constitutive models and experimental methods need to be developed. The research of nonlinear rheology under large-amplitude oscillation shear has been deepened, and the nonlinear viscoelastic parameters have been extracted through Fourier transform analysis and Lissajous curve analysis, which provides tools for distinguishing different types of nonlinear behavior and microscopic mechanisms. Quantitative characterization of complex phenomena such as thixotropy, yield behavior, wall slip, etc. continues to evolve.
Driven by Industry 4.0 and smart manufacturing, online rheological monitoring technology is being integrated into the production process. Bypass or in-line rheological sensors can monitor viscosity changes in polymer extrusion, coating production, food processing, etc. in real time, and combine with process control systems to achieve closed-loop quality control. Correlation analysis of rheological data with process parameters provides a basis for predictive maintenance and process optimization. The combination of rheology with big data and artificial intelligence is sprouting, and the correlation model between rheological behavior and formulation and process is established through machine learning to guide material design and process tuning. It is foreseeable that rheology, as the core bridge connecting microstructure and macroscopic performance, will continue to play a key role in the research and development of new materials, advanced manufacturing, and process control, driving profound changes from traditional materials engineering to soft matter science and intelligent manufacturing.