Rheological Regimes Research Articles

Thinning or thickening? Multiple rheological regimes in dense suspensions of soft particles

The shear rheology of dense colloidal and granular suspensions is strongly nonlinear, as these materials exhibit shear-thinning and shear-thickening, depending on multiple physical parameters. We numerically study the rheology of a simple model of soft repulsive particles at large densities, and show that nonlinear flow curves reminiscent of experiments on real suspensions can be obtained. By using dimensional analysis and basic elements of kinetic theory, we rationalize these multiple rheological regimes and disentangle the relative impact of thermal fluctuations, glass and jamming transitions, inertia and particle softness on the flow curves. We characterize more specifically the shear-thickening regime and show that both particle softness and the emergence of a yield stress at the jamming transition compete with the inertial effects responsible for the observed thickening behaviour. This allows us to construct a dynamic state diagram, which can be used to analyze experiments.

An Electromagnetically Actuated Oscillating Sphere Used as a Viscosity Sensor

We present a novel viscosity sensor principle which utilizes an oscillating metal sphere attached to a wire acting as mechanical spring. The oscillation is electromagnetically excited using four actuation coils. The arrangement of the coils allows a linear oscillation in one plane but also a circular motion if the actuation coils are driven accordingly. The latter causes a constant speed of the sphere and thus, a stationary flow around the sphere, which allows probing a different rheological regime compared with the oscillation mode featuring continuous acceleration and deceleration. For viscosity measurements, the drag force acting on the sphere is the crucial parameter in the sensing approach. The calculation of this force requires modeling of the magnetic field generated by the actuation currents in the coils. To verify the model for the magnetic field and the forces, a COMSOL simulation was performed and the results were compared with those obtained with the model. Finally, the approach was verified by means of measurements using different viscous liquids (viscosity standard oils and water glycerol mixtures).

Rheological properties of suspensions of the green microalga Chlorella vulgaris at various volume fractions

A systematic study of the rheological properties of solutions of non-motile microalgae (Chlorella vulgaris CCAP 211-19) in a wide range of volume fractions is presented. As the volume fraction is gradually increased, several rheological regimes are observed. At low volume fractions (but yet beyond the Einstein diluted limit), the sus- pensions display a Newtonian rheological behaviour and the volume fraction dependence of the viscosity can be well described by the Quemada model (Quemada, Eur Phys J Appl Phys 1:119-127, 1997). For intermediate values of the volume fraction, a shear thinning behaviour is observed and the volume fraction dependence of the viscosity can

Transition from the Viscous to Inertial Regime in Dense Suspensions

Non-Brownian suspensions present a transition from Newtonian behavior in the zero-shear limit to a shear thickening behavior at a large shear rate, none of which is clearly understood so far. Here, we carry out numerical simulations of such an athermal dense suspension under shear, at an imposed confining pressure. This setup is conceptually identical to recent experiments of Boyer, Guazzelli, and Pouliquen [Phys. Rev. Lett. 107, 188301 (2011)]. Varying the interstitial fluid viscosities, we recover the Newtonian and Bagnoldian regimes and show that they correspond to a dissipation dominated by viscous and contact forces, respectively. We show that the two rheological regimes can be unified as a function of a single dimensionless number, by adding the contributions to the dissipation at a given volume fraction.

Unified study of glass and jamming rheology in soft particle systems

We explore numerically the shear rheology of soft repulsive particles at large volume fraction. The interplay between viscous dissipation and thermal motion results in multiple rheological regimes encompassing Newtonian, shear-thinning, and yield stress regimes near the "colloidal" glass transition when thermal fluctuations are important, crossing over to qualitatively similar regimes near the "jamming" transition when dissipation dominates. In the crossover regime, glass and jamming sectors coexist and give complex flow curves. Although glass and jamming limits are characterized by similar macroscopic flow curves, we show that they occur over distinct time and stress scales and correspond to distinct microscopic dynamics. We propose a simple rheological model describing the glass-to-jamming crossover in the flow curves, and discuss the experimental implications of our results.

Electromagnetic sounding of the Earth’s crust in the vicinities of the SG-6 and SG-7 superdeep boreholes in the fields of natural and powerful controlled sources

The results of electromagnetic sounding of the Earth’s crust in the vicinities of the SG-6 and SG-7 superdeep boreholes (Yamal-Nenets Autonomous Okrug) are presented. The studies were conducted in the fields of natural sources (AMT-MTS) and in the field of the Zevs ULF antenna located at a distance of more than 2000 km from the receiver points. In the vicinity of the SG-7 superdeep borehole, where the small industrial noise was observed, the results of inverse problem solution are completely consistent with the electric logging data. The conducting layers have been identified at the depths of 150 m and 1.1 km. The roof of rocks having small electrical conductivity and belonging to the Permian-Triassic trappean complex has been found at the depth of about 7 km. The response of the Zevs signal (the frequency range of 44–182 Hz) has indicated the properties of the upper part of the geoelectrical section better than audiomagnetotelluric sounding for both boreholes. Based on the sounding in the vicinity of the SG-6 superdeep borehole, with the data of the Novosobirsk observatory taken into account, the distribution of resistivity down to about 800 km depth has been obtained. This distribution can serve as additional information in calculation of the temperature and rheological regime of the lithosphere and the upper mantle in the region of Western Siberia.

A full-chain constitutive model for bidisperse blends of linear polymers

We develop a full-chain tube-based constitutive model [along the lines of Graham et al. J. Rheol. 47, 1171 (2003)] for the nonlinear rheology of bidisperse blends of long and short linear polymers. For a test chain in the blend, we use the physical picture of a fat tube, representing long-lived entanglements with long chains, and a thin tube, representing entanglements with all chains. The model includes the processes of reptation, contour length fluctuation (CLF), constraint release, and stretch relaxation. In the linear rheology regime, we identify a new relaxation process: CLF along the fat tube contour, achieved via a combination of chain motion along the thin tube, and local constraint release of the thin tube as it explores the width of the fat tube. This process is sufficiently fast to relax a significant portion of the long chains before reptation. It provides an explanation of the decrease in terminal time of long chains upon dilution with short chains in a framework where motion along the thin tube is the dominant reptation mechanism. Once the linear rheology is matched, nonlinear rheology is predicted with no further adjustments to the model. The model compares well against several experimental datasets on bidisperse blends. In particular, it predicts the onset rate of extension hardening, which is often significantly below the inverse Rouse time of the long chains.

Geothermal and rheological regime in the Po plain sector of Adria (Northern Italy)

We present a thermo-rheological study of the Adriatic crust in the central Po plain (Northern Italy), which records the convergence of the Alpine and Apennine external fronts. The present thermal regime of the crust is inferred from geological and geophysical data from oil exploration. A set of temperature data from 37 deep boreholes (bottom hole, drill stem, and production test temperatures) is used to estimate undisturbed formation temperatures down to 6-7 km of depth. Best quality data are used to estimate upper crustal geotherms, which are subdivided into four groups taking into considerations the following factors: i) presence/absence of relevant fluid circulation; ii) conductive thermal refraction; iii) recent sedimentation, and iv) other disturbing tectonothermal processes (e.g., recent tectonics). Assuming average corrections for temperature data affected by recent sedimentation effects, geotherms fall within the same range and provide a homogeneous thermal signal. Temperature measurements in the upper ~7 km are used to constrain a 1-D thermal model at the crustal scale. The best fitting geotherm gives a thermal gradient of ~23 ± 5 mK m-1 (over 7 km of depth), a surface heat flow of ~46 ± 9 mW m-2, and an estimated Moho temperature of 620 ± 80 °C.Using the estimated crustal structure and composition and the best-fitting geotherm, a representative strength envelope is obtained.For hydrostatic and supra-hydrostatic pore pressures, the calculated total crustal strength of this sector of the Adria microplate (not including the upper mantle contribution) is in the 1.8-2.5 TN m-1 range. Considering also the lithospheric mantle contribution, the total lithospheric strength is estimated to be between 23 (wet peridotite)and 39 (dry peridotite) TN m-1.

Geothermal and rheological regime in the Po plain sector of Adria (Northern Italy)

The early to middle Miocene erosive plate boundary preserved in the Northern Apennines NW of the Sillaro Line is formed by two distinct units - the Sestola-Vidiciatico Tectonic Unit and the Subligurian Units. These two units occupy, respectively, the SE and the NW portions of the studied area. Upon closer examination, the features that distinguish these mapped units do not reflect differing plate boundary processes, but rather the incorporation or non-incorporation of forearc-toe mass-wasting deposits into the active subduction channel. In other respects, these two units document similar subduction channel processes, including the contemporaneous activity of multiple sub-parallel slip surfaces. This mode of subduction channel deformation leads to the ‘laminar' incorporation of distinct stacked slices within the channel.

A Well-balanced Finite Volume-Augmented Lagrangian Method for an Integrated Herschel-Bulkley Model

We are interested in the derivation of an integrated Herschel-Bulkley model for shallow flows, as well as in the design of a numerical algorithm to solve the resulting equations. The goal is to simulate the evolution of thin sheet of viscoplastic materials on inclined planes and, in particular, to be able to compute the evolution from dynamic to stationary states. The model involves a variational inequality and it is valid from null to moderate slopes. The proposed numerical scheme is well balanced and involves a coupling between a duality technique (to treat plasticity), a fixed point method (to handle the power law) and a finite volume discretization. Several numerical tests are done, including a comparison with an analytical solution, to confirm the well balanced property and the ability to cope with the various rheological regimes associated with the Herschel-Bulkley constitutive law.

Dynamic rheology of a supercooled polymer melt in nonuniform oscillating flows between rapidly oscillating plates

The dynamic rheology of a polymer melt composed of short chains with ten beads between rapidly oscillating plates is investigated for various oscillation frequencies by using the hybrid simulation of the molecular dynamics and computational fluid dynamics. In the quiescent state, the melt is in a supercooled state, and the stress relaxation function G(t) exhibits a stretched exponential relaxation on the time scale of the α relaxation time τ(α) (the structural relaxation of beads) and then follows the Rouse relaxation function characterized by the Rouse relaxation time τ(R) (the conformational relaxation of polymer chains). In the rapidly oscillating plates, nonuniform boundary layer flows are generated over the plate due to inertia of the fluid, and the local rheological properties of the melt are spatially varied according to the local flow fields. The local strain and local strain rate of the melt monotonically decrease with the distance from the plate at each oscillation frequency of the plate, but their dependencies on the oscillation frequency at a fixed distance from the plate vary with the distance. Far from the plate, the local strain decreases as the oscillation frequency increases such that the dynamic rheology deviates from the linear moduli at the low oscillation frequencies rather than high oscillation frequencies. On the contrary, near the plate, the local strain rate increases with the oscillation frequency such that the shear thinning is enhanced at high oscillation frequencies. In close vicinity to the plate, the dynamic viscosity is mostly independent of the oscillation frequency, and the shear thinning behavior becomes similar to that observed in steady shear flows. We show the diagram of the loss tangent of the melt for different oscillation frequencies and local strain rates. It is seen that the melt generates three different rheological regimes, i.e., the viscous fluid regime, liquidlike viscoelastic regime, and solidlike viscoelastic regime, according to the oscillation frequency and local strain rate. Nonlinear rheological properties are also investigated by the spectrum analysis and the Lissajous-Bowditch curve. It is found that the fractional amplitude of the higher harmonics to the linear harmonics is suppressed within the boundary layer due to the nonslip boundary on the oscillating plate. We also find that the melt exhibits intercycle shear thinning between different positions but exhibits intracycle shear thickening at a fixed position in the vicinity of the plate.

Effects of cyclic loading on the rheological properties of sandstones

Abstract This paper presents some results of the laboratory tests on the time-dependent behaviour of three types of sandstone. Research into the rheological properties of rocks is mostly done under static (quasistatic) loading. In nature, however, rocks are also often subjected to cyclic (vibration) loading as a result of vibrations from traffic or the propagation of seismic waves due to, for example, earthquakes, rock bursts, blasting operations and such like. On this account, the research presented is focused on the study of rheological rock properties during vibration (cyclic) loading. The tests of the rheological properties of a cyclic load were conducted both in creep regime and in relaxation regime, at various levels of average load or strain and for various parameters of vibration (frequency, amplitude). The measured values of different parameter settings were compared and evaluated so that it was possible to set the dependence of cyclical rock loading in the rheological regime. For the purpose of the comparison of rock behavior during vibration and static loading, other tests were also carried out. The results of the research show that, in the course of cyclical loading, the rock rheological properties depend, to a significant extent, on the parameters of this loading, especially the amplitude and frequency.

Multiscale modeling and simulation for polymer melt flows between parallel plates

The flow behaviors of polymer melt composed of short chains with ten beads between parallel plates are simulated by using a hybrid method of molecular dynamics and computational fluid dynamics. Three problems are solved: creep motion under a constant shear stress and its recovery motion after removing the stress, pressure-driven flows, and the flows in rapidly oscillating plates. In the creep/recovery problem, the delayed elastic deformation in the creep motion and evident elastic behavior in the recovery motion are demonstrated. The velocity profiles of the melt in pressure-driven flows are quite different from those of Newtonian fluid due to shear thinning. Velocity gradients of the melt become steeper near the plates and flatter at the middle between the plates as the pressure gradient increases and the temperature decreases. In the rapidly oscillating plates, the viscous boundary layer of the melt is much thinner than that of Newtonian fluid due to the shear thinning of the melt. Three different rheological regimes, i.e., the viscous fluid, viscoelastic liquid, and viscoelastic solid regimes, form over the oscillating plate according to the local Deborah numbers. The melt behaves as a viscous fluid in a region for omegatauR < approximately 1 , and the crossover between the liquidlike and solidlike regime takes place around omegataualpha approximately equal 1 (where omega is the angular frequency of the plate and tauR and taualpha are Rouse and alpha relaxation time, respectively).

The rheology of suspensions of solid particles

We present data for the rheology of suspensions of monodisperse particles of varying aspect ratio, from oblate to prolate, and covering particle volume fractions ϕ from dilute to highly concentrated. Rheology is characterized by fitting the experimental data to the model of Herschel &amp; Bulkley (Herschel &amp; Bulkley 1926 Kolloid Z. 39 , 291–300 ( doi:10.1007/BF01432034 )) yielding three rheometric parameters: consistency K (cognate with viscosity); flow index n (a measure of shear-thinning); yield stress τ 0 . The consistency K of suspensions of particles of arbitrary aspect ratio can be accurately predicted by the model of Maron &amp; Pierce (Maron &amp; Pierce 1956 J. Colloid Sci. 11 , 80–95 ( doi:10.1016/0095-8522(56)90023-X )) with the maximum packing fraction ϕ m as the only fitted parameter. We derive empirical relationships for ϕ m and n as a function of average particle aspect ratio r p and for τ 0 as a function of ϕ m and a fitting parameter τ *. These relationships can be used to predict the rheology of suspensions of prolate particles from measured ϕ and r p . By recasting our data in terms of the Einstein coefficient, we relate our rheological observations to the underlying particle motions via Jeffery’s (Jeffery 1922 Proc. R. Soc. Lond. A 102 , 161–179 ( doi:10.1098/rspa.1922.0078 )) theory. We extend Jeffery’s work to calculate, numerically, the Einstein coefficient for a suspension of many, initially randomly oriented particles. This provides a physical, microstructural explanation of our observations, including transient oscillations seen during run start-up and changes of rheological regime as ϕ increases.

Intermittency of rheological regimes in uniform liquid-granular flows

We present a detailed analysis of a free surface-saturated liquid-granular mixture flowing over a static loose bed of grains, where the coexistence of layers dominated by collisional and frictional interactions among particles was observed. Kinetic theory was applied to the flow described above and it proved suitable for describing a realistic behavior of the collisional layers, although it failed to interpret the regions of the flow domain dominated by the frictional contacts. The paper provides a conceptual scheme with which to overcome this problem by focusing on the mechanisms governing the transition from the frictional to the collisional regime. In particular we observed that in highly concentrated flows the transition layer exhibits a typical intermittency of the dominating rheological regime, switching alternately from the frictional to the collisional one. By filtering the velocity signal, we introduced an intermittency function that made it possible to extend the validity of the equations derived from dense gas analogy, typical of the collisional regimes, also in the intermittent phase of the flow. Owing to the small values of the Stokes number, in the application of the kinetic theory we accounted for the possible variation of the elastic restitution coefficient along the flow depth.

Suspension rheology under oscillatory shear and its geophysical implications

Abstract Dynamic strain generated by seismic waves is often invoked to explain coseismic responses to earthquakes, such as liquefaction, dilatancy and the remote triggering of earthquakes and eruptions. In order to expand our understanding of the conditions under which such responses occur, we measure the rheology of non-Brownian particle suspensions under oscillatory shear at frequencies corresponding to the seismic band (0.1–10 Hz). We characterize the changes in rheology as a function of volumetric particle packing fraction (0.2–0.6), particle diameter (9, 39 μm), and the viscosity of the suspending fluid (0.97, 12.14 Pas). By varying the stress (corresponding to a strain range 10− 5

The hydraulic transportation of thickened sludges

Industries which pump sludges are under continuous pressure to decrease water content, and increase concentration. Environmentally superior disposal techniques are demanding that such sludges have high mechanical strength properties. This results in a sludge with an increasing viscous character. At high concentration, the viscous forces – which are usually highly non-Newtonian and yield stress in nature – become dominant, and flows inevitably become laminar. The objective of this paper is to demonstrate the effect and evaluate the impact that increasing non-Newtonian viscous stresses – particularly yield stress – have on the pipelining problem. An industrially relevant sludge pipe flow study is presented, demonstrating and quantifying the relationship between sludge rheology and flow regime. It is argued that laminar flow will result in settlable solids accumulating on the pipe invert, leading to pipe blockage. Although some practical remedies have been proposed, this problem requires urgent and focussed research.. Water SA Vol. 30 (5) 2005: pp.66-68

Chemistry, small-scale inhomogeneity, and formation of moldavites as condensates from sands vaporized by the Ries impact

The formation of the Ries impact and the moldavites have identical radiogenic ages of 14.3 Ma. According to this conformity in age moldavites are generally regarded as products of the Ries impact. This paper, which is divided into two sections, deals with two aspects of the moldavite-forming process: the formation of moldavite bodies by accretion of small precursors, and the physical and chemical conditions under which these primary units originated from sands which covered the Ries impact site. First, the chemical inhomogeneity of moldavite glasses is investigated in sections of 11 moldavites, using back scattered electron (BSE) images and electron microprobe analyses on 0.4–2.7 mm long traverses. Schlieren and lechatelierite particles are interpreted as relics of small, chemically different precursors, which accumulated to larger moldavite bodies at temperatures too low to be efficient for mixing. The patterns of schlieren and lechatelierite inclusions represent two successive rheological regimes: Small agglomerating primary melt units were extended into thin lamellae and threads under conditions of laminar flow. As evidenced by folded textures, these fluidal arrays were later plastically deformed under conditions of compressional stress. To elucidate the production of the primary melt units by the Ries impact, in the second section the geologic situation of the Ries area is considered with regard to possible source materials. The site of the Ries impact, situated at the northern border of the pre-Alpine Molasse basin, was covered at the time of the impact by fluviatile sediments of the lower sequence of the Obere Süßwasser-Molasse (OSM) Formation of Middle Miocene age, consisting of sands, marly sands and clays. Chemical analyses for major and trace elements of 38 moldavites from Bohemia and Moravia, and of 28 samples of the OSM Formation, collected from outcrops and drill holes, immediately south of the Ries crater and south of the Danube, show chemical conformity of moldavites and sand samples with regard to the major parameters SiO 2,Al 2O 3+ FeO, and MgO + CaO, indicating that these sands were the essential source material of moldavites. But, differences in contents of individual major and trace elements between moldavites and sands show that the formation of moldavites from sands involved a specific chemical differentiation which can not be explained by selective vaporization or melting, nor by selective condensation from melt or vapeur. Because large ions were enriched and small ones depleted in moldavites, the ionic radius has controlled the distribution of elements between sands and moldavites. We assume that moldavites originated from a plasma that the impact produced at its encounter with the surficial sand formation at the impact site, and that the primary units formed as early condensates in which large ions were preferentially trapped.

Dynamic recrystallization and strain softening of olivine aggregates in the laboratory and the lithosphere

Abstract The effects of dynamic recrystallization on the deformation mechanisms and rheology of olivine aggregates in the laboratory and the lithosphere are reviewed in this paper. The low-strain rheology of olivine is well documented; however, deformation in the lithosphere often involves large strains. Large strain experiments show that recrystallization can result in both hardening and softening during deformation. Moderate strain softening in experimental shear and torsion can be explained by the operation of dislocation-accommodated grain boundary sliding in bands of fine recrystallized grains. Data on the temperature dependence of recrystallized grain size are needed to extrapolate the effects of dynamic recrystallization to the lithosphere. Theories of dynamic recrystallization suggest that grain size is strongly stress dependent and moderately temperature dependent. A re-analysis of experimental grain size data indicates that the recrystallized grain size is temperature independent for olivine aggregates with low water content (&lt;300 ppm H/Si). Rheological regime maps have been constructed for the lithospheric mantle. The maps suggest that grain size sensitive power law creep, involving both grain boundary sliding and dislocation creep, will produce strong strain softening, greater than found so far in experimental studies, in dry and wet lithosphere shear zones.

Differences in Landsat TM derived lava flow thermal structures during summit and flank eruption at Mount Etna

The simultaneous solution of the Planck equation (the so-called “dual-band” technique) for two shortwave infrared Landsat Thematic Mapper (TM) bands allows an estimate of the fractional area of the hottest part of an active flow and the temperature of the cooler crust. Here, the dual-band method has been applied to a time series of Mount Etna eruptions. The frequency distribution of the fractional area of the hottest component reveals specific differences between summit and flank lava flows. The shape of the density function shows a trend consistent with a Gaussian distribution and suggests a relationship between the moments of the distribution and the emplacement environment. Because flow composition of Etnean lavas generally remains constant during the duration of their emplacement, it appears that the shape of any particular frequency distribution is probably related to fluid mechanical aspects of flow emplacement that affect flow velocity and flow heat loss and thus the rate of formation of the surface crust. These factors include the influence of topographical features such as changes in slope gradient, changes in volume effusion rate, and progressive downflow increases in bulk or effective viscosity. A form of the general theoretical solution for the ‘dual-band’ system, which illustrates the relationship between radiance in TM bands 5 and 7, corresponding to hot fractional area and crust temperature, is presented. Generally speaking, it appears that for a given flow at any point in time, larger fractional areas of exposed hot material are correlated with higher temperatures and that, while the overall shape of that distribution is common for the flows studied, its amplitude and slope reflect individual flow rheological regimes.