Yodel: A Yield Stress Model for Suspensions

A model for the yield stress of particulate suspensions is presented that incorporates microstructural parameters taking into account volume fraction of solids, particle size, particle size distribution, maximum packing, percolation threshold, and interparticle forces. The model relates the interparticle forces between particles of dissimilar size and the statistical distribution of particle pairs expected for measured or log-normal size distributions. The model is tested on published data of sub-micron ceramic suspensions and represents the measured data very well, over a wide range of volume fractions of solids. The model shows the variation of the yield stress of particulate suspensions to be inversely proportional to the particle diameter. Not all the parameters in the model could be directly evaluated; thus, two were used as adjustable variables: the maximum packing fraction and the minimum interparticle separation distance. The values for these two adjustable variables provided by the model are in good agreement with separate determinations of these parameters. This indicates that the model and the approximations used in its derivation capture the main parameters that influence the yield stress of particulate suspensions and should help us to better predict changes in the rheological properties of complex suspensions. The model predicts the variation of the yield stress of particulate suspensions to be inversely proportional to the particle diameter, but the experimental results do not show a clear dependence on diameter. This result is consistent with previous evaluations, which have shown significant variations in this dependence, and the reasons behind the yield stress dependence on particle size are discussed in the context of the radius of curvature of particles at contact.     

Yield Stress of Multimodal Powder Suspensions: An Extension of the YODEL (Yield Stress mODEL)

The prediction of the rheological properties of concentrated suspensions is of great importance both in industrial processes (ceramics, cements, and pharmaceutics) and natural phenomena (debris flow, soil erosion). In a previous paper, we presented a new model (YODEL) that can predict the yield stress of concentrated particulate suspensions. The model is based on first principles and takes into account particle size distribution, interparticle forces, and microstructural features. It was validated using data from the literature on four different alumina powder suspensions. The current paper extends the application field of the YODEL, successfully, to multimodal distributions of much interest in the cement and concrete field. The key parameter governing the predictive capacity of the YODEL for multimodal distributions was shown to be the maximum packing fraction of the powder mixtures. The de Larrad compressive packing model was used to provide a maximum packing fraction for mixtures from their particle size distributions. The YODEL can predict yield stresses of multimodal suspensions within 10% of the experimental results. Further improvement of the maximum packing fraction prediction should help in our goal of yield stress prediction from basic powder and suspension characteristics.     

Oxidation Behavior of SiC-Whisker-Reinforced Alumina-Zirconia Composites

During high-temperature oxidation in air, SiC-whisker-reinforced Al₂O₃—ZrO₂ composites degrade by the formation of a whisker-depleted mullite-zirconia scale. The reaction kinetics have been studied as a function of time and temperature for composites with whiskers preoxidized for different times. The evolution of the microstructure has been investigated by optical, scanning and transmission electron microscopy. Possible reaction mechanisms have been discussed. A model compatible with our observations on Al₂O₃—ZrO₂—SiC and the results reported in the literature for Al₂O₃—SiC whisker composites is proposed: The oxidation occurs at an internal reaction front. Oxygen diffuses along dislocations and grain boundaries through the mullite scale to react at this front with silicon carbide, thereby forming amorphous silica and graphite. Silica penetrates grain boundaries and further reacts with alumina and zirconia to form mullite and zircon, while the second reaction product, graphite, is oxidized into carbon monoxide when the reaction front moves deeper into the sample.     

Experimental Evaluation of Toughening Mechanisms in Alumina-Zirconia Composites

The contributions of transformation toughening and microcrack toughening in an 85Al₂O₃15ZrO₂ (vol%) composite were quantitatively evaluated. Three types of hot-pressed samples with similar size (∼0.5 µm) and size distribution of ZrO₂ grains, but with different contents (vol%) of monoclinic- ( m -) ZrO₂ (0 (AZS), 45 (AZT), and 67 (AZM)) were prepared using Y₂O₃ and MoO₂ dopants. Therefore, the possible effect of ZrO₂ grain size on each toughening mechanism was eliminated. When the measured fracture toughnesses of m -ZrO₂ volume fractions before and after fracture were compared, the transformation-toughening constant was estimated as 3.0 MPam^1/2 and the microcrack-toughening constant 0.2 MPam^1/2 for a 100% monoclinic transformation of ZrO₂ grains. This result indicates that transformation toughening was the dominant toughening mechanism in the studied composite.     

Surface Strengthening of Alumina-Zirconia Composite by Addition of Molybdenum Dioxide

MoO₂ is found to stabilize m -ZrO₂ Because of the addition of MoO₂ into ZrO₂ at the surface region of an Al₂O₃-15 vol% ZrO₂composite, the volume fraction of m -ZrO₂ at the surface increases from 0.3 to 0.5–0.6 without changing the size of the ZrO₂grains. This enhanced transfomation results in an increase in flexural strength of up to 30% because of compressive stresses built in at the surface. The increase in flexural strength is proportional to the difference in volume fraction of m -ZrO₂ between the surface layer and the bulk matrix, in agreement with a previous analysis.     

Preparation of Alumina-Zirconia Powders by Evaporative Decomposition of Solutions

Fine-grained, homogeneously dispersed alumina-zirconia and zirconia powders were prepared by evaporative decomposition of solutions. The pure metastable tetragonal zirconia powder transformed to the monoclinic form when it was heated to 1150°C. The zirconia in the alumina-zirconia powder, which was also in the tetragonal form, did not transform when the powder was heated to 1150° C. This result is explained in terms of inhibition of coarsening of the zirconia grains by the alumina particles.     

Transformation Toughening in Sol–Gel-Derived Alumina-Zirconia Composites

The microstructures of α-Al₂O₃ seeded sol–gel-derived alumina-zirconia composites containing 20 wt% unstabilized zirconia (processed from zirconium n-propoxide) were very fine, with submicrometer alumina grains and small, mainly intergranular zirconia particles, the latter having a critical size for the tetragonal-to-monoclinic phase transformation of 0.45 μm. The corresponding ratios of the toughening contribution to the matrix toughness are relatively low (δK_c/K₀<1). This finding is confirmed by an analysis of the tetragonal zirconia particle size dependence of the stress-induced transformation toughening.     

Annealing and Yield Stress of NaCl Single Crystals

Annealing experiments on NaCl single crystals are reported, showing that the expected decrease in yield strength is significantly modified by stress history, impurities, and furnace atmosphere. Annealing in air can result in a higher yield stress than that obtained without annealing. The lower limit obtained for the critical resolved shear stress of NaCl single crystals is 35 g per mm².     

Modeling and Fabrication of Fine-Grain Alumina-Zirconia Composites Produced from Nanocrystalline Precursors

Fully dense fine-grained 32.6-vol%-zirconia-toughened alumina composites have been fabricated from nanocrystalline rapidly solidified material. A model considering the thermodynamics of the constrained t -ZrO₂ m -ZrO₂ phase transformation was developed for this percolated two-phase material. This analysis indicated that the grain size at which this phase transformation is thermodynamically favorable was 1.26 µm in a composite that contained 32.6 vol% ZrO₂ and was stabilized with 1.50 mol% Y₂O₃. These results of the model compared favorably with experimental results, showing that grains of this size could be retained after heating to temperatures of as high as 1600°C. The rapidly solidified precursor was ball-milled into submicrometer powder and centrifugally cast into green specimens that were pressureless sintered to full density at temperatures as low as 1500°C. A composite containing nearly 100% t -ZrO₂ was produced by pressureless sintering at 1500°C and a composite containing 45 vol% t -ZrO₂/55 vol% m -ZrO₂ was obtained by sintering at 1600°C. The resulting two-phase microstructures contained uniformly distributed, micrometer-size grains whose sizes are consistent with the facilitation of transformation and microcrack toughening.     

Suspensions and Sediments. Part II. Behavior of Concentrated Suspensions

Abstract

The behavior of concentrated suspension, the phenomenon of hindered settling, and structural characteristics of the settling suspensions are described.

The use of interface sedimentation rate the settled volume in calculating the volume of associated fluid carried down on sedimenting particles is outlined by employing a theory which assumes that particle-particle association is the factor responsible for variation of sedimentation behaviour from one suspension system to another.     

Suspensions of high-melting triglycerides

A method for preparing stable oil/water suspensions of cottonseed stearine, tristearin, tripalmitin, trimyristin, methyl stearate, and palmitic acid in concentrations up to 10% with minimum concentrations of stabilizing agents is described. Using 2.5% of polyethylene glycol 400 monostearate (based on weight of hard fat), 0.1% of Pluronic F 68, and 0.2–0.25% of Carbopol 934 (the concentrations of these two agents are based on the weight of the aqueous phase), suspensions of the hard fats were prepared by simple stirring, were stable for at least one month at room temperature, and could be sterilized. The size of the dispersed fat particles was 20–40 μ. Apparent viscosities of cottonseed stearine suspensions at 2, 5, and 10% concentrations were 3.59, 5.95, and 6.62 poises at 25C, respectively. Suspensions as described should have utility in those areas of investigation in which solid fatty materials in the form of stable dispersions are desirable. Presented at the AOCS meeting in New Orleans, La., 1962. This work was supported by funds of the Office of the Surgeon General, U. S. Army, Washington, D. C. A laboratory of the So. Utiliz. Res. & Dev. Div., ARS, U.S.D.A.     

Mixing of Flocced Suspensions

Many ceramics are polyphase, requiring the mixing of two or more powders. Recent work suggests that colloidal processing methods are desirable, i.e. the handling of powders, in either dispersed or flocced states. We have demonstrated that a high-shear-rate mixer can be used to produce a homogeneous mixture of two flocced suspensions.     

Computer Simulation of Grain Growth and Ostwald Ripening in Alumina-Zirconia Two-Phase Composites

The kinetics of grain growth and Ostwald ripening in Al₂O₃–ZrO₂ two-phase composites was systematically investigated using two-dimensional (2-D) computer simulations, based on a diffuse-interface field model. Using average values for the experimentally measured ratios of the grain boundary energies to the interphase boundary energy as the input, the predicted 2-D microstructural features and their evolution are in excellent qualitative agreement with experimental observations on 2-D cross sections of 3-D Al₂O₃–ZrO₂ two-phase composite microstructures. It was found that the coupled grain growth in Al₂O₃–ZrO₂ composites is controlled by long-range diffusion and the average size ( Rt ) as a function of time ( t ) follows the power-growth law, R ^m _t − R ^m ₀= kt with m = 3, which is independent of the initial microstructures and volume fractions of the two phases. The predicted variation of the kinetic coefficient ( k ) on the volume fraction follows a trend similar to that experimentally measured through the entire range of volume fractions. The scaling of grain size distributions is observed at a given volume fraction, i.e., they are time-invariant in the steady state. However, the characteristics of size distributions vary with the initial microstructures and the volume fractions. The relationship between matrix grain size and second-phase grain size is discussed.     

Stabilization of Ethanol-Based Alumina Suspensions

Al₂O₃ powders have been successfully dispersed in ethanol by varying the suspension acidity. An operational pH (O.pH) was defined to measure the acidity of these ethanol-based suspensions. The isoelectric point of Al₂O₃ in ethanol was at an O.pH of 8. According to Derjaguin–Landau–Verwey–Overbeek (DLVO) theory, suspensions between an O.pH of 3.5–10.5 possessed only attractive inter-particle potential. Suspensions below 3.5 had high ζ potential, fine particle size, and were Newtonian. However, suspensions at high pH were shear thinning and consisted of agglomerates, despite their high ζ potential. The use of citric acid as a dispersant has also been investigated. At an O.pH of 3, optimum additions of citric acid between 0.6 and 1.0 wt% decreased the particle size, resulted in repulsive inter-particle potentials and increased the solid loading capacity to 15 vol% from 2 vol% while maintaining Newtonian behavior and similar viscosity to suspensions at O.pH 2. Addition of citric acid created agglomerated suspensions that were negatively charged at O.pH 10.5 (obtained by adding NH₄OH), but positively charged suspensions at O.pH 13.6 (obtained by adding tetramethylammonium hydroxide).     

Temperature Dependence of Plastic Yield Stress of Single Crystals of Magnesium Oxide

The temperature dependence of the plastic yield stress of cleavage slabs of Norton Company magnesium oxide, containing approximately 0.2%, impurity, has been investigated up to 1000° C. for bending under three-point loading. Previous thermal history has been found to be an important variable. In particular, annealing followed by a rapid quenching produces a marked softening, and at the same time causes a homogenization of the starting material. Such samples have been found to display inflections in strength versus temperature, corresponding to a minimum near 500°C. followed by a maximum near 700°C. At temperatures above those associated with the inflections the samples show a pronounced drop in load after yielding, and subsequent deformation occurs by jerky flow. The various observations have been discussed in terms of the interactions of dislocations with impurities that may be in precipitate or solution form, depending on past history and conditions at the time of testing. Some experimental information has also been obtained on the effect of strain rate on the plastic yield strength.     

Viscosity and Yield Stress of Alumina Slurries Containing Large Concentrations of Electrolyte

Viscosity and yield stress measurements of A1₂O₃ slurries containing high concentrations of electrolyte are reported. Contrary to what is expected from DLVO theory, the particles in coagulated slurries produced in this way are held together by weaker forces than particles in slurries brought to the isoelectric point by changing the pH. In both cases an attractive, connective particle network is present. However, the network at the isoelectric point is stronger, as indicated by its much higher yield stress and by its higher viscosity at stresses above the yield point. An additional short-range repulsive force that appears at low pH and high electrolyte concentrations is believed to be responsible. This force prevents the particles from reaching the primary minimum associated with particle contact. The effects of solids loading, electrolyte concentration and type, and particle size have been investigated.     

Effective Viscosity of Suspensions of Spheres

Modeling the effective viscosity of suspensions of spheres beyond the dilute limit is a difficult problem that has challenged researchers for nearly a century since Einstein derived an equation for dilute suspensions. Hydrodynamics modeling requires complex mathematical treatments of integral equations describing interactions between spheres, and its solutions have been limited to semidilute dispersion of monosized hard spheres. Mechanics modeling treats suspensions in a statistical sense and generally provides upper and lower bounds solutions for polydispersed suspensions. A closed-form solution for the effective viscosity of concentrated suspensions of monosized spheres using both the elastic-viscous analogy and the analogy between the effective dielectric constant of a polarizable medium and the effective viscosity of two-phase flow is derived in the present study. Existing measurements and numerical simulations support present analytical results. A closed-form solution for polydispersed suspensions using a differential model is also derived, and the results are within existing bounds solutions.