Showing papers on "Rheometer published in 2013"

Rheology of human blood plasma: viscoelastic versus Newtonian behavior.

Abstract: We investigate the rheological characteristics of human blood plasma in shear and elongational flows. While we can confirm a Newtonian behavior in shear flow within experimental resolution, we find a viscoelastic behavior of blood plasma in the pure extensional flow of a capillary breakup rheometer. The influence of the viscoelasticity of blood plasma on capillary blood flow is tested in a microfluidic device with a contraction-expansion geometry. Differential pressure measurements revealed that the plasma has a pronounced flow resistance compared to that of pure water. Supplementary measurements indicate that the viscoelasticity of the plasma might even lead to viscoelastic instabilities under certain conditions. Our findings show that the viscoelastic properties of plasma should not be ignored in future studies on blood flow.

Extension of the Reiner–Riwlin equation to determine modified Bingham parameters measured in coaxial cylinders rheometers

Abstract: The determination of the exact rheological properties, in fundamental units, of cementitious materials has become gradually a necessary step in the domain of concrete science. Several types of rheometers and their corresponding transformation equations are described in the literature. In this paper, the Reiner–Riwlin transformation equation, valid for coaxial cylinders rheometers, is developed for the modified Bingham model, which is an extension of the Bingham model with a second order term in the shear rate. The established transformation is shown to be compatible with the Reiner–Riwlin equation for the Bingham and Herschel–Bulkley models. Its validation is further proven by means of numerical simulations applied on experimental data. The yield stress values for the three rheological models (applied on the same experimental data) are compared with the yield stress calculated by means of slump flow values. Results showed that the modified Bingham model results in the most stable yield stress values, which are independent of the non-linear behaviour.

Microdevices for extensional rheometry of low viscosity elastic liquids: a review

Abstract: Extensional flows and the underlying stability/instability mechanisms are of extreme relevance to the efficient operation of inkjet printing, coating processes and drug delivery systems, as well as for the generation of micro droplets. The development of an extensional rheometer to characterize the extensional properties of low viscosity fluids has therefore stimulated great interest of researchers, particularly in the last decade. Microfluidics has proven to be an extraordinary working platform and different configurations of potential extensional microrheometers have been proposed. In this review, we present an overview of several successful designs, together with a critical assessment of their capabilities and limitations.

Low-dimensional intrinsic material functions for nonlinear viscoelasticity

Abstract: Rheological material functions are used to form our conceptual understanding of a material response. For a nonlinear rheological response, the possible deformation protocols and material measures span a high-dimensional space. Here, we use asymptotic expansions to outline low-dimensional measures for describing leading-order nonlinear responses in large amplitude oscillatory shear (LAOS). This amplitude-intrinsic regime is sometimes called medium amplitude oscillatory shear (MAOS). These intrinsic nonlinear material functions are only a function of oscillatory frequency, and not amplitude. Such measures have been suggested in the past, but here, we clarify what measures exist and give physically meaningful interpretations. Both shear strain control (LAOStrain) and shear stress control (LAOStress) protocols are considered, and nomenclature is introduced to encode the physical interpretations. We report the first experimental measurement of all four intrinsic shear nonlinearities of LAOStrain. For the polymeric hydrogel (polyvinyl alcohol - Borax) we observe typical integer power function asymptotics. The magnitudes and signs of the intrinsic nonlinear fingerprints are used to conceptually model the mechanical response and to infer molecular and microscale features of the material.

Criteria for Shear Banding in Time-Dependent Flows of Complex Fluids

Abstract: We study theoretically the onset of shear banding in the three most common time-dependent rheological protocols: step stress, finite strain ramp (a limit of which gives a step strain), and shear startup. By means of a linear stability analysis we provide a fluid-universal criterion for the onset of banding for each protocol, which depends only on the shape of the experimentally measured time-dependent rheological response function, independent of the constitutive law and internal state variables of the particular fluid in question. Our predictions thus have the same highly general status, in these time-dependent flows, as the widely known criterion for banding in steady state (of negatively sloping shear stress vs shear rate). We illustrate them with simulations of the Rolie-Poly model of polymer flows, and the soft glassy rheology model of disordered soft solids.

Shear-Induced Nucleation and Morphological Evolution for Bimodal Long Chain Branched Polylactide

Abstract: The effects of long chain branching on the nucleation density enhancements and morphological evolution for polylactide (PLA) materials during shear-induced isothermal crystallization process were thoroughly investigated by using rotational rheometer and polarized optical microscopy (POM). Shear-induced nucleation density enhancements for the long chain branched PLA (LCB PLA) were studied on the basis of the determination of the critical shear rate, for which the stretch of the longest chains of the linear component is expected. The results of shear-induced isothermal crystallization kinetics show that the crystallization process under shear is greatly enhanced compared to the quiescent conditions and the crystallization kinetics is accelerated with the increases in shear rate and/or shear time. LCB PLA crystallizes much faster than linear PLA under the same shear condition. A saturation effect of shear time on crystallization kinetics is observed for both linear PLA and LCB PLA. In-situ POM observations d...

Melt Rheology and its Applications in the Plastics Industry

Abstract: Preface.- 1.Introduction to Rheology: 1.1 What is rheology?.- 1.2 Why rheological properties are important.- 1.3 Stress- a measure of force.- 1.4 Strain - a measure of deformation.- 1.5 Rheological Phenomena.- 1.6 Why polymeric liquids are non-Newtonian and elastic.- 2.Viscosity and the Normal Stress Differences: 2.1 Simple shear and steady simple shear.- 2.2 Viscometric flow.- 2.3 The viscometric functions.- 2.4 The Viscosity.- 2.5 Normal stress differences.- References.- 3. Linear Viscoelasticity: 3.1 Introduction.- 3.2 Stress relaxation and the relaxation modulus.- 3.3 The Boltzmann superposition principle.- 3.4 Start-up of steady simple shear.- 3.5 Relaxation moduli of rubbers and molten polymers.- 3.6 The Maxwell model for the relaxation modulus.- 3.7 The generalized Maxwell model and the discrete relaxation spectrum.- 3.8 The continuous spectrum.- .9 Creep and creep recovery: The compliance.- 3.10 Start-up of steady simple extension.- 3.11 Small amplitude oscillatory shear.- 3.12 Inferring a discrete relaxation spectrum from storage and loss moduli.- 3.13 Combining creep and oscillatory shear data.- 3.14 Time-temperature superposition.- 3.15 Cole-Cole and related plots of linear data.- 3.16 Van Gurp-Palmen Plot of Loss Angle Versus Complex Modulus.- 3.17 Storage and loss moduli of molten linear polymers.- 3.18 The plateau modulus and the molecular weight between entanglements.- 3.19 The Rouse-Bueche model for unentangled melts.- 3.20 Tube models for entangled melts.- 3.21 Molecular weights fo the onset of entanglement effects.- 3.22 Summary.- References.- 4. Nonlinear Viscoelasticity - Phenomena: 4.1 Introduction.- 4.2 Nonlinear phenomena from a tube modelp of view.- 4.3 Nonlinear stress relaxation.- 4.4 Dimensionless groups used to plot rheological data.- 4.5 The viscosity in terms of the tube model.- 4.6 Transient shear tests at finite rates.- 4.7 Extensional flow behavior - Introduction.- 4.8 Extensional Flow Behavior of Melts.- 4.9 Shear modification.- 4.10 Time-temperature superposition of nonlinear properties.- References.- 5. Nonlinear Viscoelasticity - Models: 5.1 Introduction.- 5.2 Tensor notation.- 5.3 The stress tensor.- 5.4 A strain tensor for infinitesimal deformations.- 5.5 The Boltzmann superposition principle in tensor form.- 5.6 Strain tensors for large, rapid deformations.- 5.7 Integral constitutive equations based on continuum mechanics.- 5.8 Continuum differential constitutive equations.- 5.9 Constitutive equations from molecular models.- 5.10 Numerical simulation of melt flows.- References.- 6. Measurement Techniques: 6.1. Introduction.- 6.2. Rotational and other drag-flow rheometers.- 6.3. Pressure-driven rheometers.- 6.4 On-line rheometers.- 6.5 High-throughput rheometry.- 6.6. Extensional rheometers.- 6.7 Torque Rheometers.- 6.8 Using Rheology for statistical process control.- 6.9 Sample Stability: Thermo-oxidative degradation and hydrolysis.- Reference.- 7. Rheology and molecular structure: 7.1 Rheology and structure of linear polymers.- 7.2 Long-chain branching and melt rheology.- References.- 8. Role of Rheology in Plastics Processing: 8.1.Introduction.- 8.2 Flow in simple channels and dies.- 8.3 Flow in an extruder.- 8.4 Sheet extrusion/film casting.- 8.5 Extrusion coating.- 8.6. Film blowing.- 8.7 Blow molding.- 8.8 Injection molding.- 8.9. Rotational molding.- 8.10. Foam Extrusion.- References.- Appendix A Structural and Rheological Parameters for Several Polymers.- Appendix B The Displacement Gradient Tensor.- Subject Index.

In situ rheology of Staphylococcus epidermidis bacterial biofilms

Abstract: We developed a method to grow Staphylococcus epidermidis bacterial biofilms and characterize their rheological properties in situ in a continuously fed bioreactor incorporated into a parallel plate rheometer. The temperature and shear rates of growth modeled bloodstream conditions, a common site of S. epidermidis infection. We measured the linear elastic (G′) and viscous moduli (G′′) of the material using small-amplitude oscillatory rheology and the yield stress using non-linear creep rheology. We found that the elastic and viscous moduli of the S. epidermidis biofilm were 11 ± 3 Pa and 1.9 ± 0.5 Pa at a frequency of 1 Hz (6.283 rad per s) and that the yield stress was approximately 20 Pa. We modeled the linear creep response of the biofilm using a Jeffreys model and found that S. epidermidis has a characteristic relaxation time of approximately 750 seconds and a linear creep viscosity of 3000 Pa s. The effects on the linear viscoelastic moduli of environmental stressors, such as NaCl concentration and extremes of temperature, were also studied. We found a non-monotonic relationship between moduli and NaCl concentrations, with the stiffest material properties found at human physiological concentrations (135 mM). Temperature dependent rheology showed hysteresis in the moduli when heated and cooled between 5 °C and 60 °C. Through these experiments, we demonstrated that biofilms are rheologically complex materials that can be characterized by a combination of low modulus (∼10 Pa), long relaxation time (∼103 seconds), and a finite yield stress (20 Pa). This suggests that biofilms should be viewed as soft viscoelastic solids whose properties are determined in part by local environmental conditions. The in situ growth method introduced here can be adapted to a wide range of biofilm systems and applied over a broad spectrum of rheological and environmental conditions because the technique minimizes the risk of irreversible, non-linear deformation of the microbial specimen before analysis.

Viscometric functions for noncolloidal sphere suspensions with Newtonian matrices

Abstract: We present the results of measuring the three viscometric functions [the relative viscosity ηr, and the first (N1) and second (N2) normal stress differences] for nominally monosize sphere suspensions in a silicone fluid, which is nominally Newtonian. The measurements of ηr and N1−N2 were made with a parallel-plate rheometer, while we used the open semicircular trough method to give N2 directly. With the trough method measurements of N2 could be made down to a 10% concentration (φ=0.1); measurements were continued up to 45% concentration. The trough surface shows visually that N2 is directly proportional to the shear stress τ, and the measurements of N2 agree quite well with the results of Zarraga et al. [J. Rheol. 44, 185–220 (2000)] in the range where concentrations overlap (0.3–0.45) and with those of later investigators. The results for N1 show greater scatter. In the range 0.1≤φ≤0.45, our best estimate of N2/τ is −4.4φ3 and that of N1/τ is −0.8φ3. Hence, the magnitude of N2 is much greater than that o...

Understanding mechanisms leading to asphalt binder fatigue in the dynamic shear rheometer

Abstract: Asphalt binder fatigue resistance is important in determining overall pavement fatigue performance. One procedure commonly used to characterise asphalt binder fatigue resistance is the time sweep test, which consists of repeated cyclic loading in the dynamic shear rheometer (DSR). Generally, apparent changes in complex modulus and phase angle with respect to number of loading cycles are used to define fatigue performance. Although results from DSR testing have been shown to correlate well with asphalt mixture fatigue performance, the mechanisms responsible for changes in binder properties in the DSR were previously not well understood. Results in this study demonstrate that fracture can explain the changes in loading resistance during fatigue testing in the DSR. Under cyclic torsional loading of cylindrical specimens, fracture manifests as a circumferential crack that starts at the periphery of a sample and propagates inward, reducing the effective sample radius. Digital visualisation of binder specimens ...

Evaluation of Low-Temperature and Elastic Properties of Crumb Rubber- and SBS-Modified Bitumen and Mixtures

Abstract: In this study, the performances of bitumen and asphalt mixtures modified by crumb rubber (CR) were compared with those modified by styrene-butadiene-styrene (SBS). The resultant mixtures were evaluated for their rheological and mechanical performances by different experimental techniques such as rheological bitumen tests, i.e., dynamic shear rheometer (DSR), bending beam rheometer (BBR), and hot mixture performance tests, that is, indirect tensile stiffness modulus, fatigue, semicircular bending, and toughness index. Experimental studies show that it is necessary to use twice as much CR as SBS to reach the same performance attained by SBS. CR modification at high additive content exhibits higher elastic response, i.e., recoverable strain, than the SBS-modified mixture. While the resistance to crack initiation of CR-modified mixtures increases with increasing additive content, the resistance to crack propagation decreases dramatically according to fatigue and semicircular bending tests.

Shear banding in polymer solutions

Abstract: The current theoretical belief is that the steady-state shear banding in viscoelastic liquids requires a non-monotonic constitutive relationship between shear stress and shear rate. Although existing rheological studies conclude that the constitutive equation for entangled polymers is monotonic, recent experimental evidence suggests shear banding can nevertheless occur in polymer solutions. In this work, we predict, for the first time, steady state shear banding with a realistic monotonic constitutive theory for polymeric liquids. The key is that a proper account must be taken of the coupling of polymer stress to polymer concentration. We also predict multiple steady states at some shear rates as seen experimentally, with shear banding if the flow is ramped quickly enough from rest, but homogeneous linear shear flow otherwise.

Extensional flow of hyaluronic acid solutions in an optimized microfluidic cross-slot device.

Abstract: We utilize a recently developed microfluidic device, the Optimized Shape Cross-slot Extensional Rheometer (OSCER), to study the elongational flow behavior and rheological properties of hyaluronic acid (HA) solutions representative of the synovial fluid (SF) found in the knee joint. The OSCER geometry is a stagnation point device that imposes a planar extensional flow with a homogenous extension rate over a significant length of the inlet and outlet channel axes. Due to the compressive nature of the flow generated along the inlet channels, and the planar elongational flow along the outlet channels, the flow field in the OSCER device can also be considered as representative of the flow field that arises between compressing articular cartilage layers of the knee joints during running or jumping movements. Full-field birefringence microscopy measurements demonstrate a high degree of localized macromolecular orientation along streamlines passing close to the stagnation point of the OSCER device, while micro-particle image velocimetry is used to quantify the flow kinematics. The stress-optical rule is used to assess the local extensional viscosity in the elongating fluid elements as a function of the measured deformation rate. The large limiting values of the dimensionless Trouton ratio, Tr ∼ O(50), demonstrate that these fluids are highly extensional-thickening, providing a clear mechanism for the load-dampening properties of SF. The results also indicate the potential for utilizing the OSCER in screening of physiological SF samples, which will lead to improved understanding of, and therapies for, disease progression in arthritis sufferers.

Confined flows of a polymer microgel.

Abstract: In this paper, we probe the influence of confinement on the flows of a polymer microgel, namely Carbopol. We compare its bulk rheological behavior, measured with a rheometer and well described by a Hershel-Bulkley law, to velocity profiles measured in rough microchannels, obtained with a particle tracking velocimetry technique. We show a strong disagreement between the bulk prediction for the velocity profiles and the measured ones in the microchannels. Velocity profiles in confined conditions are successfully analyzed within the framework of a non-local fluidity model introduced recently (J. Goyon et al. Nature, 454, 84 (2008)). This allows to determine a cooperativity length ξ, whose order of magnitude compares with the structure size of the microgel. Moreover, we measure flow curves using a rheometer for different gap conditions and also show that this set of data exhibit a strong effect of the confinement on the measured rheological properties. This is again characterized by a typical length of the same order as the cooperativity length scale ξ. We thus evidence confinement effects with two complementary experiments which both give the same typical length for the rearrangements in the flows.

Surface rheological properties of liquid–liquid interfaces stabilized by protein fibrillar aggregates and protein–polysaccharide complexes

Abstract: In this study we have investigated the surface rheological properties of oil–water interfaces stabilized by fibrils from lysozyme (long and semi-flexible and short and rigid ones), fibrils from ovalbumin (short and semi-flexible), lysozyme–pectin complexes, or ovalbumin–pectin complexes. We have compared these properties with those of interfaces stabilized by the native proteins. The surface dilatational and surface shear moduli were determined using an automated drop tensiometer and a stress controlled rheometer with biconical disk geometry. Results show that interfaces stabilized by complexes of these proteins with high-methoxyl pectin have higher surface shear and dilatational moduli than interfaces stabilized by the native proteins only. The interfaces stabilized by ovalbumin and lysozyme complexes have comparable shear and dilatational moduli though ovalbumin–pectin complexes are twice as large in radius as lysozyme–pectin complexes. Under most of the experimental conditions, interfaces stabilized by fibrils have the highest surface rheological moduli. The difference between long semi-flexible lysozyme fibrils or short rigid lysozyme fibrils is not pronounced in interfacial dilation rheology but significant in interfacial shear rheology. The complex surface shear moduli of interfaces stabilized by long semi-flexible fibrils are about 10 times higher than those of interfaces stabilized by short rigid fibrils, over a range of bulk concentrations. Interfaces stabilized by short and more flexible ovalbumin fibrils have a significantly higher surface shear modulus than those stabilized by longer and more rigid lysozyme fibrils. This study has shown that the use of such supra-molecular structural building blocks creates a wider range of microstructural features of the interface, with higher surface shear and dilatational moduli and a more complex dependence on strain.

Short-Term Flow Induced Crystallization in Isotactic Polypropylene: How Short Is Short?

Abstract: The so-called “short-term flow” protocol is widely applied in experimental flow-induced crystallization studies on polymers in order to separate the nucleation and subsequent growth processes [Liedauer et al. Int. Polym. Proc. 1993, 8, 236–244]. The basis of this protocol is the assumption that structure development during flow can be minimized and the rheological behavior, i.e., the viscosity, does not change noticeably. In this work we explore the validity of this assumption for short but strong flows and reveal the structure formation during the early stages of crystallization. Viscosity and structure evolution of an isotactic polypropylene (iPP, Mw ≈ 365 kg/mol and Mw/Mn = 5.4) melt at 145 °C are measured during the short-flow period (0.2–0.25 s) using the combination of a slit rheometer and fast X-ray scattering measurements. For high enough (apparent) shear rates (≥240 s–1) a viscosity rise during flow is observed; i.e., the condition for “short-term flow” is not satisfied. With a time delay with re...

Microstructure in sheared non-Brownian concentrated suspensions

Abstract: The shear-induced microstructure in non-Brownian suspensions is studied. The pair distribution function (PDF) in the shear plane is experimentally determined for particle volume fractions ranging from 0.05 to 0.56. Transparent suspensions made of polymethylmetacrylate particles (172 μm in diameter) dispersed in a fluorescent index matched Newtonian liquid are sheared in a wide-gap Couette rheometer. A thin laser sheet lights the shear plane. The particle positions are recorded and the PDF in the shear plane is computed. The PDF at contact is shown to be anisotropic, with a depleted area in the receding side of the reference particle. The angular position of the depleted zone, close to the velocity axis at low particle concentration, is tilted toward the dilatation axis as the volume fraction is increased. At high concentrations (larger than 0.45), the shape of the PDF changes qualitatively with a secondary depleted area in the compressional quadrant of the main flow and a probability peak in the velocity ...

Drop formation in non-Newtonian fluids.

Abstract: We study the pinch-off dynamics of droplets of yield stress and shear thinning fluids. To separate the two non-Newtonian effects, we use a yield stress material for which the yield stress can be tuned without changing the shear thinning behavior, and a shear thinning system (without a yield stress) for which the shear thinning can be controlled over a large range, without introducing too much elasticity into the system. We find that the pinch-off remains very similar to that of constant viscosity Newtonian liquids, and consequently thinning in shear flow does not imply a thinning in elongational flow.

The influence of shear on the dewatering of high consistency nanofibrillated cellulose furnishes

Abstract: This paper demonstrates a way to utilize the rheological properties of high consistency microfibrillated and nanofibrillated cellulose (MFC and NFC) based furnishes for improved dewatering. This is relevant to a new manufacturing platform that is being developed to form composite webs from suitable mixtures of MFC or NFC, traditional pulp fibres and pigments. The studied furnishes were evaluated in the consistencies range of 5–15 % with an MCR 300 rheometer and an immobilization cell. This setup enables us to characterize the rheology of the samples before and during the dewatering process. Classical rheological methods are used to characterise MFC and NFC furnishes. Yield stress as an indicator of the flocculated network strength was found to increase with the consistencies, following the increase in elastic moduli, which indicated a gel-like strongly flocculated matrix. The shear thinning properties of furnishes are observed to follow the Oswald’s rheological model on a wide range of shear rates. It was found that when the MFC and NFC furnishes were dewatered under vacuum conditions, the final solids content was increased with application of shear. This behaviour is more pronounced for furnishes which contained the more swollen NFC (higher WRV, i.e. higher zeta potential). This effect is further exemplified by the change of the complex and dynamic viscosities during the dewatering. The shear rate, the fibre content, and the furnish consistencies were also found to influence the dewatering rate.

A control scheme for filament stretching rheometers with application to polymer melts

Abstract: We propose a new control scheme to maintain a constant strain rate of the mid-filament diameter in a filament stretching rheometer for polymer melts. The scheme is cast as a velocity algorithm and consists of a feed-back and a feed-forward contribution. The performance of the controller is demonstrated on a commercial low-density polyethylene. Several strain rates and experimental conditions are tested to demonstrate the necessity of the control parameters and the limits of both the control scheme and the experimental apparatus. When the control parameters are properly tuned, the algorithm ensures that the applied strain stays within 2% of the set point and measurements can be made up to Hencky strains of 6.5.

Precision rheometry: Surface tension effects on low-torque measurements in rotational rheometers

Abstract: For rotational rheometers, surface tension results in a torque that should not occur in an ideal, rotationally symmetric geometry. This paper identifies and explains the effect, which is due to surface tension and contact line traction forces, and not surface rheology at the liquid-air interface. For water, we show that this torque can be more than two orders of magnitude larger than the viscous torque. In steady shear flow, the effect appears as a constant torque independent of rate, which would appear inaccurately as apparent shear thinning of water. In oscillatory tests, this may appear inaccurately as an elastic modulus. This surface tension torque is sensitive to wetting conditions and contact line asymmetries and cannot be deterministically corrected in experimental measurements. It therefore raises the lower bound of the instrument low-torque limit. The surface tension torque is reduced by maximizing rotational symmetry of the contact line, minimizing evaporation and the migration of the contact line, reducing the radial location of the contact line, and lowering the surface tension. Identifying and eliminating the surface tension torque is critical for low viscosities, intrinsic viscosities, soft materials, subdominant viscoelastic components, small gaps, and any circumstance where the low-torque limit is experimentally important.

Development of a confocal rheometer for soft and biological materials.

Abstract: We discuss the design and operation of a confocal rheometer, formed by integrating an Anton Paar MCR301 stress-controlled rheometer with a Leica SP5 laser scanning confocal microscope. Combining two commercial instruments results in a system which is straightforward to assemble that preserves the performance of each component with virtually no impact on the precision of either device. The instruments are configured so that the microscope can acquire time-resolved, three-dimensional volumes of a sample whose bulk viscoelastic properties are being measured simultaneously. We describe several aspects of the design and, to demonstrate the system's capabilities, present the results of a few common measurements in the study of soft materials.

Ageing, yielding, and rheology of nanocrystalline cellulose suspensions

Abstract: This paper investigates yielding and flow of nanocrystalline cellulose (NCC) suspensions by combining rheological measurements with light scattering echo (LS-echo). The NCC samples are characterized using static and dynamic light scattering as well as polarized optical microscopy coupled with a rotational rheometer. The storage modulus of the NCC suspensions is found to increase with waiting time after shear rejuvenation. The microscopic particle rearrangements of the NCC spindles are followed by LS-echo at both short and long waiting times under oscillatory shear flow. We find that the onset of shear-induced irreversible microscopic particle rearrangements, coincide with the strain at which storage and loss moduli cross over in the nonlinear viscoelastic regime identified by the macroscopic yield point of the sample. The yielding transition is found to occur at a higher strain as the frequency of oscillation increases.

Viscous dissipation pattern in incompressible Newtonian simple shear zones: an analytical model

Abstract: An analytical model of shear heating in an inclined simple shear zone with Newtonian rheology under a reverse shear sense and an upward resultant pressure gradient is presented. Neglecting a number of secondary factors, the shear heat is expressed as a function of the total slip rates at the boundaries, pressure gradient, dip and thickness of the shear zone, and density, viscosity, and thermal conductivity of the rock. A quartic temperature profile develops with a point of maximum temperature near the bottom part of the shear zone in general. The profile is parabolic if pressure gradient vanishes leading to a Couette flow. The profile attains a bell shape if there is no slip at the boundaries, i.e., a true Pouseille flow. The present model of shear heating is more applicable in subduction channels and some extruding salt diapirs where the rheology is Newtonian viscous and pressure gradient drives extrusion.