Power-law Rheology Research Articles

Characterizing Seasonally Rainfall-Driven Movement of a Translational Landslide using SAR Imagery and SMAP Soil Moisture

Precipitation infiltrates into basal shearing zones, triggering seasonal landslide motion by increasing pore-pressure and reducing shear resistance. This process is jointly controlled by basal depth, rainfall intensity, soil moisture, and hydraulic conductivity/diffusivity. Using interferometric synthetic aperture radar (InSAR), we detected and mapped a slow-moving slide in the southwestern Oregon. Its basal depths are estimated using InSAR-derived surface velocity fields based on the mass conservation approach by assuming a power-law rheology. The estimated maximum thickness over the central region of the landslide is 6.9 ± 2.6 m. This result is further confirmed by an independent limit equilibrium analysis that solely relies on soil mechanical properties. By incorporating satellites-captured time lags of 27–49 days between the onset of wet seasons and the initiation of landslide motions, the averaged characteristic hydraulic conductivity and diffusivity of the landslide material is estimated as 1.2 × 10−5 m/s and 1.9 × 10−4 m2/s, respectively. Our investigation layouts a framework for using InSAR and satellite-sensed soil moisture to infer landslide basal geometry and estimate corresponding hydraulic parameters.

Significance of non-Oberbeck-Boussinesq effects augmented by power-law rheology in natural convection studies around fins

The augmentation and diminution of non-Oberbeck-Boussinesq (NOB) effects due to power-law rheology cause significant changes in the results and associated implications of natural convection studies. This study focuses on the combined effect of spatial arrangement with NOB and power-law effects. Non-intuitive changes in heat transfer trends are caused by the additional effect on the shear rate distribution due to spatial arrangement of objects, represented here by an array of fins. An order of magnitude analysis was used to derive Oberbeck-Boussinesq type equations for a class of power-law fluids with all properties considered as linear functions of temperature and pressure. Significant temperature dependent properties were identified, and an explicit criterion to neglect viscous dissipation for power-law fluids in pure natural convection was derived. The identified temperature dependencies were incorporated into NOB equations and solved numerically to investigate their effect on flow field and heat transfer trends. Shear thinning significantly augmented (more than doubled) the accelerating NOB effect, while shear thickening diminished (nearly halved) it. The tendency of power-law rheology to augment or diminish NOB effects was demonstrated to considerably increase the sensitivity of results to temperature dependent properties, over and above that for the Newtonian case. Investigations to note their practical implications revealed that optimization results without NOB effects could be quite misleading for the fin array problem, due to the differing cumulative extents of augmentation. Additionally, correlation studies may be inaccurate as the nature of trends was changed fundamentally due to NOB augmentation.

Entropy Analysis of a Convective Film Flow of a Power-Law Fluid with Nanoparticles Along an Inclined Plate

Entropy generation in a two-dimensional steady laminar thin film convection flow of a non-Newtonian nanofluid (Ostwald-de-Waele-type power-law fluid with embedded nanoparticles) along an inclined plate is examined theoretically. A revised Buongiorno model is adopted for nanoscale effects, which includes the effects of the Brownian motion and thermophoresis. The nanofluid particle fraction on the boundary is passively rather than actively controlled. A convective boundary condition is employed. The local nonsimilarity method is used to solve the dimensionless nonlinear system of governing equations. Validation with earlier published results is included. A decrease in entropy generation is induced due to fluid friction associated with an increasing value of the rheological power-law index. The Brownian motion of nanoparticles enhances thermal convection via the enhanced transport of heat in microconvection surrounding individual nanoparticles. A higher convective parameter implies more intense convective heating of the plate, which increases the temperature gradient. An increase in the thermophoresis parameter decreases the nanoparticle volume fraction near the wall and increases it further from the wall. Entropy generation is also reduced with enhancement of the thermophoresis effect throughout the boundary layer.

A Thin Film Viscoplastic Theory for Calving Glaciers: Toward a Bound on the Calving Rate of Glaciers

Projections of the growth and demise of ice sheets and glaciers require physical models of the processes governing flow and fracture of ice. The flow of glacier ice has been treated using increasingly sophisticated models. By contrast, fracture, the process ultimately responsible for half of the mass lost from ice sheets through iceberg calving, is often included using ad hoc parameterizations. In this study we seek to bridge this gap by introducing a model where ice obeys a power law rheology appropriate for intact ice below a yield strength. Above the yield strength, we introduce a separate rheology appropriate for the flow of heavily fractured ice, where ice deformation occurs more readily along faults and fractures. We show that, provided the motion of fractured ice is sufficiently rapid compared to that of intact ice, the behavior of glaciers depends solely on the rheology of intact ice and the yield strength of ice and is insensitive to the precise rheology of fractured ice. Moreover, assuming that glacier ice is unyielded allows us to bound the long‐term average rate of terminus advance, providing a first principles estimate of rates of retreat associated with the marine ice cliff instability. We illustrate model behavior using idealized geometries and climate forcing and show that the model not only exhibits realistic patterns of advance and retreat but also has the potential to exhibit hysteresis. This hysteresis could provide an explanation for the sudden onset of rapid retreat observed in marine‐terminating glaciers.

Spreading behaviors of high-viscous nanofluid droplets impact on solid surfaces

In this work, the impact dynamics of high-viscous nanofluid droplets onto a solid surface has been investigated experimentally by means of high-speed camera visualization technique. We dispersed various nanoparticles (multiwall carbon nanotube (MWCNT), nano-graphene, and nano-graphite powder) into high-viscous base fluid (epoxy resin) to obtain the stable and homogenous nanofluids without surfactant additives. The well dispersed nanofluids show different degree of shear-thinning behaviors, and the shear-thinning properties of those fluids have been characterized by the power-law rheology model. The dynamic contact angle (DCA), transient dimensionless height, and transient contacting factor along with the spreading time under different Weber numbers (We) have been investigated. The results show that the nanofluid with a lower shear viscosity over the entire range of the shear rates results in larger variations of the contacting factor and the dimensionless height. The effect of surface wettability on droplet impact behaviors is more significant for the fluid with higher shear viscosity and less shear-thinning degree during the receding phase. The latter spreading and receding motions of the droplet with higher shear viscosity and shear-thinning degree are suppressed significantly, regardless of the Weber numbers in current study. Finally, a model based on experimental data has been proposed to predict the maximum spreading factor of high-viscous droplet impact on solid surface.

Removing mantle lithosphere under orogens: delamination versus convective thinning

SUMMARY Thinning of the lithosphere under continental collisional orogens is often attributed to delamination or convective thinning. Both processes remove part or all of the mantle lithosphere that has become denser and gravitationally unstable. Previous studies mostly focused on the different thermomagmatic consequences of these two processes; the dynamic links between them, and the critical conditions for one or the other process to dominate lithosphere thinning, remain uncertain. Here, we used high-resolution thermomechanical models with various rheology (linear viscous, power-law viscous and/or the extended Drucker–Prager plasticity) to systematically investigate the dynamics of delamination and convective thinning under collisional orogens. Our results show that convective thinning is favoured in models of linear (Newtonian) viscous rheology and low viscosity $({10^{19}}\!-\! {10^{20}}\,\,{\rm{Pa}} \, {\rm{s}})$. Power-law viscous rheology promotes strain localization, which reduces the effective viscosity and may lead to localized rising of the asthenosphere to the crustal base, thus triggering delamination. Further strain localization and stronger delamination are predicted with inclusion of plastic rheology in the model. These results indicate that convective thinning and delamination are dynamically linked and can occur in the same orogeny. Their relative dominance during orogenesis may be distinguished by the resulting spatiotemporal evolutions of thermal perturbation, magmatism and elevation changes. We applied the models to show that the evolution of the Central Anatolian Plateau is consistent with the dominance of convective thinning, whereas delamination played a major role in thinning the mantle lithosphere under central-northern Tibetan Plateau.

Shear localisation in anisotropic, non-linear viscous materials that develop a CPO: A numerical study

Localisation of ductile deformation in rocks is commonly found at all scales from crustal shear zones down to grain scale shear bands. Of the various mechanisms for localisation, mechanical anisotropy has received relatively little attention, especially in numerical modelling. Mechanical anisotropy can be due to dislocation creep of minerals (e.g. ice or mica) and/or layering in rocks (e.g. bedding, cleavage). We simulated simple-shear deformation of a locally anisotropic, single-phase power-law rheology material up to shear strain of five. Localisation of shear rate in narrow shear bands occurs, depending on the magnitude of anisotropy and the stress exponent. At high anisotropy values, strain-rate frequency distributions become approximately log-normal with heavy, exponential tails. Localisation due to anisotropy is scale-independent and thus provides a single mechanism for a self-organised hierarchy of shear bands and zones from mm-to km-scales. The numerical simulations are compared with the natural example of the Northern Shear Belt at Cap de Creus, NE Spain.

Traveling Waves of Some Symmetric Planar Flows of Non-Newtonian Fluids

We present some variants of Burgers-type equations for incompressible and isothermal planar flow of viscous non-Newtonian fluids based on the Cross, the Carreau and the power-law rheology models, and on a symmetry assumption on the flow. We numerically solve the associated traveling wave equations by using industrial data and in order to validate the models we prove existence and uniqueness of solutions to the equations. We also provide numerical estimates of the shock thickness as well as the maximum stress associated with the traveling waves.

Eastward “glacier-like flow” of the Tibetan crust constrained from power-law rheology

We propose that topography can be used as a proxy for the eastward lateral “glacier-like flow” of the Tibetan crust in the Himalayan-Tibetan orogenic system. Geodetic observations across the Tibetan plateau indicate ∼22 mm/yr of crustal motion with respect to stable Eurasia by considering Newtonian channel flow model. Further, correlation between regional strain rate (ė) and topographic elevation (h) is found to be statistically robust, with stress exponent (n) of 3.03 ± 0.1. Therefore, we suggest that the Tibetan crust follows well defined power-law relation that is consistent with the nonlinear deformation associated with dislocation-creep. Moreover, the predicted viscosity range of the Tibetan crust is consistent with the channel flow model proposed by previous investigators using different approaches in different time scales.

Определение дисперсной фазы буровых растворов на полимерной основе

The purpose of the article is determination of the volume of the polymer solution dispersed phase, estimation of their subordination degree to the power law of fluid flow, as well as determination of the rheological model of mud flow in order to calculate the pressure losses under fluid movement in the elements of the circulation system. Water-soluble polymers are widely used in the composition of drilling fluids and are also used independently as flushing fluids for drilling wells. Despite the wide application range of polymers, when drilling little attention is paid to the volume of the dispersed phase resulting from the dissolution of polymer in water. Particular interest is caused by so-called dilute solutions (term used in the theory of polymer solutions). They are little mentioned in drilling but their number of macromolecular coils of the polymer reaches such a value that they do not interact with each other when the fluid flows. Using a viscometric method, the molecular mass and the characteristic viscosity of each solution used for the dispersion phase volume determination are estimated. The parameters of the rheological power law are determined through the application of rotametric viscometry. As a result, it has been found out that the solutions of the considered polymers prepared for the study are referred to diluted. On example of one of them the possibility of determining the relative volume of macromolecular coils of polymer with the immobilized solvent (water) is shown. It is demonstrated that a change in the specified volume causes a change in the parameters of the rheological power law of researched solution flow. The proposed methods for determining the relative volume of the dispersed phase of drilling muds based on dilute polymer solutions allows to adjust the rheological properties of flushing fluids and set the parameters of the rheological power law describing the flow of pseudoplastic fluids.

Probing Fluctuations and Avalanches in the Cytoskeleton with Active Micropost Arrays

The cellular actomyosin network plays an important role in a wide range of cell behavior, including motility, morphology and mechanotransduction. Although the building blocks of actomyosin networks are well understood at the molecular level, the picture connecting these microscale units to cell-scale behavior remains incomplete. Here we present results using active micropost array detectors (AMPADS) to characterize the dynamical fluctuations and local rheology of cellular actomyosin networks in detail. AMPADS are poly(dimethylsiloxane) (PDMS) micropillar arrays with embedded magnetic nanowires that enable mechanical actuation of an adherent cell. We classified the cell-associated microposts based on their traction force, and identified two distinct populations, one containing posts coupled to stress fibers and the other containg posts coupled to the actomyosin cortex. Both groups show weak power law rheology, but we find that the fluctuations of stress fiber-associated posts are more active and highly anisotropic in comparison to the cortically-associated posts. Notably, the fluctuations of both populations are highly heterogenous and resemble a Lévy process. Specifically, the mean-squared displacements of both types of posts display broadly distributed amplitudes and super-diffusive behavior. We find that the amplitude distribution is fat-tailed, and is dominated by a corresponding distribution of intermittent, large step-like displacements, resembling avalanches and earthquakes in physical systems. Our regular array of detectors also allows us to determine the spatial extent and average symmetry of the largest rearrangements in the cortex, which are both spatially and temporally complex, resembling those in plastic solids. These results suggest that the dynamics of the cellular actomyosin network resembles what is seen in soft matter systems such as sandpiles and foams, where constituent components self-organize into marginally stable, plastic networks, with significant implications for future models of the cortex.

Numerical simulation of mud-flows impacting structures

The study of the interaction of mud-flows with obstacles is important to define inundation zones in urban areas and to design the possible structural countermeasures. The paper numerically investigates the impact of a mud-flow on rigid obstacles to evaluate the force acting on them using two different depth-integrated theoretical models, Single-Phase Model (SPM) and Two-Phase Model (TPM), to compare their performance and limits. In the first one the water-sediment mixture is represented as a homogeneous continuum described by a shear-thinning power-law rheology. Alternatively, the two-phase model proposed by Di Cristo et al in 2016 is used, which separately accounts for the liquid and solid phases. The considered test cases are represented by a 1D landslide flowing on a steep slope impacting on a rigid wall and a 2D mud dam-break flowing on a horizontal bottom in presence of single and multiple rigid obstacles. In the 1D test case, characterized by a very steep slope, the Two-Phase Model predicts the separation between the two phases with a significant longitudinal variation of the solid concentration. In this case the results indicate appreciable differences between the two models in the estimation of both the wave celerity and the magnitude of the impact, with an overestimation of the peak force when using the Single-Phase Model. In the 2D test-cases, where the liquid and solid phases remain mixed, even if the flow fields predicted by the two models present some differences, the essential features of the interaction with the obstacles, along with the maximum impact force, are comparable.

Role of Lower Crust in the Postseismic Deformation of the 2010 Maule Earthquake: Insights from a Model with Power-Law Rheology

The surface deformation associated with the 2010 Mw 8.8 Maule earthquake in Chile was recorded in great detail before, during and after the event. The high data quality of the continuous GPS (cGPS) observations has facilitated a number of studies that model the postseismic deformation signal with a combination of relocking, afterslip and viscoelastic relaxation using linear rheology for the upper mantle. Here, we investigate the impact of using linear Maxwell or power-law rheology with a 2D geomechanical-numerical model to better understand the relative importance of the different processes that control the postseismic deformation signal. Our model results reveal that, in particular, the modeled cumulative vertical postseismic deformation pattern in the near field ( 50 km depth as suggested in previous studies. The explanation for this difference is that in the model with power-law rheology the relaxation of coseismically imposed differential stresses occurs mainly in the lower crust. However, even though the model with power-law rheology probably has more potential to explain the vertical postseismic signal in the near field, the uncertainty of the applied temperature field is substantial, and this needs further investigations and improvements.

Mimicking Active Biopolymer Networks with a Synthetic Hydrogel.

Stiffening due to internal stress generation is of paramount importance in living systems and is the foundation for many biomechanical processes. For example, cells stiffen their surrounding matrix by pulling on collagen and fibrin fibers. At the subcellular level, molecular motors prompt fluidization and actively stiffen the cytoskeleton by sliding polar actin filaments in opposite directions. Here, we demonstrate that chemical cross-linking of a fibrous matrix of synthetic semiflexible polymers with thermoresponsive poly(N-isopropylacrylamide) (PNIPAM) produces internal stress by induction of a coil-to-globule transition upon crossing the lower critical solution temperature of PNIPAM, resulting in a macroscopic stiffening response that spans more than 3 orders of magnitude in modulus. The forces generated through collapsing PNIPAM are sufficient to drive a fluid material into a stiff gel within a few seconds. Moreover, rigidified networks dramatically stiffen in response to applied shear stress featuring power law rheology with exponents that match those of reconstituted collagen and actomyosin networks prestressed by molecular motors. This concept holds potential for the rational design of synthetic materials that are fluid at room temperature and rapidly rigidify at body temperature to form hydrogels mechanically and structurally akin to cells and tissues.

New analogue materials for nonlinear lithosphere rheology, with an application to slab break-off

Stress-dependent nonlinear upper mantle rheology has a firm base in rock mechanical tests, where this nonlinearity results from dislocation creep of minerals. In the last few decades there has been some attention to nonlinear, power-law, materials for application in scaled analogue experiments for tectonic processes. However, studies describing the rheology of analogue materials with the same nonlinear dependency on stress as observed for lithospheric mantle materials at relevant stress levels, are still lacking.In this study we have developed and rheologically tested materials based on combinations of silicone polymers and plasticine, with the aim of obtaining a material that can serve as a laboratory analogue to the power-law rheology of olivine aggregates at lithospheric mantle conditions. From our steady-state creep tests we find that it is possible to obtain such a power-law material, with effective viscosities over relevant model stress ranges [5–4000 Pa] that allow for nonlinear deformation at laboratory time scales.We apply the developed material to a process where localized deformation of the lithosphere can be expected: slab break-off. We study this process using analogue models, where we apply the new nonlinear material to the lithospheric mantle domains, while we use Newtonian glucose to represent the low viscous asthenosphere. Now that we properly manage power-law behavior in our analogue lithosphere materials, we are able to model localized lithospheric tearing.

Viscous Accretionary Prisms: Viscoelastic Relaxation of the Makran Accretionary Prism Following the 2013 Baluchistan, Pakistan Earthquake

AbstractGeodetic observations of postseismic transients following earthquakes commonly help to inform the rheology of the lower crust and mantle, frictional properties of faults, and the kinematics of deformation across the earthquake cycle. Here we use interferometric synthetic aperture radar time series observations of postseismic deformation following the 2013 Mw 7.7 Baluchistan, Pakistan earthquake to investigate the viscoelastic rheology of the Makran accretionary prism. Using observations that began 15 months after the earthquake and a suite of potential fault geometries, we show that the ongoing deformation transient in the vicinity of the earthquake cannot be explained by afterslip alone. Instead, the gross spatial and temporal characteristics of the transient can be explained by viscoelastic relaxation of a shallow (>6 km) weak zone bounded by the Baluchistan earthquake and the underthrusting Arabian oceanic plate. Our first‐order results show that the viscoelastic lower accretionary prism has a thickness of 8–12 km and exhibits power law (n = 3.5) behavior with viscosities of 1017–1018 Pa·s. These estimated viscosities may be higher if afterslip occurred during the initial period of postseismic deformation not constrained by our observations. The power law rheology suggests that creep processes common at lower crustal and mantle temperatures may be active at comparatively lower temperatures in the Makran. We hypothesize that the weak nature of the Makran accretionary prism is driven by high pore fluid pressures introduced by underplated sediments and/or hydrocarbon development, and we show a mechanically weak accretionary prism may lead to overestimates of plate coupling when linear elasticity is assumed.

Structure and Nanomechanics of Dry and Hydrated Intermediate Filament Films and Fibers Produced from Hagfish Slime Fibers.

Intermediate filaments (IFs) are known for their extensibility, flexibility, toughness, and their ability to hydrate. Using keratin-like IFs obtained from slime fibers from the invertebrate Atlantic hagfish ( Myxine glutinosa), films were produced by drop-casting and coagulation on the surface of a MgCl2 buffer. Drop-casting produced self-supporting, smooth, and dense films rich in β-sheets (61%), whereas coagulation formed thin, porous films with a nanorough surface and a lower β-sheet content (51%). The films hydrated and swelled immediately when immersed in water and did not dissolve. X-ray diffraction showed that the β-crystallites remained stable upon hydration, that swelling presumably happens in the amorphous C-terminal tail-domains of the IFs, and that high salt conditions caused a denser network mesh size, suggesting polyelectrolyte behavior. Hydration resulted in a roughly 1000-fold decrease in apparent Young's modulus from 109 to 106 Pa as revealed by atomic force microscopy nanoindentation. Nanoindentation-based power-law rheology and stress-relaxation measurements indicated viscoelasticity and a soft-solid hydrogel character for hydrated films, where roughly 80% of energy is elastically stored and 20% is dissipated. By pulling coagulation films from the buffer interface, macroscopic fibers with highly aligned IF β-crystals similar to natural hagfish fibers were produced. We propose that viscoelasticity and strong hydrogen bonding interactions with the buffer interface are crucial for the production of such long biomimetic fibers with aligned β-sheets. This study demonstrates that hagfish fiber IFs can be reconstituted into functional biomimetic materials that are stiff when dry and retain the ability to hydrate to become soft and viscoelastic when in water.

Consistent formulation of the power-law rheology and its application to the spreading of non-Newtonian droplets

In this work, we introduce a general form of the Navier-Stokes equations for Generalized Newtonian fluids with an Ostwald power-law. The derivation, based on the covariant formalism, is frame-independent and gives rise to a source term in the Navier-Stokes equations referred to as the Ostwald vector which is characterized by the power-law exponent. The governing equations are then simplified in the long-wave approximation framework and applied to the spreading of an axisymmetric gravity current in the creeping flow regime. Well-known spreading laws are recovered through similarity solutions and a new derivation based on scaling arguments is proposed. Experimental results related to the spreading of gravity current are then presented and the potential to infer unknown rheological parameters from spreading rates is critically discussed in the context of a thorough error analysis.

Power law viscoelasticity of a fractal colloidal gel

Power law rheology is of widespread occurrence in complex materials that are characterized by the presence of a very broad range of microstructural length and time scales. Although phenomenological models able to reproduce the observed rheological features exist, in general a well-established connection with the microscopic origin of this mechanical behavior is still missing. As a model system, this work focuses on a fractal colloidal gel. We thoroughly characterize the linear power law rheology of the sample and its age dependence. We show that at all sample ages and for a variety of rheological tests, the gel linear viscoelasticity is very accurately described by a fractional Maxwell (FM) model, characterized by a power law behavior. Thanks to a unique setup that couples small-angle static and dynamic light scattering to rheological measurements, we show that in the linear regime, shear induces reversible nonaffine rearrangements which might be at the origin of the power law rheology and we discuss the possible relationship between the FM model and the microscopic structure of the gel.

Modeling of multiple fractures growth during multistage hydraulic fracturing based on cell-based pseudo 3D model

The paper presents a mathematical model describing the process of formation of multiple fractures in inhomogeneous rock formation. The features of its numerical implementation and the results of implementation are given. Modelling of fracture growth dynamics is carried out in the frame of cell-based pseudo 3D model, taking into account the associated solution of the problems of fracture mechanics and multiphase flow of a proppant mixture acting as a proppant dispersed phase and a power law rheology fluid. To calculate the flow parameters at the points of initiation of multiple fractures for given wellhead data, the model implements the calculation of hydraulics in the wellbore based on a homogeneous multiphase model. Pathway of fracture development is determined for arbitrary field of the strained deformed state of the formation and takes into account its change caused by stress shadow effect. The developed model allows to evaluate the efficiency of the application of the multi-stage fracturing technology with several perforation clusters or hydraulic fracturing ports in a single stage, as well as to optimize the completion of a horizontal well.