Josef Ježek

The behaviour of rigid triaxial ellipsoidal particles in viscous flows—modeling of fabric evolution in a multiparticle system

Abstract The behaviour of rigid triaxial ellipsoidal particles in slowly moving viscous flows has been studied by means of numerical solution of Jefferys (1922) equations. The motion of a single particle as well as a multiparticle system evolution in the combined pure shear and simple shear flow was modeled. The development of a preferred orientation depends on particle axial ratios and the flow geometry. Stable fabrics are produced only for sufficiently high components of pure shear. For lower pure-shear components oscillating fabrics develop, periodic in the case of spheroidal (biaxial) particles and irregularly oscillating in the case of triaxial ones. The fabric symmetries may not directly reflect the flow geometry in the case of triaxial particles.

Fabric evolution of rigid inclusions during mixed coaxial and simple shear flows

Abstract In a slowly moving viscous fluid, a population of non-interacting, rigid inclusions evolves in an oscillatory fashion or creates a stable fabric, depending on the flow geometry and the shape of the inclusions. Using Jefferys equations for the motion of a rigid ellipsoidal inclusion, a mixed coaxial and simple shear flow was investigated, both analytically and by numerical modeling. Exact results were obtained for spheroidal inclusions. Depending on the axial ratio of the inclusion and the amount of the coaxial component of flow, individual inclusions can move cyclically or rotate to a stable orientation in one of two mutually orthogonal directions. Equations were found which allow us to distinguish between these types of motion and to determine the stable inclusion orientation. The relative motions of individual inclusions determine the preferred orientation in a population of inclusions. In a heterogeneous population with diverse axial ratios, the fabric evolves as the superposition of subfabrics corresponding to subsets with different axial ratios. The orientations of stable subfabrics depend on axial ratios, and could thus be used as kinematic indicators. In cases of a sufficiently large coaxial component of flow, the fabric created by a heterogeneous population may comprise two stable, mutually orthogonal subfabrics. No exact results are available for general (i.e., non-spheroidal) ellipsoidal inclusions, and numerical modeling must be used. If the coaxial component of flow is sufficiently strong, the non-spheroidal inclusions move much like the spheroidal ones. Orthogonal subfabrics may appear as transient features in the evolution of a homogeneous population of non-spheroidal ellipsoidal inclusions.

Magnetic fabric and rheology of co-mingled magmas in the Nasavrky Plutonic Complex (E Bohemia): implications for intrusive strain regime and emplacement mechanism

Abstract The fabrics of mafic microgranular enclaves (MME) and of the host granodiorite of the old granodiorite intrusion of the Nasavrky Plutonic Complex (E Bohemia) were investigated by means of magnetic anisotropy. The magnetic fabric in MME is oriented coaxially with the magnetic fabric of the host granodiorite which is undoubtedly magmatic (intrusive) in origin. Consequently, the magnetic fabric in MME originated during the same process as the magnetic fabric in granodiorite, i.e. during the granodiorite emplacement. In addition, also the degree of anisotropy and the shapes of susceptibility ellipsoids are very similar in MME and in granodiorite, which probably indicates that the MME had probably a similar viscosity to that of granodiorite and behaved as passive markers whose shapes resembled those of the intrusive strain ellipsoids. Petrological and geochemical approaches coupled with rheological modelling allow the prediction of the physical states of magmas and of the development of their internal fabrics. Observed fabrics were compared to the results of numerical modelling of multiparticle systems slowly moving in viscous fluid. The steep magnetic foliations and almost vertical magnetic lineations suggest that todays erosion level represents a relatively deep intrusive level where magma flowed vertically and its intrusion was controlled by the shape of the feeder zone used for magma ascension.

Software for modeling the motion of rigid triaxial ellipsoidal particles in viscous flow

Abstract Three MS-FORTRAN programs are presented which enable study of the behavior of rigid triaxial ellipsoidal particles in slowly moving viscous flow. The modeling is based on numerical solution of Jefferys equations. These programs allow the investigation of individual particle motion as well as the evolution of a multiparticle system composed of noninteracting particles. In the combined pure shear and simple shear flow, it is possible to estimate the character of multiparticle system evolution by diagrams of time derivatives of Euler angles. The programs are interactive with graphical output on the screen and run on a standard IBM-PC with VGA. Some examples of graphical output of the modeling are presented.

Three-dimensional hydrodynamical modelling of viscous flow around a rotating ellipsoidial inclusion

Abstract A procedure and a FORTRAN program are presented which enable numerical modelling of viscous flow around a rotating rigid ellipsoidal inclusion. For any homogeneous flow given by a velocity gradient tensor it is possible to trace the rotation of the inclusion, velocity field around it, and also the motion of a chosen set of passive markers within the fluid. Examples of modelling were visualized using the MATLAB Package.

Some remarks on fabric overprints and constrictional AMS fabrics in igneous rocks

During the ascent, emplacement and post-emplacement deformation of igneous rocks, two or more phases of deformation that overprint each other are often depicted. These overprints, when magnetic minerals are present, are recorded in magnetic fabric. In this contribution, overprints are studied by means of numerical modeling, following several basic scenarios common to igneous rocks. Biotite and amphibole that occur often together in igneous rocks are considered as carriers of the anisotropy of magnetic susceptibility. Modeling shows that (1) a constrictional fabric with a low degree of anisotropy as commonly recorded in magmatic rocks may result from a deformation overprint and not necessarily from an extensional/transtensional regime, and (2) that the constrictional AMS fabrics originates from orthogonal superimposition of a deformation event on an AMS fabric inherited from earlier magma emplacement history. Therefore, the interpretation of a constrictional fabric must be performed with caution. Numerical modeling may provide a suitable help in strengthening the interpretation of real magnetic fabric data.

Magnetic anisotropy indications of deformations associated with diagenesis

Abstract Anisotropy of magnetic susceptibility (AMS), as revealed by mathematical modelling and empirical studies, sensitively reflects initial ductile deformation associated with diagenesis and early tectonism. In rocks shortened vertically because of the gravitational loading by the weight of overlying strata, the degree of AMS increases and the magnetic fabric becomes more oblate. The magnetic foliation remains parallel to the bedding and the magnetic lineation remains near the water current directions. In rocks shortened laterally, usually by tectonic forces, the degree of AMS and the magnetic fabric oblateness initially decrease and only later increase. The magnetic lineation deflects from the water current direction and the magnetic foliation from the bedding, with its poles creating a girdle pattern. The AMS changes are due to the physical rotation of magnetic grains, which has serious implications for palaeomagnetism, but are major indicators of the change from a diagenetic to a tectonically controlled regime.

A technique for numerical modeling of magnetic anisotropy to strain relationship

Abstract The anisotropy of magnetic susceptibility (AMS) is controlled by the preferred orientation of magnetic minerals in rocks which may be significantly influenced by deformation. This allows us to replace difficult estimation of strain parameters by indirect AMS measurements and the interpretation based on the models of AMS to strain relation. The nature of recently used models is rather simple but the modeling itself is necessarily complex due to large number of input parameters: different carriers of magnetism and their magnetic properties, their initial distribution, the manner how the deformation influences reorientation of magnetic carriers, the character and duration of deformation. A technique is presented for numerical modeling simultaneous temporal evolution of strain and AMS, taking into account these parameters. The presentation of computing procedure is accompanied by an example. A Matlab program for modeling can be obtained on request from authors.

Association of trace elements with colloidal fractions in leachates from closed and active municipal solid waste landfills.

Leachates from two Czech municipal solid waste (MSW) landfills (closed site and active site) were size-fractionated using the cascade frontal filtration/ultrafiltration procedure with filter cut-offs of 3 μm, 0.8 μm, 0.45 μm, 0.1 μm, 10 kDa and 1 kDa. To evaluate the binding of trace elements to colloidal particles, the filtrates were analyzed for major compounds (FAAS, ICP-OES and HPLC) and trace elements (ICP-MS) and the obtained elemental patterns were statistically evaluated. Transmission electron microscopy (TEM) indicated that the colloids were mostly inorganic, mainly composed of carbonates and clays. Characteristic features of the behaviour of trace elements and the main compounds were more pronounced at the active landfill site. Amongst the main compounds, only Fe and Ca decrease significantly and have similar patterns to numerous trace elements, indicating their capture by colloidal particles (at least 25%). Arsenic, Se and Rb exhibit zero or negligible decrease in concentration in the leachate during the filtration procedure. This fact indicates their particularly high mobility, which should be considered in preventing the flux of harmful compounds from landfill systems.

The relationship between the Lisle orientation tensor and the susceptibility tensor

Abstract Lisle (1989) introduced an orientation tensor of orthogonal orientation data as summed cross products of the direction cosines of the X axes minus the summed cross products of the direction cosines of the Z axes. The contribution deals with the relationship between the Lisle orientation tensor and the tensor of magnetic susceptibility. The bulk magnetic susceptibility is generated by a system of triaxial magnetic grains. In the case of “ideally” triaxial magnetic grains, the eigenvectors of the tensor of Lisle are parallel to the eigenvectors of magnetic susceptibility, and in the case of general triaxial grains they are close to them. Analytical results and numerical modelling confirm the intuitive feeling that AMS of a system composed of triaxial magnetic grains reflects the mean orientation of X as well as Z grain axes.