Shear Velocity Gradient Research Articles

Examination of flow birefringence induced by the shear components along the optical axis using a parallel-plate-type rheometer

In this study, the concept of rheo-optics was applied to explore the flow birefringence induced by the stress components along the camera’s optical axis since it is often overlooked in the traditional theories of photoelastic flow measurement. A novel aspect of this research is that it involved conducting polarization measurements on simple shear flows, specifically from a perspective in which a shear-velocity gradient exists along the camera’s optical axis. A parallel-plate-type rheometer and a polarization camera are employed for these systematic measurements. The experimental findings for dilute aqueous cellulose nanocrystal suspensions demonstrate that the flow birefringence can be expressed as a power law based on the power of the second invariant of the deformation-rate tensor. This suggests that flow birefringence can be universally characterized by the coordinate-independent invariants and a pre-factor determined by the direction of polarization measurement. By adjusting the nonlinear term in the stress-optic law, its applicability could be expanded to include three-dimensional fluid stress fields in which the stress is distributed along the camera’s optical axis.

Role of minimization entropy generation and heat transfer on the nanofluid peristaltic flow via Reiner-Philippoff model

The primary objective of this study is to explore the effects of minimizing entropy generation in the context of peristaltic flow within an asymmetric tapered channel, using Buongiorno’s nanofluid model to account for pseudoplastic and dilatant behaviors of the nanofluid. To accurately represent the non-Newtonian characteristics of the fluid, we employ the Reiner-Philippoff (RPh) fluid model, known for its intricate nature among non-Newtonian models. In the RPh model, the relationship between shear stress and velocity gradient is nonlinear, and it also accounts for the implicit coupling between stress and deformation rate, presenting a formidable challenge. Our investigation incorporates the effects of thermophoresis motion, the viscosity parameter of the RPh fluid, and Brownian motion into the governing equations. We simplify these equations under the assumptions of low Reynolds numbers and long wavelengths. Subsequently, we numerically solve the resulting nonlinear equations. We thoroughly discuss the significant impact of RPh nanofluid parameters on entropy generation and the Bejan number by presenting graphical representations. Notably, we observe that the fluid transitions from a dilatant behavior to Newtonian behavior and from Newtonian behavior to pseudoplastic behavior as we vary the RPh fluid parameter. Furthermore, we briefly address the influence of thermophoretic diffusion, the Brinkman number, the RPh fluid parameter, Prandtl number, and Brownian motion parameters on entropy production and the Bejan number. It is experimented that the entropy generation is less for dilatants fluid and higher for pseudoplastic fluids. We can also notice that the entropy generation significantly increases by Brinkman number Br for both types of fluid. We also provide a mathematical and graphical examination of the effects of all these significant parameters.

Building a model of the abrasion grinding mechanism in a tumbling mill based on data visualization

The object of this study is the grinding process in a tumbling mill when the mechanism of destruction by abrasion is implemented, which is caused by the mechanism of shear loading. The abrasive effect due to the impulse interaction during the mutual chaotic movement of granular particles in the shear layer of loading, characterized by the granular temperature, is taken into account. The task solved was determining the parameters of the shear interaction, which is caused by the difficulties of modeling and complexity of the hardware analysis of behavior of the internal loading in the mill. A mathematical model was built based on data visualization for the abrasion grinding mechanism. The power of the shear interaction forces was taken as an analog of the grinding performance. The initial shear characteristic was considered to be the average value of the shear velocity gradient in the central averaged normal section of the shear layer. The impact on productivity of the granular temperature and mass fraction of the shear layer and loading turnover was taken into account. The effect of rotation speed on performance was evaluated by experimental modeling at a chamber filling degree of 0.45 and a relative particle size of 0.0104. The maximum value of the energy and productivity of grinding by abrasion was established at the relative speed of rotation ψω=0.55–0.6. The results have made it possible to establish a rational speed when grinding by abrasion, ψω=0.5–0.6. This value is smaller in comparison with grinding by crushing ψω=0.55–0.65 and breaking ψω=0.75–0.9. The established effect is explained by the detected activation of the chaotic quasi-thermodynamic movement of particles of the shear layer at slow rotation. The model built makes it possible to predict rational technological parameters of the energy-saving process of fine grinding in a tumbling mill by abrasion

Numerical investigation of clocking effect on irreversible energy loss in volute for centrifugal pump with vaned diffuser based on entropy generation method

In order to study temporal and spatial variation of energy loss and reveal influence rule of clocking effect on energy loss and flow field in centrifugal pump with vaned diffuser, numerical simulations were carried out. Numerical simulations were validated by experiments. Local equilibrium of turbulence generation and dissipation was verified to state feasibility of energy loss methods. Hydraulic loss in each component was assessed, which shows that variation of hydraulic loss in volute is more significant due to clocking effect than that in other components. Vortical structure in volute varies greater under different guide vane positions than it in other components. The results show that positive and negative flow angle appears interlaced in tongue region with high velocity gradient, especially when diffuser is mounted at θd1. Since a clearance presents between tongue and vane trailing edge at θd1, a small vortex forms. Which promotes the blocking effect of the large-scale vortex at volute outlet pipe. Therefore, high velocity gradient appears at small vortex region and volute outlet pipe region. The shear strain rate at the tongue and volute outlet pipe is more significant than that at other diffuser mounted positions. Energy loss at these regions increases. This situation can be improved by a more suitable diffuser mounted position θd4, where the clearance and small vortex vanishes, the shear strain rate, velocity gradient, and energy loss decrease.

Impact of pseudoplastic and dilatants behavior of Reiner-Philippoff nanofluid on peristaltic motion with heat and mass transfer analysis in a tapered channel

<abstract> <p>The main goal of this article is to investigate the effects of pseudoplastic, and dilatants behavior of non-Newtonian based nanofluid on peristaltic motion in an asymmetric tapered channel. Buongiorno's nanofluid model is considered for the study to investigate the heat and mass transfer analysis. The Reiner-Philippoff fluid model is considered to depict the non-Newtonian characteristics of the fluid. The Reiner Philippoff fluid model is the most challenging model among other non-Newtonian fluid models in such a way that shear stress and velocity gradient are non-linearly proportional to each other in this model. This model also represents the implicit relation between stress and deformation rate. The governing equations are based on the dispersion model for nanofluid which incorporates the effects of thermophoretic and Brownian diffusions. The governing equations are simplified in the account of the small Reynolds number and long wavelength assumptions. The solution of the equations is retrieved numerically by the help of built in ND-Solve function of MATHEMATICA software. The sound effects of Reiner-Philippoff based nanofluid on the behavior of velocity and temperature profiles of the fluid, streamlines, pressure gradient fields, and concentration of the nanoparticles are discussed thoroughly. The interesting behavior of Reiner-Philippoff fluid for two limiting shear stress cases when shear stress parameter is very small and very large, for which Reiner-Philippoff fluid behaves like a Newtonian fluid, is also verified. It is observed that fluid flow changes its properties from dilatants fluid to Newtonian and from Newtonian to pseudoplastic fluid by varying the Reiner-Philippoff fluid parameter. According to the findings, the temperature graphs rise against higher thermophoretic diffusion and Brownian motion parameters and falls with higher Prandtl number. Further, the impacts of all the significant parameters are investigated briefly by mathematically as well as graphically.</p> </abstract>

A PIV investigation of laminar and turbulent viscoplastic fluid flow on axisymmetric abrupt contraction

The current work is devoted to analyzing viscoplastic fluid flow in a circular axisymmetric abrupt contraction with ratio . The velocity fields and static pressure along a hydraulic loop were measured employing Particle Image Velocimetry technique and a pressure transducers system, respectively. Four aqueous solutions of Carbopol 940 with different rheological parameters were used as viscoplastic fluids. Laminar and turbulent flow conditions are evaluated and compared with the generalized Hagen–Poiseuille law and the Malin friction factor correlations supported by turbulent fluctuations measurements. The formation of a plug core region is observed around the centerline of the pipe. The relationships between the velocity profiles and the shear stress distribution with the plug core were investigated supported via shear rate calculations. The results show that the yield stress highly influences the shape of the velocity profiles and the appearance of unyielded regions at the contraction edges. The shear stress maps show a layered distribution across the pipe diameter with higher values located at the contraction entrance. Instead, a constant shear stress distribution is found in the unyielded regions. The size of these unyielded regions increases with the yield stress but is reduced at regions with high shear rates due to increased inertial forces. Pressure drop measurements contrasted with the shear stress and velocity gradients maps illustrated that the pressure losses along the pipe are affected by the yield stress and the Reynolds number. However, a non-dependence of the pressure loss coefficient at the contraction plane with the rheological parameters is evidenced, as presented in earlier experimental results. This differs from many numerical studies since the contraction’s pressure loss coefficient for viscoplastic fluids is directly affected by the increase of inertial forces at this region.

Experimental Analysis of Wall Flow Pattern and Fluid Shear Stress Effects on Creeping Flow Field in Convergent-Divergent Microchannels

The flow of fluids including micron particles in micro channels and manufacturing microfluidics tools have been one of the important topics in last decades and are utilized in different industries. The research procedure is experimental in this work. The experimental tests are carried out on the flow in a convergent-divergent microchannel having 200 $mu$m height. The utilized experimental method in this research is particle tracking based on the xerography technique, observation, record and data processing. The results showed that the velocity of the particles in Y-direction has a great effect on their motion in the convergent-divergent channel. Study of the particles' sedimentation in different Reynolds showed that it can be eliminated the destructive effect of channel obstruction using convergent-divergent channel which is originated from increasing sedimentation in low Reynolds. The shear stress and velocity gradient are two main factors of the particles' velocity in the convergent-divergent channel. The results showed that the shear stress has an excessive impact on the particles' velocity than the velocity gradient. Moreover, besides the upper and bottom walls, side walls affect the particles' velocity. The flow of fluids including micron particles in micro channels and manufacturing microfluidics tools have been one of the important topics in last decades and are utilized in different industries. The research procedure is experimental in this work. The experimental tests are carried out on the flow in a convergent-divergent microchannel having 200 $mu$m height. The utilized experimental method in this research is particle tracking based on the xerography technique, observation, record and data processing. The results showed that the velocity of the particles in Y-direction has a great effect on their motion in the convergent-divergent channel. Study of the particles' sedimentation in different Reynolds showed that it can be eliminated the destructive effect of channel obstruction using convergent-divergent channel which is originated from increasing sedimentation in low Reynolds. The shear stress and velocity gradient are two main factors of the particles' velocity in the convergent-divergent channel. The results showed that the shear stress has an excessive impact on the particles' velocity than the velocity gradient. Moreover, besides the upper and bottom walls, side walls affect the particles' velocity.

Ferrocholesteric-ferronematic transitions induced by shear flow and magnetic field.

We study the unwinding of the ferrocholesteric helical structure induced by a combined action of a magnetic field and a shear flow. Both influences are able to induce the ferrocholesteric–ferronematic transition independently; however, the differences between the magnetic field orientation and the flow alignment direction lead to a competition between magnetic and hydrodynamic mechanisms of influence on the ferrocholesteric structure. We analyze various orientations of a magnetic field relative to the direction of a shear flow. The pitch of the ferrocholesteric helix is obtained as function of the strength and the orientation angle of the magnetic field, the shear velocity gradient and a reactive parameter. Phase diagrams of ferrocholesteric–ferronematic transition and the pitch of the ferrocholesteric helix as functions of the material and the governing parameters are calculated. We find out that imposing a shear flow leads to a shift of the magnetic field threshold. The value of the critical magnetic field depends on the magnetic field orientation, the velocity gradient, and the viscous coefficients. We show that the interplay of a magnetic field and a shear flow can induce reentrant orientational transitions that are ferrocholesteric–ferronematic–ferrocholesteric.

Study of shear stress in laminar pipe flow using entropy concept

In fluid mechanics, the shear stress is calculated from the frictional force caused by viscosity and fluctuating velocity. Shear stress equations are used widely because of their simplicity. On the other hand, they have a critical limitation of requiring an energy gradient, which is generally difficult to estimate in practice. In particular, measuring the shear stress and velocity gradient on the boundary layer is difficult. The point velocity throughout the entire cross section is needed to calculate the velocity gradient. This study proposes the shear stress distribution equations for laminar flow based on entropy theory using the mean velocity and entropy coefficient. The proposed equations were compared with the measured shear stress distribution using Nikuradse’s data. The results revealed a correlation coefficient of approximately 0.99, indicating that the proposed method fits the Nikuradse’s data. Therefore, the shear stress distribution can be estimated easily and accurately using the proposed equations, which can be used in future for the management and design of a water pipeline.

Effect of uniform electric field on the drop deformation in simple shear flow and emulsion shear rheology

Electrohydrodynamic deformation and orientation of a neutrally buoyant, leaky dielectric, Newtonian drop suspended in another immiscible, leaky dielectric, Newtonian medium is analyzed under the combined influence of uniform electric field and simple shear flow. Application of uniform electric field, perpendicular to the direction of shear flow, not only deforms the drop but also modifies the rheological behavior of a dilute emulsion. In the creeping flow limit, an analytical solution for the deformed drop shape is obtained when the drop shape remains nearly spherical and the surface charge convection is weak. The effective shear rheology is obtained for a dilute emulsion of non-interacting drops by calculating the one-particle contribution to the emulsion stress. The results show that the combined influence of uniform electric field and shear flow is not a simple linear superposition of the independent contributions from electric field and shear flow. Application of uniform electric field always leads to larger drop deformation with drop inclination more towards the direction of velocity gradient for the particular case of perfectly dielectric drops. Presence of surface charge convection for a leaky dielectric drop can increase or decrease the drop deformation with the drop inclination more towards either the direction of shear flow or velocity gradient. The effective shear viscosity and normal stress differences are found to be independent of shear rate. These quantities are significantly affected by the surface charge convection and shape deformation. Shape deformation always increases the effective viscosity of a dilute emulsion composed of perfectly dielectric drops. Interestingly, for a dilute emulsion composed of leaky dielectric drops, results show that the combined influence of charge convection and shape deformation can augment or decrease the effective shear viscosity.

Cavitation about a jet in crossflow

Cavitation occurrence about a jet in crossflow is investigated experimentally in a variable-pressure water tunnel using still and high-speed photography. The 0.012 m diameter jet is injected on the centreplane of a 0.6 m square test section at jet to freestream velocity ratios ranging from 0.2 to 1.6, corresponding to jet-velocity-based Reynolds numbers of$25\times 10^{3}$to$160\times 10^{3}$respectively. Measurements were made at a fixed freestream-based Reynolds number, for which the ratio of the undisturbed boundary layer thickness to jet diameter is 1.18. The cavitation number was varied from inception (up to about 10) down to 0.1. Inception is investigated acoustically for bounding cases of high and low susceptibility to phase change. The influence of velocity ratio and cavitation number on cavity topology and geometry are quantified from the photography. High-speed photographic recordings made at 6 kHz provide insight into cavity dynamics, and derived time series of spatially averaged pixel intensities enable frequency analysis of coherent phenomena. Cavitation inception was found to occur in the high-shear regions either side of the exiting jet and to be of an intermittent nature, increasing in occurrence and duration from 0 to 100 % probability with decreasing cavitation number or increasing jet to freestream velocity ratio. The frequency and duration of individual events strongly depends on the cavitation nuclei supply within the approaching boundary layer. Macroscopic cavitation develops downstream of the jet with reduction of the cavitation number beyond inception, the length of which has a power-law dependence on the cavitation number and a linear dependence on the jet to freestream velocity ratio. The cavity closure develops a re-entrant jet with increase in length forming a standing wave within the cavity. For sufficiently low cavitation numbers the projection of the re-entrant jet fluid no longer reaches the cavity leading edge, analogous to supercavitation forming about solid cavitators. Hairpin-shaped vortices are coherently shed from the cavity closure via mechanisms of shear-layer roll-up similar to those shed from protuberances and jets in crossflow in single-phase flows. These vortices are shed at an apparently constant frequency, independent of the jet to freestream velocity ratio but decreasing in frequency with reducing cavitation number and cavity volume growth. Highly coherent cavitating vortices form along the leading part of the cavity due to instability of the jet upstream shear layer for jet to freestream velocity ratios greater than about 0.8. These vortices are cancelled and condense as they approach the trailing edge in the shear layer of opposing vorticity associated with the cavity closure and the hairpin vortex formation. For lower velocity ratios, where there is decreased jet penetration, the jet upstream shear velocity gradient reverses and vortices of the opposite sense form, randomly modulated by boundary layer turbulence.

Characteristics of velocity gradient jumping discontinuity in steady Poiseuille flow of Johnson–Segalman fluid

The characteristics of velocity gradient jumping discontinuity are studied in pipe flow of a Johnson–Segalman fluid model, which allows for the non-monotonic relationship between the shear stress and velocity gradient in a simple shear flow for a certain domain range of the material parameters, including slip parameter, Weissenberg number and ratio of viscosities. This non-monotonic constitutive equation admitting multiple steady-state solutions is characterized by shear rate discontinuities. Firstly, the analytical solutions of critical maximum pressure gradient and minimum pressure gradient are calculated with material parameters. Then the properties of “top jumping” and “bottom jumping” of velocity gradient, which are introduced by increasing and decreasing of pressure gradient respectively, and their relation with spurt phenomena, are investigated in this paper. We find that the non-overlapping processes of velocity gradient “top jumping” and “bottom jumping” are in analogy to the variation process for amplitude/frequency relationship in non-linear vibration mechanics. It means two jumping processes cannot occur in the same way of pressure gradient increasing or decreasing. This exploring point is distinctly different from the present literatures. And we have made a confirmation that the flow would be subdivided into two layers when velocity gradient jumping happens in the processes of pressure gradient increasing and pressure gradient decreasing in steady flow. Especially the effects of the velocity gradient jumping on the flow rate are considered quantitatively. Besides, there is a linear relationship between pressure gradient and shear stress. However the varying process of velocity gradient is characterized by jumping discontinuities between two critical pressure gradients. Additionally, the effects of material parameters on the top jumping and bottom jumping locations have been considered to find out where the spurt phenomena occur.Finally, the flow rates in different processes of pressure gradient increasing and pressure gradient decreasing have been discussed to provide potential opportunity for practical application in industrial transportation.

Influence of shear processing on morphology orientation and mechanical properties of styrene butadiene triblock copolymers

The influence of ram extrusion on structure and mechanical properties of a triblock copolymer consisting of polystyrene (S) outer blocks and poly(styrene–stat–butadiene) (S/B) middle block is studied for a wide range of shear rates. Structural features on the mesoscale (10–100 nm) are investigated by small angle X-ray scattering (SAXS) and transmission electron microscopy (TEM). Transition Moment Orientation Analysis (TMOA) is applied to quantify the orientation on the molecular (segmental) scale (<1 nm). All extruded samples microphase-separate and show a lamellar morphology with periodicities of about 33 nm. Significant orientation is observed on the mesoscale where the surface normals of the lamellae are preferentially perpendicular to the extrusion direction. The corresponding degree of orientation drops slightly at elevated shear rates of about 600 s−1. Interestingly, Chevron-like pattern with two preferred orientations of the lamellae are observed in cross-sections probably due to shear velocity gradients in the rectangular die. In contrast, significant orientation on the molecular scale is absent for styrene and butadiene units indicating basically random orientation of the chain segments. The mechanical properties are, however, strongly anisotropic. Uniaxial tensile tests performed parallel and perpendicular to the extrusion direction reveal higher E∥ moduli (1.1 – 0.6 GPa) along with yielding but significantly smaller E⊥ moduli (100−250 MPa) without pronounced yielding. Main trends in both moduli, E∥ and E⊥, can be explained based on mesoscale orientation using the analytical composite model. In general, the results demonstrate that orientation effects on the mesoscale have a strong influence on the mechanical properties and must be considered during the optimization of extruded or injection-molded components made from microphase-separated block polymers.

Ion temperature profile stiffness: non-linear gyrokinetic simulations and comparison with experiment

Recent experimental observations at JET show evidence of reduced ion temperature profile stiffness. An extensive set of nonlinear gyrokinetic simulations are performed based on the experimental discharges, investigating the physical mechanism behind the observations. The impact on the ion heat flux of various parameters that differ within the data-set are explored. These parameters include the safety factor, magnetic shear, toroidal flow shear, effect of rotation on the magnetohydrodynamic equilibrium, R/Ln, βe, Zeff, Te/Ti, and the fast-particle content. While previously hypothesized to be an important factor in the stiffness reduction, the combined effect of toroidal flow shear and low magnetic shear is not predicted by the simulations to lead to a significant reduction in ion heat flux, due both to an insufficient magnitude of flow shear and significant parallel velocity gradient destabilization. It is however found that nonlinear electromagnetic effects due to both thermal and fast-particle pressure gradients, even at low βe, can significantly reduce the ion heat flux, and is a key factor in explaining the experimental observations. A total of four discharges are examined, at both inner and outer radii. For all cases studied, the simulated and experimental ion heat flux values agree within reasonable variations of input parameters around the experimental uncertainties.

A sharp cratonic lithosphere–asthenosphere boundary beneath the American Midwest and its relation to mantle flow

Beneath the American Midwest, S-to-P (Sp) converted wave imaging and multi-mode surface wave tomography identify a north-trending transition in seismic structure at 150–250 km depth. To the east of this American Midwest transition (AMT), the lithosphere–asthenosphere boundary (LAB) is imaged as a 1–2% Sp/Sv amplitude arrival at 200–240 km depth, consistent with the depth of negative shear velocity and azimuthal anisotropy gradients imaged by surface wave tomography. To the west of the AMT, Sp conversions are much shallower at 150–190 km depth and are much weaker (<0.7%) or absent. Azimuthal anisotropy constrained by surface wave tomography also changes across the AMT, with stronger anisotropy to the east of the transition beneath the thicker lithospheric root. We suggest that the seismic changes across the AMT can be explained by considering the effects of asthenospheric flow beneath the leading edge of the thick lithospheric root. The mantle flow is dominantly driven by the drift of the North America plate. Locally higher flow velocities are expected where the asthenosphere is forced to flow beneath the thicker root. This mantle underflow could create a sharper seismic LAB east of the AMT via two effects. First, the local increase in flow velocities could steepen the thermal gradient at the base of the lithosphere, and hence the isotropic velocity contrast. Second, the increased strain rate along edge of the lithosphere could enhance the magnitude of azimuthal anisotropy. Our results suggest that seismically detectable LAB sharpness variations could be used to constrain geographic variations in coupling between plates and mantle convection. A secondary result is the image of a Mid-Lithospheric Discontinuity arrival at 80–110 km depth that is found primarily to the east of the AMT. This arrival is interpreted as produced by a layer of low-velocity metasomatic minerals that have accumulated since the >1.8 Ga creation of the lithosphere.

Elasticity and lattice dynamics of enstatite at high pressure

The behavior of synthetic‐powdered 57Fe‐enriched enstatite (Mg0.980Fe0.020(5))(Mg0.760Fe0.240)Si2O6 has been explored by X‐ray diffraction (XRD) and nuclear resonant inelastic X‐ray scattering (NRIXS). The Pbca‐structured enstatite sample was compressed in fine pressure increments for our independent XRD measurements. One structural transition between 10.1 and 12.2 GPa has been identified from the XRD data. The XRD reflections observed for the high‐pressure phase are best matched with space group P21/c. We combine density functional theory with Mössbauer spectroscopy and NRIXS to understand the local site symmetry of the Fe atoms in our sample. A third‐order Birch‐Murnaghan (BM3) equation of state fitting gives KT0=103±5 GPa and KT0′=13±2 for the Pbca phase. At 12 GPa, a BM3 fitting gives KT12=220±10 GPa with KT12′=8±4 for the P21/c phase. NRIXS measurements were performed with in situ XRD up to 17 GPa. The partial phonon density of states (DOS) was derived from the raw NRIXS data, and from the low‐energy region of the DOS, the Debye sound velocity was determined. We use the equation of state determined from XRD and Debye sound velocity to compute the isotropic compressional (VP) and shear (VS) wave velocities of enstatite at different pressures. Our results help constrain the high‐pressure properties of Pbca‐structured enstatite in the Earth's upper mantle. We find that candidate upper mantle phase assemblages containing Pbca‐structured enstatite are associated with shear velocity gradients that are higher than the average Earth model PREM but lower than regional studies down to about 250 km depth.

Parameter effects on shear stress of Johnson–Segalman fluid in Poiseuille flow

Exact solutions of shear stress versus velocity gradient and the numerical solutions of streamwise velocity distribution in radial direction of a Johnson–Segalman fluid in a circular pipe are obtained. The effects of material parameters, Weissenberg number, ratio of viscosities and slip parameter, on shear stress and streamwise velocity have been considered to investigate the discontinuous velocity derivatives and stick-slip phenomenon at the wall. We find that there is a non-monotonic relationship between the shear stress and rate of shear for certain values of the material parameters and consequently, the velocity profile has discontinuous derivatives. Also the non-monotonic region is shortening with the increasing of ratio of viscosities, and is lengthening with the increasing of slip parameter. For the flow with larger slip parameter, the initially driving pressure gradient has to be larger for the appearance of spurt phenomenon. Moreover, the variational range of material parameters is given for the appearance of a non-monotonic relationship between the shear stress and the rate of shear. Finally, we have shown the exact expression of critical pressure gradient and also have given the conditions where spurt phenomena occur.

Benchmark problems for mixtures of rarefied gases. I. Couette flow

The planar Couette flow for gaseous mixture He–Ar is calculated by the direct simulation Monte Carlo method based on ab initio potential over the whole range of the gas rarefaction for several values of the mole fraction and for two values of the wall speed. The smaller value of the speed corresponds to the limit when the nonlinear terms are negligible, while the larger value describes a nonlinear flow. The shear stress, velocity gradient, temperature, and mole fraction profiles are presented. The reported results can be used as benchmark data to test model kinetic equations for gaseous mixtures. To study the influence of the intermolecular potential, the same simulations are carried out for the hard sphere molecular model. A relative deviation of the results based on this model from those based on the ab initio potential are analyzed. It is pointed out that the difference between the shear stresses of the two potentials for the linearized solution is within 1%, while it reaches 6% for the nonlinear cases.

水と微細砂からなる混合体のレオロジー測定装置

The equipment for measuring rheological characteristics of water-fine sediment mixture is studied. The relations among wall shear stress, average velocity, velocity gradient and kinematic viscosity are derived for pipe flows assuming Bingham fluid. The equipment which is composed of a tank and several small pipes is proposed based on these theoretical relations. The diameters and the lengths of these small pipes are determined in order to obtain data on the relation between shear stress and strain rate in laminar flow conditions. Measured data on yield stress and kinematic viscosity for water and kaolin mixture suggest that the measurements are performed properly, which means we are able to measure rheological parameters of water-fine sediment mixtures fully, simply and economically.

Mantle transition zone shear velocity gradients beneath USArray

Broadband P-to-s scattering isolated by teleseismic receiver function analysis is used to investigate shear velocity (VS) gradients in the mantle transition zone beneath USArray. Receiver functions from 2244 stations were filtered in multiple frequency bands and migrated to depth through P and S tomography models. The depth-migrated receiver functions were stacked along their local 410 and 660km discontinuity depths to reduce stack incoherence and more accurately recover the frequency-dependent amplitudes of P410s and P660s. The stacked waveforms were inverted for one-dimensional VS between 320 and 840km depth. First, a gradient-based inversion was used to find a least-squares solution and a subsequent Monte Carlo search about that solution constrained the range of VS profiles that provide an acceptable fit to the receiver function stacks. Relative to standard references models, all the acceptable models have diminished VS gradients surrounding the 410, a local VS gradient maximum at 490–500km depth, and an enhanced VS gradient above the 660. The total 410 VS increase of 6.3% is greater than in reference models, and it occurs over a thickness of 20km. However, 60% of this VS increase occurs over only 6km. The 20km total thickness of the 410 and diminished VS gradients surrounding the 410 are potential indications of high water content in the regional transition zone. An enhanced VS gradient overlying the 660 likely results from remnants of subduction lingering at the base of the transition zone. Cool temperatures from slabs subducted since the late Cretaceous and longer-term accumulation of former ocean crust both may contribute to the high gradient above the 660. The shallow depth of the 520km discontinuity, 490–500km, implies that the regional mean temperature in the transition zone is 110–160K cooler than the global mean. A concentrated Vs gradient maximum centered near 660km depth and a low VS gradient below 675km confirms that the ringwoodite to perovskite+magnesiowüstite reaction is the dominant cause of the 660 in the region.