Definition and basic concept of shear rate
Shear rate is the core physical quantity in rheology and fluid mechanics that describes the state of fluid flow, and it is defined as the rate of change of velocity with distance perpendicular to the direction of flow. Essentially, the shear rate reflects the relative intensity of motion between adjacent layers within a fluid. When fluid flows through pipes, moves in rotating machinery, or is subjected to shear action in processing equipment, fluid particles at different locations have different velocities, and this difference in velocity is quantified by shear rate. The shear rate is usually expressed as the reciprocal of the second, and the higher the value, the more intense the relative motion between the tropospheres and the stronger the shear effect of the fluid. Understanding the concept of shear rate is crucial for grasping the behavior of non-Newtonian fluids, as the viscosity of most actual fluids varies with the shear rate, a relationship that forms the basis of rheological research.
Physics of shear rate
The physical nature of shear rate is based on the gradient analysis of velocity field in continuous medium mechanics. Consider simple steady-state shear flow, where the fluid is confined between two parallel plates, the lower plate is fixed, and the upper plate moves uniformly in one direction at a constant speed. Due to the viscous action of the fluid, the motion of the upper plate is transmitted to the layers of fluid, forming a linear velocity distribution along the vertical direction. In this state of flow, the shear rate is defined as the rate of change in velocity along the vertical direction, and its mathematical expression is:
γ̇ = dv / dy
In the formula, γ̇ represents the shear rate, v represents the velocity of the fluid particles in the flow direction, and y represents the coordinates perpendicular to the flow direction. For the linear velocity distribution of Newtonian fluids in a simple shear flow, the shear rate is constant, which is equal to the upper plate velocity divided by the spacing between the two plates.
In actual flow geometry, the expression of shear rate is more complex. For laminar flow in round tubes, the velocity is parabolically distributed along the radial direction, and the shear rate varies with the radial position, reaching the maximum at the pipe wall and zero at the center of the tube. Its expression is:
γ̇(r) = -dv(r)/dr
where r represents the radial distance from the center of the pipe, and v(r) represents the flow rate at the radial position r. For the flow of power-law fluid in a round tube, the formula for calculating the shear rate at the pipe wall is:
γ̇w = (3n + 1)/(4n) · (8V/D)
In the formula, γ̇wIt represents the shear rate of the pipe wall, n represents the power law index, V represents the average flow rate, and D represents the pipe diameter. 8V/D is called the apparent shear rate or Newtonian shear rate of the pipe wall, and when the fluid is Newtonian fluid, n is equal to 1, and the apparent shear rate is the true shear rate.
At the molecular level, the shear rate reflects the degree of disturbance of the microstructure of the fluid by the external force field. In the resting state, molecules or particles in a fluid are in a state of random thermal motion and random distribution. When shear is applied, the flow field orients the microscopic units in the direction of flow, the molecular chains stretch, the particles rearrange, and the interactions between the structural units change. This change in microstructure in turn affects the macroscopic flow resistance of the fluid, as the viscosity changes with the shear rate. At low shear rate, the thermal motion is sufficient to keep the microstructure in equilibrium, and the viscosity tends to be constant, which is manifested as the Newtonian plateau region. At the moderate shear rate, the flow field begins to destroy the microstructure, the molecular chains are detangled, the particles are deaggregated, and the viscosity decreases with the increase of the shear rate, showing shear thinning behavior. At high shear rates, the structure is fully destroyed, and the viscosity tends to be constant again, manifesting as the second Newtonian platform region.
The relationship between shear rate and shear stress is related by the rheological equation of state, that is, the constitutive equation. For Newtonian fluids, the two are directly proportional, and the proportional constant is viscosity. For non-Newtonian fluids, the relationship is complex and is usually expressed in terms of apparent viscosity:
η(γ̇) = τ(γ̇) / γ̇
where η (γ̇) represents the apparent viscosity, which is a function of the shear rate; τ(γ̇) represents the shear stress, which also depends on the shear rate. By measuring the shear stress at different shear rates, a complete flow curve can be constructed to describe the viscosity behavior of the fluid.
The magnitude of shear rate varies greatly between flow processes. The shear rate of the slow flow of liquid under gravity can be as low as less than per second. The shear rate in polymer processing such as extrusion and injection molding can reach thousands to tens of thousands per second; Higher shear rates for high-speed spraying, printing, and other processes. Understanding the range of shear rates in specific processes is important for selecting test conditions and predicting material behavior.
Measurement method of shear rate
Laboratory measurements of shear rate are usually not performed directly, but are calculated by means of a rheometer or viscometer to determine the flow parameters under specific geometries and flow conditions, and then according to the corresponding formulas. According to the different measurement principles and geometric structures, it is mainly divided into rotation method, capillary method and slit method.
Measuring shear rate is the most commonly used method for measuring shear rate with rotary rheometers, which can be set or calculated directly by controlling the shear rate or shear stress mode. The cone plate measuring system provides a uniform shear rate and is preferred for rotational measurements. In the cone plate structure, the plate is stationary, the cone rotates at the angular velocity ω, and the angle between the cone and the plate α is very small, usually less than 4 degrees. The shear rate is independent of radial position and is calculated as:
γ̇ = ω / α
where ω represents the angular velocity of the cone rotation, α represents the angle between the cone and the plate. Because the shear rates are equal everywhere, the cone system is particularly suitable for the characterization of non-Newtonian fluids, and the viscosity changes with the shear rate can be directly obtained.
In the parallel plate measurement system, the upper plate rotates at the angular velocity ω, the lower plate is stationary, and the distance between the two plates is H. The shear rate varies with the radial position r, which is the largest at the edge and zero at the center, and its calculation formula is:
γ̇(r) = ω·r / H
The shear rate of parallel plate systems is not uniform, and the shear rate at the edge is usually used as the nominal shear rate for data processing. The system is suitable for high viscosity fluids and suspensions, but requires Rabinowitsch-like correction for shear thinning fluids.
In a coaxial cylinder measurement system, the outer cylinder rotates at an angular velocity ω, while the inner cylinder is stationary, or vice versa. The inner and outer cylinder radii are R respectivelyiand Ro, a shear flow is formed in the gap. For narrow gap cases, the shear rate is approximately uniform, and the calculation formula is:
γ̇ ≈ ω· Ri / (Ro - Ri)
For wide gap cases, the shear rate varies radially, and data processing is required according to the rheological model. The coaxial cylinder system is suitable for low-viscosity fluids, provides precise temperature control, and easily prevents sample volatilization.
Capillary rheometers measure shear rates for high shear rate ranges and simulate machining processes. The fluid is extruded from the capillary under pressure, and the shear rate of the pipe wall is calculated by measuring the volume flow Q and the capillary radius R and length L. For Newtonian fluids, the true shear rate of the pipe wall is:
γ̇w = 4Q / (πR³)
For non-Newtonian fluids, the Rabinowitzch correction is introduced, and the true shear rate of the pipe wall is:
γ̇w = (3n + 1)/(4n) · 4Q/(πR³)
The power law index n is determined by the slope of the relationship curve between the shear stress of the pipe wall and 4Q/(πR³) in double logarithmic coordinates. Bagley correction can be performed to eliminate the effect of inlet pressure loss by measuring capillaries with different length-diameter ratios.
The slit rheometer measures the shear rate and is suitable for in-line monitoring and process control. The fluid flows through the rectangular slit channel, and the wall shear rate is calculated by measuring the pressure drop ΔP and the volumetric flow Q. For Newtonian fluids, the wall shear rate is:
γ̇w = 6Q / (W· H²)
where W represents the slit width and H represents the slit height. For non-Newtonian fluids, a Rabinowitsch-like correction is also required.
Regardless of the method, the accuracy of shear rate measurements relies on precise calibration, temperature control, and proper data processing of the instrument. Before measurement, the instrument should be calibrated for inertia, friction and temperature control. During measurement, it is necessary to ensure that the flow state is stable to avoid abnormal phenomena such as turbulence, wall slip and edge instability. When processing data, it is necessary to choose the appropriate correction method according to the type of fluid.
Key factors that affect shear rate measurements
The accuracy and reliability of shear rate measurement results are influenced by a combination of factors, from fluid properties to instrument conditions, each of which can have a significant impact on the measured value.
The rheological properties of the fluid itself are intrinsic factors that affect shear rate measurements. For Newtonian fluids, the shear rate is directly proportional to the shear stress, the viscosity is constant, and the measurement is relatively simple. For non-Newtonian fluids, viscosity varies with shear rate, making accurate setting and calculation of shear rate more complex. The shear rate of pseudoplastic fluid is thinner, and the shear rate is higher than that of Newtonian fluid at the same stress level. The shear thickening of expansive plastic fluids is lower than that of Newtonian fluids at the same stress level. Fluids with yield stress do not flow when the stress is lower than the yield value, and the shear rate is zero, so special attention should be paid to the selection of measurement mode. The viscosity of thixotropic fluids is time-dependent, and the measurement of shear rate is affected by loading history and test time.
The geometry of the measurement system directly affects the calculation accuracy of the shear rate. The determination of cone angle accuracy and plate spacing zero point is critical in a taper plate system, and small deviations can lead to systematic errors in shear rates. The measurement accuracy of plate spacing and the parallelism of plates in parallel plate systems affect the shear rate distribution, especially for small gap measurements. The concentricity and radius measurement accuracy of the inner and outer cylinders in a coaxial cylinder system determine the calculation accuracy of the shear rate. The geometric dimensional accuracy of capillaries and slits directly affects the flow rate and shear rate, and any dimensional deviations are carried over to the final result.
The stability of the flow state is a prerequisite for obtaining reliable shear rate measurements. Laminar flow at low Reynolds number is the basis for the definition of shear rate, and when the flow changes to turbulence, the velocity distribution changes and the concept of shear rate is no longer applicable. Flow instabilities such as Taylor eddies and secondary flows can disrupt simple shear flows, resulting in abnormal measurement data. For the flow of high-viscosity fluids at high shear rates, the heat generated by viscous dissipation may increase the temperature of the fluid, change the rheological properties, and affect the calculation of the shear rate.
The phenomenon of wall slip is often overlooked in the measurement of shear rate, but its impact is significant. When the adhesion between the fluid and the wall is insufficient, the flow occurs at the interface between the fluid and the wall, rather than inside the fluid, resulting in a lower true shear rate than the nominal shear rate. Wall slip is especially common in high-packing systems, gels, and polymer melts. By using rough surface fixtures and changing geometric clearances, the effects of wall slip can be judged and corrected.
Edge and end effects are present in both rotary and capillary rheometers. In cone plate and parallel plate measurement, the morphology of the sample edge affects the stress distribution, and the effective shear area will be changed by the excess or insufficient sample. In capillary rheometers, the convergent flow in the inlet area and the expansion flow in the outlet area deviate the pressure measurement from the pure shear flow, and Bagley correction is required by capillaries with different length-diameter ratios.
The accuracy of temperature control has an important impact on shear rate measurement. Fluid viscosity is sensitive to temperature, and temperature fluctuations can lead to changes in shear stress, affecting the setting and calculation of shear rates. Especially under high-speed shear conditions, viscous dissipation increases the sample temperature, and it is necessary to use small gaps, control the measurement time, or use pre-temperature control fixtures to reduce thermal effects. Temperature uniformity in the measurement area is equally important, with temperature gradients causing viscosity gradients and non-uniform flow.
The instrument's dynamic response and signal processing capabilities affect shear rate determination in transient and oscillatory measurements. The response speed of the motor, the sensitivity of the torque sensor, and the sampling frequency of the data acquisition system together determine the accuracy of the shear rate control and the authenticity of the response. For dynamic oscillation measurements, the accuracy of strain amplitude and frequency directly affects the amplitude calculation of the shear rate.
The standardization of operators cannot be ignored. Sample loading methods, bubble exclusion, thermal equilibration time, and measurement mode selection all require standardized operation and rich experience. For structural fluids, the shear history of the loading process affects the initial structural state, and a uniform pretreatment procedure needs to be developed to ensure comparable results.
Application of shear rate in the industrial field
As the core parameter describing the flow state, the shear rate has a wide range of application value in many industrial fields, and is an important basis for process design, equipment selection, quality control and product development.
In the field of polymer processing, shear rate is the bridge between the rheological properties of materials and processing conditions. During the extrusion process, the shear rate of the material in the screw groove, head runner and mouth die varies, ranging from tens per second to thousands per second. The viscosity of the polymer melt in the corresponding shear rate range can be measured by capillary rheometer, which can predict the extrusion pressure, calculate the mouth die size, and optimize the screw speed. During the injection molding process, the shear rate during melt filling can reach tens of thousands per second, which has a significant impact on viscosity. In blow molded film, the shear rate of melt in the annular mold affects the extrusion stability, and the tensile flow during the traction process determines the film performance. In the processing of polymer alloys and composites, the morphological evolution of the dispersed phase is controlled by the shear rate, and the ideal microstructure is achieved by adjusting the local shear rate.
In the coatings and inks industry, the shear rate determines the flow behavior of the application process and the quality of the final coating. During the brushing process, the shear rate between the brush and the substrate is about tens to hundreds per second, and the viscosity of the paint in this range affects the brush resistance and coating thickness. During the roll coating process, the coating is subjected to high shear between the roll gaps, and the shear rate can reach thousands per second, and the viscosity determines the transfer amount and film thickness uniformity. During the spraying process, the coating experiences extremely high shear rates at the nozzle, and the atomization effect is directly related to the high shear viscosity. After spraying, the coating is leveled under the action of gravity, at this time the shear rate is extremely low, and the zero shear viscosity and yield stress determine the leveling and sagging resistance. By comprehensively characterizing the rheological behavior of coatings over a wide range of shear rates, formulations and construction conditions can be optimized to ensure coating quality and construction efficiency.
In the petroleum industry, shear rates affect all aspects of oil and gas extraction. During the drilling fluid circulation, different shear rates are experienced in the drill pipe, drill bit nozzle and annulus, and the drilling fluid has high viscosity under low shear to suspend rock chips and low viscosity under high shear to reduce flow resistance through rheological adjustment. In fracturing operations, the shear rate of fracturing fluid in the pumping pipeline, perforation hole and fracture varies greatly, and the shear thinning characteristics of viscosity determine the friction loss and sand carrying ability. The shear rate of the polymer solution in the formation pores in tertiary oil recovery depends on the pore size and flow rate, and the shear behavior and mechanical degradation of the polymer in the porous medium can be studied to optimize the injection scheme to improve the oil recovery. In crude oil pipeline transportation, the stop-and-restart process involves the yield of the cementitious structure under low shear, and the operation process involves the flow at different shear rates.
In the food industry, shear rates affect the processing process and the sensory quality of the product. In dairy processing, milk undergoes a very high shear rate in the homogenization valve, and the fat globules are broken and refined. Yogurt is subjected to shear during fermentation and filling, which disrupts the gel structure and leads to a decrease in viscosity, optimizing the product texture by controlling the shear history and rate. During chocolate refining, shear promotes particle refinement, surface wetting, and flavor release, and the shear rate and time together determine the final rheological properties and taste. During the dough preparation process, the shear rate provided by the mixer affects the development of the gluten network and the gas retention capacity, and controls the dough quality by adjusting the mixing speed and time. The flow behavior of sauces and condiments during pipeline conveying and filling is governed by the shear rate, and the pumping and filling process is optimized by rheological measurements.
In the field of daily chemical products, the shear rate is closely related to the product experience. Shampoo and shower gel should be in low shear when pouring, and the viscosity should be moderate and easy to pour; It is moderately sheared when rubbing in the palm of the hand, and the viscosity decreases and is easy to disperse; When applied to hair or skin, it is subject to different shears, and spreadability and foaming properties are controlled by rheological properties. Cream products are subjected to low shear when taken out of the bottle and should have sufficient consistency to maintain their shape; High shear when applied, viscosity decreases, making the product easy to spread; Structure is restored after application, providing a feeling of hydration and longevity. The toothpaste is subjected to high shear during extrusion, and the shear thinning makes the paste easy to squeeze out of the tube, and the structure is quickly restored after extrusion, keeping the shape of the strip from collapsing. By adjusting the rheological behavior of the product at different shear rates, the ideal usability and functional performance are achieved.
In the biomedical field, shear rate holds significant importance in physiological processes and medical device design. In blood circulation, the shear rate of blood in different blood vessels varies greatly, with higher shear rates in arteries, lower in veins, and extremely high shear rates but small sizes in capillaries. The deformation and orientation of red blood cells under shear affect the apparent viscosity of blood, and the shear thinning behavior is crucial for maintaining circulatory stability. In the design of artificial heart valves and vascular grafts, it is necessary to consider the damage to blood components caused by the shear rate generated by flow to avoid hemolysis and thrombosis caused by high shear. During drug injection, the shear rate of the drug solution in the injection needle is extremely high, which may cause shear denaturation to biomacromolecule drugs.
In the field of building materials, shear rates affect construction performance and final quality. The fresh concrete is subjected to low shear rolling in the mixer truck, moderate shear flow in the pumping pipeline, and high shear compaction in pouring and vibrating. Self-compacting concrete requires low yield stress and proper viscosity, and can flow to fill the formwork with low shear generated by its own weight. Mortar and putty are subjected to shear action in plastering construction, and the rheological characteristics determine the construction feel, bonding with the substrate and surface flatness. Asphalt mixtures undergo different shear rates and temperatures during mixing, paving and rolling, and rheological testing optimizes the ratio and construction process to ensure pavement performance.
Summary and outlook
As the core physical quantity describing the flow state of fluids, the shear rate reveals the internal laws of friction and microstructure evolution in fluids from the rate gradient of simple shear flow. Through standardized measurement systems such as cones, parallel plates, coaxial cylinders, capillaries, and slits, shear rates can be correlated with rheological parameters, providing a scientific tool for understanding the complex behavior of non-Newtonian fluids and quantifying flow processes. The combination of factors, from the characteristics of the fluid itself to measurement geometry, flow state, temperature control and operating specifications, requires rheological testers to have a deep theoretical foundation and rigorous practical skills. In a wide range of fields, including polymer processing, coating inks, oil extraction, food engineering, daily chemical products, biomedicine, and building materials, shear rate is a key process parameter and quality control indicator, guiding process optimization, equipment design, formulation development, and product innovation.
Looking ahead, shear rate-dependent detection technology is evolving towards a wider range, higher accuracy, and more modes. Advances in ultra-low shear rate measurement techniques have made it possible to study structural relaxation, yield behavior, and gelling processes near zero shear, providing a window into understanding the equilibrium and metastable properties of complex fluids. The development of ultra-high shear rate measurement technology has expanded to millions of orders per second, simulating flow behavior under extreme conditions such as high-speed spraying, inkjet printing, and micro-nano processing, providing a rheological basis for emerging manufacturing technologies. The study of shear rate under multiphysics coupling, such as the compound effect of electric field, magnetic field, temperature field and shear field, is driving the development of intelligent fluids and functional materials.
The research on microscale rheology and interfacial rheology has been deepened. The shear rate distribution in microchannels in microfluidic chips is complex and the size effect is significant, and the velocity field measurement technology and rheological characterization methods at the microscale continue to develop, providing support for microfluidic device design and biochemical analysis. The concept and measurement method of two-dimensional shear rate at the liquid-liquid interface and gas-liquid interface are becoming more and more mature, and the interface rheometer can study the dynamic behavior of the adsorption layer at the interface, providing an in-depth understanding of emulsion stability, foam properties and biofilm mechanics. The influence of interfacial shear rate on interfacial rheological parameters is becoming a frontier field in colloidal and interface science.
With the advancement of computational fluid dynamics, the precise calculation of shear rates in numerical simulations is becoming increasingly important. The shear rate distribution in complex geometries is obtained by CFD simulation, which is compared with the actual machining process and verified, providing a virtual testing method for mold design and process optimization. The integration of rheological measurement and flow simulation, and the extraction of constitutive parameters from flow responses through inversion methods, is driving the transformation of rheological characterization technology. The combination of online shear rate monitoring and process control, the closed-loop control system based on rheological signals is gradually being implemented under the framework of intelligent manufacturing, providing technical support for real-time optimization and quality stability of continuous production processes. Shear rate, a fundamental concept in rheology, will continue to be revitalized in the intersection of materials science, engineering and advanced manufacturing.