Eva Gregorová

A note on particle size analyses of kaolins and clays

Abstract Based on paradigmatic experimental results for one selected type of kaolin the systematic differences in the measurement of particle size distributions of kaolins and clays by the sedimentation method and by the low angle laser light scattering (LALLS) method are studied. A theoretically sound shape transformation procedure for sedimentation results is proposed, based on a physically justified modification of the Stokes law, which takes into account the oblate (plate-like) shape of kaolin and clay particles. It is found that, with realistic estimates of the shape factor (aspect ratio), the corrected sedimentation data come very close to the light scattering data. This indicates at the same time a way to extract shape information from the comparison of two independent size measurements. Scanning electron microscopy of the 2-μm-undersize sedimentation fraction shows kaolin particles with a disc diameter of 3–5 μm and is thus in full agreement with the interpretation of the size measure as an “equivalent disc diameter”.

Phase Mixture Models for the Thermal Conductivity of Nanofluids and Nanocrystalline Solids

Nanofluids exhibit enhanced thermal conductivity with decreasing particle size, while nanocrystalline solids show a thermal conductivity reduction with decreasing grain size. Both phenomena can be modeled as being due to a boundary phase acting as a thermal bridge or barrier, respectively. In this paper a new phase mixture model is presented, based on a “mixed average” of the upper and lower Wiener bounds. It is shown that in the case of alumina‐water nanofluids our model is able to describe very well the experimentally measured data for nanofluids with 38, 25 and 13 nm alumina particles, when the solid‐like boundary phase is assumed to possess ice‐like thermal conductivity (2 W/mK) and a thickness of 1–5 nm. For nanocrystalline alumina (assuming a grain boundary with thickness 1 nm and a glass‐like conductivity value of 1.1 W/mK), it is shown that significant grain size effects cannot be expected for grain sizes above 100 nm and a more than 10% conductivity reduction requires grain sizes below 50 nm.

Application of Stereological Relations for the Characterization of Porous Materials via Microscopic Image Analysis

In this work we demonstrate the application of stereology-based image analysis for the characterization of highly porous cellular ceramics (alumina foams) prepared by biological foaming with yeast and subsequent drying (80-105 °C) and firing (1570 °C). It is shown that the ceramics prepared usually have total porosities in the range 78-84 % and that the porosities made up by large pores (volume fraction of foam bubbles) are usually in the range 58-75 %. Further it is shown that the mean chord length and the Jeffries size, i.e. pore size measures related to the interface density and the mean curvature integral density, respectively, are relatively close to each other (usually 0.8-1.4 and 0.8-1.2 mm) with a ratio close to unity (0.9-1.3) and that the mean surface-to-surface distance of pores gives a realistic picture of the average pore wall thickness (usually 0.46-0.69 mm). Using a special processing variant (excess ethanol addition) it is possible to obtain microstructures with lower porosity (total porosity 68-70 %, foam bubble volume fractions 50-56 %) and smaller pore size (approx. 0.5 mm). Absolute errors are calculated using normalized deviations corresponding to 95 % reliability in the Student distribution and the standard errors for the quantities in question (both observed and estimated). Relative errors are found to be below 12 % when the number of measurements is of order 400-1000.

High-Temperature Elastic Properties of Ceramics in the System MgO-Al2O3-SiO2 Measured by Impulse Excitation

Youngs moduli of talc-based ceramics from the system MgO-Al2O3-SiO2 are measured for temperatures up to 1000 °C via impulse excitation. It is shown that, after pressing at 50 MPa and firing at 1280 °C, MgO-rich compositions exhibit higher porosity and lower Youngs moduli (approximately 2030 % lower than predicted via micromechanical relations). The Young moduli of materials with less MgO decrease with temperature, but those of MgO-rich ceramics increase with temperature and exhibit a large hysteresis between heating and cooling. Lower absolute values are mainly due to increased porosity, but the reason for the modulus increase with temperature and the hysteresis is the higher enstatite content in the MgO-rich compositions. For a special composition the Youngs moduli are more or less temperature-independent and without significant hysteresis effects, probably due to the low content of enstatite and the high content of sapphirine.

Anisometric Particle Systems—from Shape Characterization to Suspension Rheology

Methods for the characterization of anisometric particle systems are discussed. For prolate particles, the aspect ratio determination via microscopic image analysis is recalled, and aspect ratio distributions as well as shape‐size dependences are commented upon. For oblate particles a simple relation is recalled with can be used to determine an average aspect ratio when size distributions are available from two methods, typically from sedimentation analysis and laser diffraction. The connection between particle shape (aspect ratio) and suspension rheology is outlined and it is shown how a generic procedure, based on Brenner’s theory, can be applied to predict the intrinsic viscosity when the aspect ratio is known. On the other hand it is shown, how information on the intrinsic viscosity and the critical solids volume fraction can be extracted from experiments, when the measured concentration dependence of the effective suspension viscosity is adequately interpreted (using the Krieger relation for fitting)...

Elastic Properties of Porous Alumina, Zirconia and Composite Ceramics

Micromechanical calculations and elasticity standard relations are used to predict the elastic properties of porous alumina, zirconia and kaolin-based ceramics, as well as the high-temperature Young moduli of alumina-zirconia and alumina-mullite composites. The predictions are compared with experimental results obtained via impulse excitation. It is found that the Young moduli of highly porous (cellular) alumina ceramics can be predicted via the Gibson-Ashby power-law relation, whereas for partially sintered kaolin-based ceramics our exponential relation, albeit better than the Gibson-Ashby relation, does not give a satisfactory prediction. However, once the Young moduli are known, the shear and bulk moduli can be reliably predicted in both cases, based on rough information on the Poisson ratio. The temperature dependence of the Youngs moduli of two-phase composites can be quite precisely predicted as soon as the master curves of the constituent phases and the type of porosity (convex, concave, or saddle-point) are known.

Layered Alumina Ceramics with Porosity Steps

This work deals with the preparation and characterization of macroporous alumina ceramics and permeable laminates with a stepwise (layerwise) porosity gradient in the range of approx. 20–50 %. Layered structures are made by sequential casting and draining of ceramic suspensions containing corn starch (median size approx. 14 micrometers), using both traditional slip casting (TSC) and starch consolidation casting (SCC). In both techniques starch acts as a poreformer, which is eliminated during firing. The influence of the alumina concentration and starch content in the suspension on the porosity, pore size and pore connectivity in the individual layers is studied. It is shown that differential shrinkage of the layers in the case of SCC, caused by the different starch content, may be avoided by controlling the alumina content. The distribution of pore throat diameters (cell window sizes) is determined by mercury porosimetry, whereas the distribution of pore cavity diameters (cell sizes) is measured by microscopic image analysis.