Abstract: The amount of particle breakage of Tacheng rockfill material (TRM) in the process of shearing was quantitatively measured by a relative breakage index. The fractal dimension of TRM at the final state of the tests was found to be linearly related to the void ratio and logarithm of the confining pressure. The influences of the relative breakage index on the friction angle, modulus, and deformation were investigated based on a series of large-scale triaxial compression tests on TRM. An increase in the relative breakage index leads to an increase in the volumetric strain and to decreases in the peak state friction angle, critical state friction angle, deviatoric strain, and critical state void ratio. The test results were used to propose simple formulations pertaining to the relative breakage index for the strength and deformation indexes (e.g., peak state friction angle, critical state friction angle, initial elastic modulus, secant modulus at 50% of the peak strength, volumetric strain, deviatoric s...

Abstract: To ensure high quality of granular products post-industrial operations, it is necessary to precisely define their micro–macro mechanical properties. However, such an endeavor is arduous, owing to their highly inhomogeneous, anisotropic and history-dependent nature. In this article, we present the distributed granular micromechanical and macromechanical, energetic and breakage characteristics using statistical distributions. We describe the material behavior of elastoplastic zeolite 4AK granules under uniaxial compressive loading until primary breakage, and localized cyclic loading up to different maximum force levels, at different displacement-controlled loading rates. The observed force-displacement behavior had been approximated and further evaluated using well-known contact models. The results provide the basis for a detailed analysis of the viscous behavior of zeolite 4AK granules in the moist and wet states, indicating that higher compressive loads are required at higher displacement-controlled loading rates to realize equivalent deformation and breakage probability achieved by loads at lower displacement-controlled loading rates. © 2014 American Institute of Chemical Engineers AIChE J 60: 4037–4050, 2014

Abstract: Aggregates prepared under fully destabilized conditions by the action of Brownian motion were exposed to an extensional flow generated at the entrance of a sudden contraction. Two noninvasive techniques were used to monitor their breakup process [i.e. light scattering and three-dimensional (3D) particle tracking velocimetry (3D-PTV)]. While the first one can be used to measure the size and the morphology of formed fragments after the breakage event, the latter is capable of resolving trajectories of individual aggregates up to the breakage point as well as the trajectories of formed fragments. Furthermore, measured velocity gradients were used to determine the local hydrodynamic conditions at the breakage point. All this information was combined to experimentally determine for the first time the breakage rate of individual aggregates, given in the form of a size reduction rate KR, as a function of the applied strain rate, as well as the properties of the formed fragments (i.e., the number of formed fragme...

Abstract: The particle breakage during specimen compaction had more significant influence on the position of the breakage critical-state line (BCSL) of Tacheng rockfill material (TRM) in the e-lnp′ plane than the particle breakage during shearing, based on the large-scale triaxial compression tests on TRM in a wide range of densities and pressures. The state-dependent dilatancy and the plastic modulus were correlated to the breakage index, based on the formulations of the BCSL of TRM in the e-lnp′ plane. The state-dependent model considering particle breakage was proposed for TRM within the framework of the generalized plasticity theory. The proposed model contained fourteen material constants. The test data of TRM from Group A were adopted to determine these material constants, while the test data from Group B were used independently to validate the model predictive capacity. The comparisons between model simulations and test data illustrated that the model with consideration of particle breakage could well represent the stress-strain behaviors of TRM, e.g., the strain hardening and volumetric contraction behaviors at a loose state and the strain softening and volumetric expansion behaviors at a dense state, and also the particle breakage behaviors of TRM.

Abstract: An experimental and theoretical study was carried out regarding the evolution of droplet size distributions for the flow of water in oil emulsions through a valve-like element that simulates a mixing valve. The water droplets had diameters in the 0.1–100 μm range, which includes droplets that are either smaller or larger than the Kolmogorov length scale for the experimental conditions. Droplet breakage and coalescence models that can be used for this size range were proposed. A simplified population balance model was developed to interpret the experimental data and solved by the method of classes. The model parameters were estimated by the orthogonal distance regression method. The simplifying assumption of the model was verified by global optimization using a parallel implementation of the particle swarm optimization method. The agreement between simulated and experimental droplet volume size distributions was good. The predictions of the DeBroukere mean diameter, d 43 , were unbiased with mean errors of 8%.

Abstract: Ultrasound-facilitated particle breakage has been proven to be a good technique for size reduction. However, because of the difficulties associated with the solution of population balance equation (PBE), there has been little attention on the estimation of kinetics of this process. In this paper an attempt has been made to develop a generic approach for solving PBE with a given particle size distribution (PSD) data to estimate the breakage kinetics. For this purpose, discretization technique along with gPROMS parameter estimation tool was used. This method was found to be a comprehensive method for the estimation of breakage kinetics in general and was subsequently used for the estimation of ultrasound-facilitated breakage kinetics, using a simple model system. Potassium nitrate (KNO3) particles suspended in toluene was used as model system, and the effect of induced power on breakage strength was studied. The data obtained were used for the estimation of specific breakage rate with different particle size distribution function. The distribution function, for which simulated PSD was found to match with the experimental PSD, was considered for deriving energy-size reduction law.

Abstract: Background Crystallization is a widely used unit operation in the pharmaceutical industry where high aspect ratio crystals are often produced. To avoid undesired shape i.e. high aspect ratio crystals according to downstream operations, appropriate level of understanding process is necessary. Breakage often occurs during the process and gives rise to change the Crystal shape. A well-adjusted, detailed model can be usable tool for investigation and optimization of control. Method A two-dimensional population balance model of continuous cooling crystallization, involving nucleation, growth of two characteristic crystal facets and random binary breakage of high aspect ratio crystals is developed. The randomness of breakage is described by beta distribution of broken fractions. The population balance model is reduced into a closed moment equation model for the joint moments of the two size variables of crystals by means of which the influence of parameters of breakage on the dynamic and steady state behavior of crystallizer is analyzed according to understand the impact of complex kinetic on crystal shape. Results Analysis of the process provides information of breakage influence on aspect ratio of crystal. It is shown that the mean value of crystal width increases as the intensity of breakage along the crystal length resulted in increasing number of crystals.

Abstract: In this paper, the drained triaxial shear strength of four carbonate sands having different physical properties is investigated based on energy approach. Three sands were obtained from north shores of the Persian Gulf, Iran, and one from the south of England. The studied sands showed different shear strength in relation to different particle size distribution, grains shapes, and fabric. Analyses based on the energy approach in these soils with crushable grains demonstrated that the total internal friction angle consists of three components: friction angle between soil particles, dilation angle, and particle breakage angle. It was considered that inter-particle friction, dilation, and particle breakage cause different shear strength and volumetric strains for each sand. The consumed energy for particle breakage and particle breakage angle is added with increasing confining pressure and total consumed energy. However, regardless of soil type, the particle breakage angle to total internal friction angle rati...

Abstract: Bubble splitting in 2D gas-solid freely bubbling fluidized beds is experimentally investigated using digital image analysis. The quantitative results can be applied for the development of a new breakage model for bubbly fluidized beds, especially discrete bubble models. The variation of splitting frequency with bubble diameter, new resulting bubble volumes, positions, and also the assumptions of mass and momentum conservation for bubbles after breakage are studied in detail. Small bubbles are found to be more stable than large ones and nearly all mother bubbles split into two almost equally sized daughter bubbles. The momentum of gas bubbles in the vertical direction remains approximately constant after breakage, whereas that of bubbles in the horizontal direction changes with no clear trend. The effect of fluidizing gas velocity in breakage frequency is also examined.

Abstract: Aiming to study the mechanical enhancement by the filler network in a rubber composite, three-dimensional images are acquired with in situ full field transmission X-ray microscopy (TXM), and the network structure of carbon black (CB) aggregates in a rubber matrix are studied with and without strain. Statistical analysis shows that the frequency of similar-sized aggregates decreases with the increase of aggregate size as well as the inter-aggregate distance monotonically without strain. An oscillation of the frequency-size plot is induced by strain on top of the damping trend, which is interpreted as stretch-induced breakage and re-aggregation of CB aggregates. Calculations adopting a soft-hard network model, predict a reduction of the contribution of the CB network to the mechanical property of the rubber composite by about 60%, caused by the breakage and re-aggregation of CB aggregates compared to those without strain. The experimental results directly prove the structural origin of the Payne effect and also show that TXM is a valuable tool to study the mechanical enhancement mechanism of filled rubber composites.