Jeffery Model Research Articles

A Second-Gradient Theory of Dilute Suspensions of Flexible Rods in a Newtonian Fluid

Mostsuspensiondescriptionsusednowadaysare based on Jeffery's model or some phenomenological modi- fications of it that do not take into account size effects: the kinematics and stresses do not involve a micro-mechanical characteristiclengthandthus,thepredictedrheologicalprop- ertiesarenecessarilyindependentofrodlength.Moresophis- ticatedmodelsabletoenrichfirst-gradientkinematicsaswell as to activate rod-bending mechanisms are needed, in partic- ulartoexplainthemildelasticityobservedexperimentally.In thispaperweproposeasecond-gradienttheoryfordilutesus- pensions of flexible rods in a Newtonian fluid that is indeed able to activate rod bending and predict viscoelastic behav- iour.

Modified Jeffery model: Influence of particle concentration on mineral fabric in moderately concentrated suspensions

AbstractA modified Jeffery model involving particle interactions allows the simulation of preferred orientation of crystals and the anisotropy of magnetic susceptibility in magmatic flow with up to 40% of rigid particle fraction. Numerical simulations are compared to analogue and natural fabrics. A study of the role of particle concentration shows that the increasing percentage of crystal fraction in dilute suspensions leads to progressive attenuation of the fabric intensity and cyclicity. At high strains in simple shear flow, the lineation converges to a constant value close to the shear plane. With increasing particle concentration, the fabric diverges from the shear direction reflecting the effect of increased crystal tiling. The model can be applied to quantify mineral preferred orientations of crystal mushes in magmatic fabric studies.

Rheology and processing of suspensions with fiber, disk and magnetic particles

This paper introduces recent development and progress in rheology and processing of suspension materials. In particular, three topics with different suspensions will be discussed, which are relevant in polymer- and powder-based manufacturing industries for various applications. The paper begins with a fundamental study of rheological modeling for short fiber suspension in a viscoelastic liquid. Irreversible thermodynamics based approach is presented to describe the polymer viscoelastic deformation with the fiber anisotropy effect taken into account. Several distinguishing features of the model are presented. Then we turn our attention to more industry-oriented subject of pigment disk orientation in injection molding of aesthetic plastic parts. The major difference between fiber and disk orientation kinematics is briefly discussed using Jeffery model. Experimental and numerical results for the disk orientation and the surface color of the molded part are presented. Finally, we introduce our recent efforts regarding the rheology of magnetic particle suspension, which is an essential part for a development of precision magnetic powder injection molding process. Some rheometer data for stainless steel powder suspensions are presented.

Biases in three-dimensional vorticity analysis using porphyroclast system: limits and application to natural examples

Abstract A description of the systematic errors associated with the measurement of the vorticity number from poryhroclasts in natural systems is presented and discussed. We show that strong biases and systematic errors could derive both from some erroneous physical (i.e. no slip across clast/matrix boundary, homogeneity within the matrix) as well as geometrical assumptions (i.e. the radius ratio and angular measurements carried out in two dimensions on outcrop surfaces and thin section). By comparing natural datasets of porphyroclast shape preferred orientation (SPO) with different theoretical curves plots, we suggest that at least one of the Jeffery physical assumptions can be tested when applying vorticity techniques. The comparison of different possible sources of systematic errors indicates that, for medium-to-low vorticity numbers ( W m <0.8), vorticity data are strongly biased and that a minimum systematic error of 0.2 should be taken into account. Finally, we use data from natural shear zones from the Southern Variscan Belt in Sardinia to test and discuss the starting assumptions of the Jeffery model.

Rigid inclusions rotate in geologic materials as shown by torsion experiments

Jeffery showed 86 years ago that a sphere rotates synthetically with applied simple shear, at a rate equal to half the shear strain rate. However, it can be argued that rocks do not behave like viscous fluids hence Jeffery's model does not apply. In order to test this argument, we took a two-phase synthetic aggregate (rock) made of 70% halite and 30% muscovite (as anisotropic ductile matrix) with embedded rigid bodies with contrasting shapes: circular cylinder, sphere and cube. The sphere approximates the shape of a garnet and the cube the shape of pyrite crystals, both so common in nature. When subject to torsion at 250 MPa and 100 °C, the matrix deformed homogeneously and all rigid bodies rotated as theoretically predicted for a viscous fluid matrix. Therefore, we conclude that rocks deforming in a ductile fashion behave macroscopically like a continuum hence fluid mechanics can be used to study rigid inclusion rotation behaviour.

The experimental basis for interpreting particle and magnetic fabrics of sheared till

AbstractParticle fabrics of basal tills may allow testing of the bed‐deformation model of glacier flow, which requires high bed shear strains (>100). Field studies, however, have not yielded a systematic relationship between shear‐strain magnitude and fabric development. To isolate this relationship four basal tills and viscous putty were sheared in a ring‐shear device to strains as high as 714. Fabric was characterized within a zone of shear deformation using the long‐axis orientations of fine‐gravel and sand particles and the anisotropy of magnetic susceptibility (AMS) of small (∼5·8 cm3) intact samples. Results indicate that till particles rotate toward the plane of shearing with long‐axis orientations that become tightly clustered in the direction of shear (0·78 < S1 < 0·94 for three‐dimensional data). These strong, steady‐state fabrics are attained at shear strains of 7–30, with no evidence of fabric weakening with further strain, regardless of the specific till or particle‐size fraction under consideration. These results do not support the Jeffery model of particle rotation, which correctly describes particle rotation in the viscous putty but not in the tills, owing to fluid‐mechanical assumptions of the model that are violated in till. The sensitivity of fabric development to shear‐strain magnitude indicates that, for most till units where shear‐strain magnitude is poorly known, attributing fabric variations to spatial differences in other variables, such as till thickness or water content, will be inherently speculative. Attributing fabric characteristics to particular basal till facies is uncertain because shear‐strain magnitude is unlikely to be closely correlated to till facies. Weak or spatially variable fabrics, in the absence of post‐depositional disturbance or major deviations from unidirectional simple shear, indicate that till has not been pervasively sheared to the high strains required by the bed‐deformation model. Strong flow‐parallel fabrics are a necessary but insufficient criterion for confirming the model. Copyright © 2008 John Wiley & Sons, Ltd.

Applications of inclusion behaviour models to a major shear zone system: The Nordfjord-Sogn Detachment Zone in western Norway

Rigid inclusion models have reached a stage where one should be able to use them to obtain quantitative values from ductile shear zones. We used natural data collected in three sites and combined analogue and theoretical modelling to assess vorticity, strain, nature of rigid inclusion/matrix interface and confinement in the large-scale, ductile Nordfjord-Sogn Detachment Zone (NSDZ) of the Caledonides of western Norway. Our study shows that: (1) the observed shape preferred orientation (SPO) at higher structural levels of the NSDZ at Site 1, Gjervika, can be explained by simple shear (pure shear/simple shear ratio S r = 0) associated with a slipping inclusion/matrix interface. (2) The observed SPO at deeper structural levels of the NSDZ at Site 2, near Sandane can be produced by simple shear associated with a significant amount of shortening across the shear zone ( S r ≈ 1), acting upon rigid inclusions in slipping contact with the enclosing matrix. (3) Observed back rotated boudins deeper in the NSDZ at Site 3, Biskjelneset, can form in confined flow associated with a considerable amount of shortening across the shear zone ( S r ≥ 0.4). (4) The observed tails of porphyroclasts indicate a minimum (at least local) strain of ca. γ ≈ 20. (5) The clasts in the studied shear zones strongly depart from Jeffery's model [Jeffery, G. B., 1922. The motion of ellipsoidal particles immersed in a viscous fluid. Proceedings of the Royal Society of London A102, 161–179]. The large scale extensional NSDZ under investigation shows evidence of strain partitioning: rocks vary from protomylonites to ultramylonites, and the simple shear and pure shear components are heterogeneously distributed. Therefore, we conclude that flow in the NSDZ was very heterogeneous both at the kilometre and the metre scale. However, the present study suggests that the amount of shortening across the shear plane throughout the NSDZ increases with depth, and the flattening component contributes to exhumation of the eclogite facies rocks in its footwall.

COMPARISON OF RHEOLOGICAL PROPERTIES OF FIBER SUSPENSIONS WITH MODEL PREDICTIONS

The rheological behavior of fiber suspensions in a Newtonian fluid is compared with the simulations results of two families of models. The well-known Folgar-Tucker model for fiber motion, combined with the Lipscomb constitutive equation, was used and compared to an extended Jeffery model developed by Grmela et al. (2004). The high shear-thinning behavior and the constant normal stress differences predicted by this model, for the fiber suspensions in Newtonian matrix, required modifications and the stress tensor equation was replaced by the Lipscomb constitutive equation. The steady-state and stress growth behavior of fibers suspensions in a Newtonian polybutene are fairly well predicted by both models. The viscosity and normal stress overshoots during stress growth in forward and reverse flows are better described by both models when using a slip parameter and λ larger than I in the Folgar-Tucker-Lipscomb model. The extended Jeffery model has more potential to describe properly the behavior of concentrated fiber suspensions, but this is achieved by using a large number of parameters.

Clast-fabric development in a shearing granular material: Implications for subglacial till and fault gouge

Research Article| May 01, 2000 Clast-fabric development in a shearing granular material: Implications for subglacial till and fault gouge Thomas S. Hooyer; Thomas S. Hooyer 1Department of Geological and Atmospheric Sciences, Iowa State University, Ames, Iowa 50011, USA Search for other works by this author on: GSW Google Scholar Neal R. Iverson Neal R. Iverson 1Department of Geological and Atmospheric Sciences, Iowa State University, Ames, Iowa 50011, USA Search for other works by this author on: GSW Google Scholar GSA Bulletin (2000) 112 (5): 683–692. https://doi.org/10.1130/0016-7606(2000)112<683:CDIASG>2.0.CO;2 Article history received: 17 Sep 1998 rev-recd: 06 Apr 1999 accepted: 15 Jun 1999 first online: 01 Jun 2017 Cite View This Citation Add to Citation Manager Share Icon Share MailTo Twitter LinkedIn Tools Icon Tools Get Permissions Search Site Citation Thomas S. Hooyer, Neal R. Iverson; Clast-fabric development in a shearing granular material: Implications for subglacial till and fault gouge. GSA Bulletin 2000;; 112 (5): 683–692. doi: https://doi.org/10.1130/0016-7606(2000)112<683:CDIASG>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 Elongate clasts in subglacial till and in fault gouge align during shearing, but the relation between clast-fabric strength and cumulative shear strain for such materials is effectively unknown. This relation was explored in experiments with a large ring-shear device in which a till and a viscous putty that contained isolated clasts were sheared to high strains. As expected, rotation of clasts in the putty is closely approximated by the theory of G.B. Jeffery, who derived the orbits of rigid ellipsoids in a slowly shearing fluid. Clast rotation in the till, however, is strikingly different. Rather than orbiting through the shear plane as predicted by Jeffery, most clasts rotate into the shear plane and remain there, resulting in strong fabrics regardless of the aspect ratios and initial orientations of clasts. This divergent behavior is likely due to slip of the till matrix along the surfaces of clasts, which is a natural expectation in a granular material but violates the no-slip condition of Jeffery's model. These results do not support the widespread belief that subglacial till deformation results in weak clast fabrics. Thus, many tills with weak fabrics thought to have been sheared subglacially to high strains, like many basal tills of the Laurentide Ice Sheet, may have been sheared only slightly with little effect on either ice-sheet dynamics or sediment transport. In addition, these results indicate that in simple shear the rotation of clasts in till and in fault gouge is best analyzed with the model of A. March, who treated inclusions as passive markers. You do not have access to this content, please speak to your institutional administrator if you feel you should have access.

Clast-fabric development in a shearing granular material: Implications for subglacial till and fault gouge

Research Article| May 01, 2000 Clast-fabric development in a shearing granular material: Implications for subglacial till and fault gouge Thomas S. Hooyer; Thomas S. Hooyer 1Department of Geological and Atmospheric Sciences, Iowa State University, Ames, Iowa 50011, USA Search for other works by this author on: GSW Google Scholar Neal R. Iverson Neal R. Iverson 1Department of Geological and Atmospheric Sciences, Iowa State University, Ames, Iowa 50011, USA Search for other works by this author on: GSW Google Scholar Author and Article Information Thomas S. Hooyer 1Department of Geological and Atmospheric Sciences, Iowa State University, Ames, Iowa 50011, USA Neal R. Iverson 1Department of Geological and Atmospheric Sciences, Iowa State University, Ames, Iowa 50011, USA Publisher: Geological Society of America Received: 17 Sep 1998 Revision Received: 06 Apr 1999 Accepted: 15 Jun 1999 First Online: 01 Jun 2017 Online ISSN: 1943-2674 Print ISSN: 0016-7606 Geological Society of America GSA Bulletin (2000) 112 (5): 683–692. https://doi.org/10.1130/0016-7606(2000)112<683:CDIASG>2.0.CO;2 Article history Received: 17 Sep 1998 Revision Received: 06 Apr 1999 Accepted: 15 Jun 1999 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 Thomas S. Hooyer, Neal R. Iverson; Clast-fabric development in a shearing granular material: Implications for subglacial till and fault gouge. GSA Bulletin 2000;; 112 (5): 683–692. doi: https://doi.org/10.1130/0016-7606(2000)112<683:CDIASG>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 Elongate clasts in subglacial till and in fault gouge align during shearing, but the relation between clast-fabric strength and cumulative shear strain for such materials is effectively unknown. This relation was explored in experiments with a large ring-shear device in which a till and a viscous putty that contained isolated clasts were sheared to high strains. As expected, rotation of clasts in the putty is closely approximated by the theory of G.B. Jeffery, who derived the orbits of rigid ellipsoids in a slowly shearing fluid. Clast rotation in the till, however, is strikingly different. Rather than orbiting through the shear plane as predicted by Jeffery, most clasts rotate into the shear plane and remain there, resulting in strong fabrics regardless of the aspect ratios and initial orientations of clasts. This divergent behavior is likely due to slip of the till matrix along the surfaces of clasts, which is a natural expectation in a granular material but violates the no-slip condition of Jeffery's model. These results do not support the widespread belief that subglacial till deformation results in weak clast fabrics. Thus, many tills with weak fabrics thought to have been sheared subglacially to high strains, like many basal tills of the Laurentide Ice Sheet, may have been sheared only slightly with little effect on either ice-sheet dynamics or sediment transport. In addition, these results indicate that in simple shear the rotation of clasts in till and in fault gouge is best analyzed with the model of A. March, who treated inclusions as passive markers. You do not have access to this content, please speak to your institutional administrator if you feel you should have access.

Analogue and numerical modelling of shape fabrics: application to strain and flow determination in magmas

We summarise numerical and analogue models of shape fabrics, and discuss their applicability to the shape preferred orientation of crystals in magmas. Analyses of flow direction and finite strain recorded during the emplacement of partially crystallised magmas often employ the analytical and numerical solutions of the Jeffery's model, which describe the movement of noninteracting ellipsoidal particles immersed in a Newtonian fluid. Crystallising magmas, however, are considered as dynamic fluid systems in which particles nucleate and grow. Crystallisation during magma deformation leads to mechanical interactions between crystals whose shape distribution is not necessarily homogeneous and constant during emplacement deformation. Experiments carried out in both monoparticle and multiparticle systems show that shape fabrics begin to develop early in the deformation history and evolve according to the theoretical models for low-strain regimes. At large strains and increasing crystal content, the heterogeneous size distribution of natural crystals and contact interactions tend to generate steady-state fabrics with a lineation closely parallel to the direction of the magmatic flow. This effect has been observed in all threedimensional experiments with particles of similar size and for strain regimes of high vorticity. On the other hand, studies of feldspar megacryst sub-fabrics in porphyritic granites suggest that these record a significant part of the strain history. Thus, the fabric ellipsoid for megacrysts evolves closer to the strain ellipsoid than for smaller markers. This behaviour results from the fact that the matrix forms of the melt and smaller crystals behave like a continuous medium relative to the megacrysts. Consequently, in the absence of these markers, and because the fabric intensities of smaller particles such as biotite are stable and lower than predicted by the theory, finite strain remains indeterminate. In that case, strain quantification and geometry of the flow requires the addition of external constraints based on other structural approaches.

Shape preferred orientations of survivor grains in fault gouge

Survivor grains are rounded, isolated clasts in fault gouge that escaped the grain fracturing so evident in fault breccia. Surrounded by a matrix of clay or comminuted parent rock, they are free to rotate without interference from other clasts. Using an optical microscope, electron microprobe images, and image analysis software, I collected data on the long axis orientations of elongate ( a/ b>1.4) survivors in 15 samples of fault gouge and breccia from Death Valley, California. Survivor grains display a profound shape preferred orientation (SPO) which can be used to infer kinematic parameters of gouge deformation. The SPO depends on the gouge type. In clay gouge the SPO is inclined to the shear plane, similar to the P-foliation usually defined by a phyllosilicate fabric. In flow-banded granular gouge the SPO is parallel to the shear plane and banding. To explore the implications of the SPO data, kinematic models of passive markers in simple shear (March model), rigid ellipsoids in simple shear (Jeffery model), and rigid ellipsoids in general shear (Ghosh and Ramberg model) were numerically implemented. Comparison of SPO data and model results suggests two explanations for the inclined SPO of clay gouge: either the simple shear strain experienced by clay gouge is low ( γ<4) or the shear strain is unlimited but gouge deformation included apparent thickening of the shear zone. In the accompanying paper the latter option is assumed and a kinematic model of brittle shear zones which includes another commonly observed microstructure of fault gouge, Riedel shears, is developed to explain the inclined SPO in clay gouge.

Matching simulated fracture data with field measurements using joint intensity

Survivor grains are rounded, isolated clasts in fault gouge that escaped the grain fracturing so evident in fault breccia. Surrounded by a matrix of clay or comminuted parent rock, they are free to rotate without interference from other clasts. Using an optical microscope, electron microprobe images, and image analysis software, I collected data on the long axis orientations of elongate (a/b>1.4) survivors in 15 samples of fault gouge and breccia from Death Valley, California. Survivor grains display a profound shape preferred orientation (SPO) which can be used to infer kinematic parameters of gouge deformation. The SPO depends on the gouge type. In clay gouge the SPO is inclined to the shear plane, similar to the P-foliation usually defined by a phyllosilicate fabric. In flow-banded granular gouge the SPO is parallel to the shear plane and banding. To explore the implications of the SPO data, kinematic models of passive markers in simple shear (March model), rigid ellipsoids in simple shear (Jeffery model), and rigid ellipsoids in general shear (Ghosh and Ramberg model) were numerically implemented. Comparison of SPO data and model results suggests two explanations for the inclined SPO of clay gouge: either the simple shear strain experienced by clay gouge is low (γ<4) or the shear strain is unlimited but gouge deformation included apparent thickening of the shear zone. In the accompanying paper the latter option is assumed and a kinematic model of brittle shear zones which includes another commonly observed microstructure of fault gouge, Riedel shears, is developed to explain the inclined SPO in clay gouge.

Numerical simulation of fiber orientation in injection mold filling

A finite element method is used to simulate the moving boundary, the flow and thermal field, and the fiber orientation during injection mold filling. Jeffery's model is employed to predict the fiber orientation. The influence of the fountain flow effect and process conditions on fiber orientation is examined.

Strain and fabric analyses based on porphyroclast interaction

Two-dimensional computer models of the interaction of elliptical clasts in a variety of kinematic conditions are used to study how clast imbrication and shape fabric development relate to strain and strain history. The models provide templates, for a known clast density and clast ellipticity, that correlate clast imbrication, angle of collision and clast shape fabric to strain and kinematics of deformed rocks. Modeling also shows that the mode of clast interaction plays a significant role in the accumulation of imbricated clasts and the development of shape fabric. Upon collision between clasts, the trains formed can remain fixed or rotate. If they rotate, imbricated clasts can become independent when they are no longer forced together by the flow. Based upon the mode of clast and train rotation (using the March rotation of passive lines and the Jeffery rotation of rigid particles as end-members), three models are defined in an attempt to simulate the conditions of clast interaction under varying conditions. The March-fixed train, March-rotating train and Jeffery-rotating train models simulate solid-state, intermediate and magmatic conditions, respectively. Modeling shows that the two March models produce similar results, but the Jeffery model of train rotation always produces a lower proportion of imbricated clasts and a much weaker shape fabric. Application of the modeling to the study of a syntectonic granite in the Sierra Nevada suggests that deformation was dominated by simple shear. Some K-feldspar imbrication and fabric development took place initially in the magmatic stage, and culminated in the solid state to produce a large proportion of imbricated K-feldspar porphyroclasts which define a strong shape fabric. This type of analysis provides a rationale to determine syn-vs post-emplacement deformation in the granite.

Rotations of elongate rigid particles in slow non-Newtonian flows

In Jeffery's well-known theoretical model each end of the symmetry axis of an isolated rigid prolate ellipsoid embedded in a Newtonian matrix undergoing simple shear flow describes one of an infinite family of accurately closed periodic orbits. The usefulness of this model in relating particle orientation distributions to bulk finite strain is reassessed in the light of recent theoretical and experimental work. This work shows that Jeffery's analysis is readily extended to include any axisymmetric particle shape (with a centre of symmetry), and that small surface irregularities may be neglected. In nonNewtonian media (both power-law and elasticoviscous) particle motions, although still periodic, show a progressive drift through the family of Jeffery orbits. In a secondorder Rivlin—Ericksen fluid the orbital drift estimated for the strain magnitudes and particle axis ratios likely in most tectonites is slight, and leads to negligibly small departures from the predictions of Jeffery's model. More orbital drift is anticipated in powerlaw fluids although Jeffery's model is still likely to yield an acceptable approximation except for very high strains.