Ziegler's Model Research Articles

Dissolution Kinetics of Ilmenite Ore in A Binary Solution

Leaching of iron from ilmenite ore using a binary solution (HCl-NaNO3) was investigated. The raw ilmenite ore sample was characterized using Scanning Electron Microscopy (SEM), X-ray diffraction spectroscopy (XRD) and X-ray Flourescence (XRF) techniques. The influence of acid concentration, oxidant concentration, particle size, solution temperature, stirring speed and liquid-to-solid ratios on the extent of dissolution was examined. The experimental data obtained at various process parameter conditions were tested in six kinetics models: shrinking core model’s diffusion through liquid film model(DTLF), diffusion through product layer model (DTPL), surface chemical reaction model (SCR)); mixed kinetics model (MKM), Jander (three dimensional) model and Kröger and Ziegler model. The crystalline morphology of the sample was displayed by the SEM micrograph. XRF result revealed the dominance of titanium and iron in ilmenite while XRD confirmed that ilmenite exist mainly as FeTiO2. The results of the leaching studies showed that ilmenite dissolution in the binary solution increases with increasing acid concentration, oxidant concentration, reaction temperature, stirring speed and liquid-to-solid ratio; while it decreases with particle size. The study showed that 94.77% iron was dissolved by 1MHCl-0.6M NaNO3 at 75μm particle size, 75˚C reaction temperature, 300rpm stirring speed and 30L/g liquid-to-solid ratio. The kinetics of the leaching process was best described by Kröger and Ziegler model with diffusion through the product layer as rate controlling step. The activation energy, Ea, was calculated to be 6.42kJ/mol. The results indicate that HCl-NaNO3 binary solution can be used as an effective lixiviant for extracting iron from ilmenite ores.

Dissolution Kinetics of Ilmenite Ore in A Binary Solution

Leaching of iron from ilmenite ore using a binary solution (HCl-NaNO3) was investigated. The raw ilmenite ore sample was characterized using Scanning Electron Microscopy (SEM), X-ray diffraction spectroscopy (XRD) and X-ray Flourescence (XRF) techniques. The influence of acid concentration, oxidant concentration, particle size, solution temperature, stirring speed and liquid-to-solid ratios on the extent of dissolution was examined. The experimental data obtained at various process parameter conditions were tested in six kinetics models: shrinking core model’s diffusion through liquid film model(DTLF), diffusion through product layer model (DTPL), surface chemical reaction model (SCR)); mixed kinetics model (MKM), Jander (three dimensional) model and Kröger and Ziegler model. The crystalline morphology of the sample was displayed by the SEM micrograph. XRF result revealed the dominance of titanium and iron in ilmenite while XRD confirmed that ilmenite exist mainly as FeTiO2. The results of the leaching studies showed that ilmenite dissolution in the binary solution increases with increasing acid concentration, oxidant concentration, reaction temperature, stirring speed and liquid-to-solid ratio; while it decreases with particle size. The study showed that 94.77% iron was dissolved by 1MHCl-0.6M NaNO3 at 75?m particle size, 75?C reaction temperature, 300rpm stirring speed and 30L/g liquid-to-solid ratio. The kinetics of the leaching process was best described by Kröger and Ziegler model with diffusion through the product layer as rate controlling step. The activation energy, Ea, was calculated to be 6.42kJ/mol. The results indicate that HCl-NaNO3 binary solution can be used as an effective lixiviant for extracting iron from ilmenite ores.

듀플렉스 스테인레스 소재의 고온 변형 안정성 및 어닐링 온도에 따른 특성 분석

The aim of this study was to analyze high temperature deformation stability and properties of duplex stainless steels(DSS) according to annealing temperature. In order to analyze high temperature deformation stability, a number of compression tests were carried out with a stain rate of 10 s~10 s up to a compression ratio of 50% in a temperature range of 950°C-1300°C. The analysis of high temperature deformation stability of DSS was performed based on the Ziegler model. In order to analyze the high temperature properties of DSS, annealing treatments were conducted by isothermal holding for 1 hr at 950°C to 1300°C with 50°C intervals followed by water cooling. The hardness and tensile tests were performed on specimens with different volume fractions of constituent phases, such as austenite, ferrite and sigma. The hardness and tensile strength of 2507 according to the annealing temperature are better than those of 2205. The strain rate sensitivity and Ziegler parameter are higher in 2205 than in 2507 as a whole, which implies that 2205 is better than 2507 in terms of forgeability at high temperature. (Received January 25, 2012)

Nonlinear Damping as a Stabilizating Factor and Resolving Ziegler's Paradox

Nonlinear model obtained from notorious Ziegler model by adding nonlinear terms is considered. Ziegler's paradox is explained from nonlinear point of view. It is known that our world is nonlinear. In order to describe it, it is necessary to use nonlinear models. But linear models continue playing an independent and auxiliary (linearization) role as they are more simply. However there are situations general enough when paradoxical effects in linear models disappear after adding nonlinear terms. For example one of such situations is the Ziegler paradox. There is a jump of value of the critical force (at which the system loses stability) in a linear not conservative system in which damping is taken into account. In this paper it is shown that if one changes the Ziegler's system a little with adding nonlinear damping that the jump disappears. In the nonlinear system depending on values of parameters we have either a "soft" type of loss of stability with appearance a stable limit cycle or a "sharp" type of loss of stability. The most interesting and important fact is that the difference between "soft" and "sharp" losses of stability is equal the magnitude of the jump of the critical force in the linear Ziegler system.

On the stability and instability regions of non-conservative continuous system under partially follower forces

The transition between stability and instability of a uniform cantilever beam subjected to a partially follower load is discussed by means of the finite element method. The stability diagram in terms of the load versus the non-conservativeness loading parameter is obtained both in the hypothesis of linearized (small displacements) and non-linearized (large displacements) analysis. It is found that the regions of divergence and flutter instability of the finite element model of continuous system are quite different from the corresponding ones obtained for the classical 2 degrees of freedom Ziegler's model (i.e. the inverted double pendulum), both quantitatively and qualitatively. The transition from the 2 degrees of freedom model to the continuous model is investigated through the study of some multi degrees of freedom approximation models (i.e. the 3, 4, 5 and 10 degrees of freedom models) of the continuous column. Finally, the effect of damping in the stability diagram of the finite element model of continuous system is discussed and the destabilizing effect of small damping is emphasized.

Collision of eigenvalues in linear oscillatory systems

Autonomous oscillatory systems depending on several parameters are considered. The behaviour of the eigenvalues is considered in the neighbourhood of a multiple point. The method of perturbations is used to show that the interaction of eigenvalues in the neighbourhood of the point in question is described by a family of hyperbolae. The coefficients of the equations of these hyperbolae are calculated using an eigenvector and an associated vector, an eigenvector of the adjoint problem at the multiple point, and the increments of the parameters. The relationships obtained enable an analytical description and geometrical interpretation to be given of two interesting phenomena frequently observed in the literature: the shift of the critical mode of an oscillatory system [1–3], and the destabilization of a system by weak damping [4–8]. Examples considered are the shift of the critical mode of an articulated pipe through which a liquid is flowing, and the destabilization of a non-conservative two-degree-of-freedom Ziegler model.

On the reliability of classical divergence instability analyses of Ziegler's nonconservative model

The critical states of divergence instability of the two-degree-of-freedom Ziegler's model under a nonconservative follower load are reexamined with the aid of a nonlinear static and dynamic analysis. The long-term postcritical response is studied by discussing the effect of various parameters such as geometric and stiffness nonlinearities, linear viscous damping and initial geometric imperfections. To this end the stability of equilibria and limit cycles is explored with the aid of global solutions based on the original nonlinear equations of motion in order to include nonperiodic (chaotic) motion phenomena. New important results obtained by nonlinear static and dynamic analyses contradict existing findings based on classical linearized solutions. It is found that the critical load coincides with the corresponding dynamic one (associated with a divergent motion) only for models without precritical deformations. Some chaoslike phenomena of dissipative or non-dissipative autonomous systems due to competing equilibrium point attractors are also presented.

The Fujita-Ziegler model: a new semi-quantitative technique for estimating paleoclimate from paleogeographic maps

The Fujita-Ziegler model combines approaches developed by T.T. Fujita and A.M. Ziegler of the University of Chicago to produce semi-quantitative retrodictions of paleoclimates based on paleogeographic maps that include the sizes and positions of land and sea areas and the positions and extents of upland areas. Based on such paleogeographic maps, the Fujita model extrapolates past values of surface air pressure from present-day relationships among air pressure, land area, latitude and season. Zonal mean air pressure for each latitude and season is hypothesized to depend on the amount of land area at that latitude and deviations from this mean over major bodies of land or water are hypothesized to depend on the area of the relevant body at that latitude. Fujita diagrams both illustrate these hypottheses and permit application of the model to paleogeographic maps. Surface air pressure maps based on these diagrams can be used to qualitatively retrodict seasonal windflow patterns and ocean currents. Tests of the Fujita model on the Recent geography suggest that most major air pressure cells are positioned accurately and that the values at the centers of cells are within 2–3 mb of measured values at low and middle latitudes and within 5 mb at the poles. Because the Fujita model extrapolates from a partly glaciated world, its retrodictions for ice-free times are suspect, particularly near the poles. The Ziegler model infers the areal and seasonal distribution of precipitation from reconstructed patterns of winds and ocean currents on paleogeographic maps. Retrodictions are based on (1) mechanisms that lift air, including global patterns of atmospheric circulation (Intertropical Convergence Zone), regional storm systems (extratropical cyclones) and relatively local lifting mechanisms (orographic effects, land-sea breezes and summer convective thunderstorms); (2) sources of moist air (i.e., bodies of warm water upwind); and (3) mechanisms that interfere with convection (e.g., upwelling zones and trade wind inversions). Tests of the Ziegler model on the Recent geography accurately retrodicted seasonal precipitation at low and middle latitudes but did less well near the poles. Comparison with maps of the seasonality of precipitation in the Recent shows that the model accurately retrodicted most ever-dry and ever-dry regions. Results emphasize the importance of accurately retrodicting the effects of orography, moisture source and upwelling zones on precipitation.

Influence of various types of elastic foundation on the divergence and flutter of Ziegler's model structure

Ziegler's model structure (consisting of two rigid massless bars connected by a frictionless joint, with two rotational springs under follower force) is utilized in order to illustrate the influence of various types of elastic foundation on the buckling loads. In particular, continuous rotary or translational (Winkler) foundations are studied, whereas in the case of discrete foundation two translational springs are introduced in addition to the rotary springs.