Effect Of Viscosity Contrast Research Articles

Rheological implications of heterogeneous deformation at multiple scales in the Late Cretaceous Sierra Nevada, California

Late Cretaceous deformation in the east-central Sierra Nevada arc of California was heterogeneous at multiple scales. We quantify this heterogeneous deformation at centimeter, meter, and kilometer scales in the vicinity of the Gem Lake shear zone and infer variations in effective viscosity from our data. At the centimeter scale, variations in strain of different clast types in conglomerate suggest that effective viscosities varied by less than an order of magnitude. Lithology controlled the magnitude and nature of deformation recorded by clasts. At the meter scale, cleavage refraction between stratigraphic layers records variations in finite strain. Comparison of our observations with cleavage refraction models suggests a maximum effective viscosity contrast of ∼10 between layers. Bulk composition controls variations in deformation of the different layers. At the kilometer scale, variation in finite-strain magnitude and orientation in similar rock types both within and outside the shear zone demonstrates that deformation inside the zone was relatively intense. Comparing these results to numerical models of heterogeneous regional deformation, we estimate that the angle of oblique convergence inside the zone was ∼15 ± 10°, while outside it was greater than 60°. These kilometer-scale results imply regional deformation was moderately strike-slip partitioned during the Late Cretaceous and suggest regional effective viscosity varied by a factor between 6 and 17. At each scale of observation, the apparent range of effective viscosity varies by an order of magnitude or less. Consequently, we infer that relatively modest strength variations produced the structures observed at hand sample to tectonic scales.

Dynamics of surfactant‐covered drops in linear flows

AbstractSurfactants modify interfacial properties and significantly affect drop behavior in flow. We study the dynamics of a drop, which is covered with a monolayer of insoluble surfactant, in linear viscous flows, both unbounded and in the presence of a wall. The effect of viscosity contrast is included. Analytical results in a form of expansions for weak flows and high viscosity drops are developed. Numerical results with three‐dimensional boundary integral simulations are used to explore large deformations. The results show that surfactant generally enhances drop deformation, certainly under small‐deformation conditions. The steady‐state drop shape and surfactant distribution are independent of viscosity contrast in straining flows (e.g. hyperbolic, axisymmetric strain). The drop shape and surfactant distribution are insensitive to viscosity contrast under small deformation conditions for any linear flow; the effect of the rotational component at higher‐order. The theory quantifies the effect of surfactant on drop migration away from a bounding wall as well as the rheology of dilute emulsions. It predicts non‐Newtonian features such as shear thinning viscosity and normal stress. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Mantled porphyroclast gauges

We investigate the behavior of the isolated mantled porphyroclast in a shear zone. The method employed is a finite element model. Three distinct phases, clast, mantle and matrix are present, the rheologies are power-law with exponents ranging from 1 to 5 and the far-field boundary condition is simple shear. The effective viscosity of the mantle is assumed to be less than those of the clast and the matrix. We show for which parameter sets mantled porphyroclasts reach super-horizontal stabilization with respect to the shear plane and sense. Clasts in natural mylonites frequently exhibit similar orientations, which are interpreted as stable inclinations. The systematic examination of the matrix–mantle–clast system allows for the construction of attractor maps that can be directly used as gauges for (i) the effective viscosity contrast between matrix and mantle, (ii) the production rate of mantle material around the clast as a function of the bulk shear strain, and (iii) for the total shear strain. The necessary data required to use the attractor maps are simple geometrical parameters that can be measured in the field, i.e. clast aspect ratio, clast inclination versus the shear plane, mantle thickness, and mantle and clast area. This new method successfully reproduces the characteristics of natural porphyroclasts and is in good agreement with data from natural shear zones.

Influence of object concentration on finite strain and effective viscosity contrast: insights from naturally deformed packstones

Deformed conglomerates and ooidal/oncoidal packstones are commonly used to evaluate finite strain in deformed sedimentary successions. In order to obtain a correct estimate of finite strain, it is necessary to consider not only the different behaviour of matrix and objects, but also object concentration. The analysis of two-component rocks characterised by high values of packing commonly results in a substantial underestimate of bulk strain and of viscosity contrast between objects and matrix. In this study, the effects of the volumetric fraction of competent inclusions on both object and bulk measured finite strain, as well as on apparent viscosity contrast, have been investigated in naturally deformed packstones characterised by variable object concentration on the scale of the hand specimen (and hence for homogenous viscosity contrast). Object finite strain has been obtained by Rf/ ϕ analysis, whereas the Fry method provides a measure of whole-rock strain that is also a function of inclusion concentration. Therefore, the finite strain measured by the Fry method is better termed effective bulk strain. In order to investigate the role of object concentration, this parameter has been plotted against object and effective bulk strain, and also against viscosity contrast. These diagrams show that: (i) for high values of packing, measured object and effective bulk strain show values that are significantly lower with respect to the calculated maximum value (that would result in the ideal case of no particle interaction and represents therefore the real bulk strain of the samples); (ii) the viscosity contrast shows lower values with respect to the calculated maximum one (that is equal for the three principal sections of the finite strain ellipsoid), and as packing reaches the maximum value, the viscosity contrast approaches a unit value. Empirical equations have also been found that link object concentration with both object and effective bulk finite strain.

Evolution into the stagnant lid convection regime with a non‐Newtonian water ice rheology

We study and compare the evolution into the stagnant lid regime with a non‐Newtonian water ice and a silicate rheology by solving the equations of thermal convection. Dislocation creep of water ice is characterized by a larger stress dependence (n = 4) than silicates (n = 3) and with this water ice rheology, the stagnant lid regime is attained at a temperature determined viscosity contrast greater than 1010 and at an effective viscosity contrast of ∼105. We also determine a Nusselt‐Rayleigh number scaling law for the n = 4 rheology.

Folding of a finite length power law layer

Folding of an isolated finite length power law layer embedded in a Newtonian viscous matrix is investigated and compared to conventional folding experiments where the layer is of infinite length or in direct contact with lateral boundaries. The approach employed is a combination of the complex potential method for the basic state and the thin plate approximation for the linear stability analysis and is verified by finite element models. The resulting theory reveals that the aspect ratio of a layer has a first‐order influence on the development of folds. The aspect ratio competes with the effective viscosity contrast for dominant influence on the folding process. If the aspect ratio is substantially larger than the effective viscosity contrast, the conventional theories are applicable. In other situations, where the aspect ratio is smaller than the effective viscosity contrast, substantial corrections must be taken into account, which lead to a new folding mode that is mainly characterized by decreasing growth rates with increasing effective viscosity contrast (relative to the far‐field shortening rate). This new folding mode helps explain the absence of large wavelength to thickness ratio folds in nature, which may be due to the limitations of aspect ratios rather than large effective viscosity contrasts.

Timing of formation of Beta Regio and its geodynamical implications

Recent evidence suggests that the Beta Regio equatorial highland, generally considered to be a plume‐related structure, was emplaced over a relatively short period of time in the recent Venus history (100–400 m.y.). We perform numerical simulations which use this evidence as a new constraint on geodynamic models and find that it is difficult to satisfy simultaneously the constraint on the uplift rate and the constraints on gravity, topography, and rheology. One possible solution is that the effective viscosity contrast between the mantle and the lithosphere does not exceed about 104. If our simple models do capture the basic dynamics of formation of Beta Regio, this value implies that the viscosity of the lithosphere is softer than olivine at subsolidus temperatures and that the Venusian lithosphere may not be much stronger than the terrestrial one.

Finite-element modelling of shear zone development in viscoelastic materials and its implications for localisation of partial melting

The development of shear zones initiating on random weaker initial perturbations is modelled numerically for low Deborah number viscoelastic materials, considering the influence of effective viscosity contrast, power law rheology, strain softening, and different imposed bulk deformation geometries, ranging from pure to simple shear. Conjugate shear zones initiate at ∼90° to one another, and rotate with increasing bulk deformation, the basic pattern not being markedly influenced by the vorticity of imposed deformation. The rate of propagation of individual conjugate shear zones is little affected by increased effective viscosity contrast between matrix and inclusion but is promoted by power-law rheology. However, the most marked effect is observed for strain softening behaviour, where rapid propagation produces straighter and narrower shear zones. The localisation of strain is reflected in a correspondingly heterogeneous stress distribution. In particular, mean stress or pressure is higher in the extending, near planar, weaker zones of localised shear. Melting of gneissic or pelitic compositions is pressure dependent. With free water present, increased pressure promotes melting, whereas the opposite is true for water-absent melting. For water-present conditions, a positive feedback could develop between localised shearing, increased pressure and partial melting. This is potentially more effective in concentrating melt in shear zones than shear heating, where melt-related softening has a negative feedback effect.

Control of folding by gravity and matrix thickness: Implications for large‐scale folding

We show that folding of a non‐Newtonian layer resting on a homogeneous Newtonian matrix with finite thickness under influence of gravity can occur by three modes: (1) matrix‐controlled folding, dependent on the effective viscosity contrast between layer and matrix, (2) gravity‐controlled folding, dependent on the Argand number (the ratio of the stress caused by gravity to the stress caused by shortening), and (3) detachment folding, dependent on the ratio of matrix thickness to layer thickness. We construct a phase diagram that defines the transitions between each of the three folding modes. Our priority is transparency of the analytical derivations (e.g., thin‐plate versus thick‐plate approximations), which permits complete classification of the folding modes involving a minimum number of dimensionless parameters. Accuracy and sensitivity of the analytical results to model assumptions are investigated. In particular, depth dependence of matrix rheology is only important for folding over a narrow range of material parameters. In contrast, strong depth dependence of the viscosity of the folding layer limits applicability of ductile rheology and leads to a viscoelastic transition. Our theory is applied to estimate the effective thickness of the folded central Asian upper crust using the ratio of topographic wavelength to Moho depth. Phase diagrams based on geometrical parameters show that gravity does not significantly control folding in the Jura and the Zagros Mountains but does control folding in central Asia. Applicability conditions of viscous and thin sheet models for large‐scale lithospheric deformation, derived in terms of the Argand number, have implications for the plate‐like style of planetary tectonics.

The rheology and morphology of phase-separating fluids with viscosity contrast

In this paper, the effects of viscosity contrast between the components on the rheology and morphology of phase-separating binary fluids have been studied by numerically solving time-dependent Ginzburg–Landau equation and Navier–Stokes equation. It is found that, the viscosity contrast between the components strongly affects the bulk contribution to the overall rheological behavior. When the viscosity of the minor phase is higher, the trend of bulk contribution is contrary with that of interfacial contribution. Therefore, the non-Newtonian behavior is weakened. When the viscosity of the minor phases is lower, the evolution of bulk contribution is the same as interfacial contribution, and thus the non-Newtonian behavior is strengthened. However, the interfacial contribution still plays the crucial role in the overall rheological behavior. When the system contains two droplets or many domains, due to the merging of domains induced by shear flow, there is a decrease of interfacial volume fraction. Therefore, the interfacial contribution of rheology decreases and forms a peak at small shear strain. Correspondingly, the bulk contribution has also been altered. However, whether the bulk contribution increases or decreases will depend on the viscosity contrast.

Miscible rectilinear displacements with gravity override. Part 1. Homogeneous porous medium

Rectilinear homogeneous miscible displacements with gravity override are analysed by means of direct numerical simulations on the basis of the vorticity–streamfunction formulation of the governing equations. The vorticity-based point of view offers the advantage of clearly attributing the dominant flow characteristics to the effects of viscosity contrast, density difference, impermeable boundary conditions, or interactions among the above. Basic considerations regarding the vorticity field show that in an integral sense the coupling between viscosity and gravity vorticity is predominantly one way in nature, in that the gravity vorticity can amplify the viscous vorticity, but not vice versa. In particular, the vorticity point of view provides an explanation for the formation of the gravity tongue in terms of a focusing mechanism, which results from the combined action of the unfavourable viscosity gradient and the potential flow field generated by the interaction of the gravitational vorticity with the horizontal boundaries. This potential velocity field locally enhances the uniform global displacement velocity near the upper boundary, and thereby amplifies the viscous fingering instability along this section of the interface. In some parameter ranges, the gravity tongue exhibits interesting interactions with the viscous fingers next to it, such as pinching and partial merging. The influence of the Péclet number, the viscosity and density contrasts, and the aspect ratio on the dynamic evolution of the displacement is investigated quantitatively.

A New Mathematical Model For 1D Miscible Displacement

Abstract This paper presents a new model for one-dimensional miscible displacement. The model was constructed using Darcy's law, Fick's dispersion law and the continuity equation. The effects of viscosity contrast between the displaced and displacing fluids and the heterogeneity of a porous medium can be investigated using the model. An approximate analytical solution to the model was developed and it indicates that the transition zone grows with the square root of time at early times when dispersion dominates. As the displacement goes on, the transition zone grows linearly with time when the effect of dispersion is negligible. Introduction When two fluids mix in all proportions and their mixtures remain a single phase, they are called first-contact miscible. When one such fluid is injected into a porous medium, which is pre-saturated with the other miscible fluid, a transition zone is developed wherein the fluid compositions change continuously from the injected to the displaced fluid. If the porous medium is homogeneous, and if the miscible fluids have the same viscosity, the performance of the process can be described by the traditional convection- dispersion equation(1). The solution to this equation for an infinitely long, one-dimensional system indicates that the concentration of the displaced fluid in the effluent versus time (effluent curve) is sigmoid and the length of the transition zone increases with the square root of time(2). If the injected fluid has a lower viscosity than that of the displaced fluid and/or if the porous medium is not homogeneous, the effluent curve may demonstrate a skewed "S" shape and the transition zone grows linearly with time(3–7). A significant effort has been made to develop mathematical models capable of describing adequately the miscible displacement process(3, 6–10). If the porous medium is homogeneous, and if the fluid viscosities are equal, Fick's diffusion law may be combined with the continuity equation to obtain the standard dispersion- convection equation which may be expressed as follows: Equation 1 (available in full paper) As noted by Mannhardt and Nasr-El-Din(11), this equation predicts that the transition-zone length grows with the square root of time, and that the effluent concentration curve is symmetrically "S" shaped under certain boundary conditions. If the assumptions concerning homogeneity of the formation and equality of the fluid viscosities are violated, Equation (1) is no longer able to describe adequately the miscible displacement process. In particular, for inhomogeneous formations and/or unmatched fluid viscosities, the effluent concentration curve may no longer have a symmetrical "S" shape, and the length of the transition-zone no longer grows with the square root of time(2, 7). To enable the prediction of unfavourable viscosity ratio displacements in inhomogeneous formations, some researchers(6, 10) have suggested using immiscible, two-phase flow theory to describe the miscible displacement process. When this approach is taken, dispersion is neglected and the transition zone grows linearly with time. However, it can be inferred from recent experimental work(7) that, when the porous medium is inhomogeneous, the transition zone grows at a rate intermediate between that predicted by the standard dispersionconvection equation and that predicted by immiscible two-phase flow theory.

Time-dependent formation of mantled inclusion structures for different rheologies under a simple shear

Mantled inclusions, commonly encountered in mylonites, sometimes represent the only recorders of the deformation history. Understanding the influence of rheology on the structure of mantled inclusion is important for its interpretation and also for the retrieval of the deformation regime. This paper is devoted to the 2D numerical investigation of time-dependent deformation behavior of inclusion and its dependence on rheology under simple shear. The numerical model is based on an iterative finite-difference scheme. The inclusion is taken to be deformable and having its own intrinsic rheological properties differing from those of the matrix. The diffusion between the matrix and the inclusion is assumed to be insignificant. In order to emulate natural mantled inclusion, we imposed passive mantle around the inclusion, which efficiently monitors the deformation. The results of numerical modeling show that a key factor of structural appearance is the effective viscosity contrast (ratio of the inclusion to matrix effective viscosities). In the power-law rheology, even a small difference in rheological parameters may result in a high effective viscosity contrast of around 10 between matrix and inclusion. The high contrast inhibits stretching of the inclusion, preserving its round shape, which, in turn, may create an illusion of the seeming rigidity of the inclusion. Wings or tails are developed only in the systems with a high effective viscosity contrast. They are not influenced by whether the high viscosity contrast is produced by non-Newtonian medium or by the highly contrasting viscosity between the matrix and the inclusion in the linear rheology.

Stress gradients around porphyroclasts: palaeopiezometric estimates and numerical modelling

Based on strain gradients commonly found around porphyroclasts, the mechanical interaction of porphyroclasts and recrystallized mylonite matrix in a retrograde amphibolite-facies shear zone of the Ivrea-Verbano Zone, Italy, was investigated. Differential stresses inferred from recrystallized grain size and dislocation density indicate stress concentrations at the porphyroclast-matrix interface of about 1.7–2.0 with respect to the average in the matrix. The palaeopiezometric stress data are compared to the results of a finite-element model composed of two rheologically different phases. In this model, the local distribution and concentration of stresses around porphyroclasts mostly depend on clast-matrix coupling and the effective viscosity contrast of the two phases. The bulk strength and work hardening of the composite system increases with interface coupling. Both the modified stress field and the reduced average grain size around porphyroclasts may result locally in instabilities, and promote strain localization and a change in the dominant deformation mechanism.

Viscous fingering in miscible displacements: Unification of effects of viscosity contrast, anisotropic dispersion, and velocity dependence of dispersion on nonlinear finger propagation

The two-dimensional (2-D) isotropic simulations of Tan and Homsy [Phys. Fluids 31, 1330 (1988)] are extended to much broader and longer domains, and the 2-D anisotropic simulations of Zimmerman and Homsy are extended to include a general velocity dependence. The mechanisms of nonlinear interaction of viscous fingers found for the first time in the anisotropic simulations recur in isotropic simulations, but at weaker levels of dispersion. An appropriate scaling to unify the average long time growth of the instability with both anisotropy in geometry and dispersion is provided. The long time growth of the instability from simulations agrees with acoustic measurements in 3-D porous media, Bacri et al. [Phys. Rev. Lett. 67, 2005 (1991)], elucidating the effects of viscosity contrast, anisotropy, and velocity dependence of longitudinal dispersion. The combination of sufficiently high viscosity contrast, weak transverse dispersion, and strong dependence of longitudinal dispersion on velocity results in an augmentation to the long time growth of the instability. The associated critical parameter found by linear stability theory of Yortsos and Zeybek [Phys. Fluids 31, 3511 (1988)] predicts accurately this same long time growth increase.

The effect of initial perturbation shape and symmetry on fold development

Single-layer fold experiments were carried out to study the influence of initial perturbation symmetry on the symmetry of folds developed using paraffin wax as a rock analogue. Under experimental conditions, both matrix and layer have a power-law rheology, with an initial effective viscosity contrast of ca 17:1. The matrix flows in steady state with n = 2.7 and the layer work softens with n eff = 10. Folds developed from an initially symmetric perturbation remain symmetric, reflecting the pure shear-plane strain boundary conditions. Folds developed from an initially asymmetric perturbation, however, show a progressive exaggeration of this asymmetry, such that the introduced 3.5° difference in limb dip increases to 65° at 23% bulk shortening. These experiments indicate that, for low competence contrast between layer and matrix, the geometry of initial perturbations of finite amplitude (e.g. ripple marks, channels, half-graben structures) may be an important factor in determining the geometry and distribution of folds.

External shapes, strain rates, and dynamics of salt structures

Research Article| March 01, 1986 External shapes, strain rates, and dynamics of salt structures M.P.A. JACKSON; M.P.A. JACKSON 1Bureau of Economic Geology, The University of Texas at Austin, Austin, Texas 78713 Search for other works by this author on: GSW Google Scholar C. J. TALBOT C. J. TALBOT 2Institute of Geology, University of Uppsala, S-751 22 Uppsala, Sweden Search for other works by this author on: GSW Google Scholar GSA Bulletin (1986) 97 (3): 305–323. https://doi.org/10.1130/0016-7606(1986)97<305:ESSRAD>2.0.CO;2 Article history first online: 01 Jun 2017 Cite View This Citation Add to Citation Manager Share Icon Share Facebook Twitter LinkedIn MailTo Tools Icon Tools Get Permissions Search Site Citation M.P.A. JACKSON, C. J. TALBOT; External shapes, strain rates, and dynamics of salt structures. GSA Bulletin 1986;; 97 (3): 305–323. doi: https://doi.org/10.1130/0016-7606(1986)97<305:ESSRAD>2.0.CO;2 Download citation file: Ris (Zotero) Refmanager EasyBib Bookends Mendeley Papers EndNote RefWorks BibTex toolbar search Search Dropdown Menu toolbar search search input Search input auto suggest filter your search All ContentBy SocietyGSA Bulletin Search Advanced Search Abstract Salt structures continue to attract attention as petroleum traps and as storage vessels for wastes or fuels. Drawing on field studies, experiment, and theory, we examine the megascopic structure and large-scale dynamics of salt structures.Salt flowage can transform a tabular salt body into nondiapiric rollers, anticlines, and pillows; into diapiric walls, stocks, massifs, and nappes; and into extrusive domes and salt glaciers. These structures distort at widely variable strain rates of 10−8 s−1 to 1016 s−1, with a comparatively restricted range of dominant wavelengths of 7–26 km.Buoyancy is an ineffective diapiric mechanism unless the salt structure has pre-existing relief of at least 150 m beneath a denser overburden of terrigenous clastics. Differential loading is a far more effective mechanism in the early stages of diapirism and commonly results in asymmetric salt structures. Gravity spreading modifies the shape of salt structures with negative buoyancy. With a heat-induced density inversion, thermal convection may lead to internal circulation and stirring of a still-tabular salt body. At least four mechanisms may form broad bulbs on mature salt stocks. Consideration of the effective viscosity contrast between salt and its cover suggests that mature stocks may have stems much more narrow than is commonly envisaged.Salt tectonics is classified here on the basis of change of gravity potential energy that promotes or retards salt flow. Halokinetic movements can be initiated, succeeded, retarded, or accelerated by regional tangential forces that stretch, wrench, or compress sedimentary basins. This content is PDF only. Please click on the PDF icon to access. First Page Preview Close Modal You do not have access to this content, please speak to your institutional administrator if you feel you should have access.

Estimation of viscosity contrast and finite strain from deformed elliptical inclusions

A method of strain analysis is described which takes into account a possible competence difference between the strain markers and the rest of the rock. Using data consisting of the sectional shapes and orientations of groups of inclusions from conglomerate-like rocks, limits are placed on the possible effective viscosity contrast between the inclusions and the rock as a whole as well as on the bulk finite strain suffered by the rock. These results are calculated using a computer program, based on the theory for the deformation of elliptical cylinders. The method can be considered an extension of the Rf/ φ method, but provides more information and involves less restrictive assumptions.