Blending of irregularly shaped particles

Existing blending theories have mostly been verified in the past by mixing of monosized, smooth, spherical particles. In this study, binary mixing of non-spherical particles with rough surfaces is shown to adhere to diffusional mixing equations as long as the mean diameters of the two fractions (A and B) are identical, i.e.d_A = d_B. When this is not the case, blending rates (diffusional coefficients of blending, D) reduce drastically when the small particles are not of such a size that they will fit into the interstices between the larger particles. It is shown also that the final standard deviation in these cases is many orders of magnitude higher than the predicted random standard deviation. When d_A = d_B, the diffusion coefficient will depend on the magnitude of d_A. The diffusion coefficient is not a function of the ratio of A to B. In blending in a horizontal mixer, D decreases with addition of lubricant. This is not the case in a V-blender, where bulk mass transfer appears to be the controlling step. In all other respects, V-blending is identical, functionally, to the profiles obtained in cylindrical blending.     

Drag coefficients of irregularly shaped particles

The steady-state free-fall conditions of isolated groups of ordered packed spheres moving through Newtonian fluids have been studied experimentally. Measurements of the drag coefficients are reported in this paper for six different geometrical shapes, including isometric, axisymmetric, orthotropic, plane and elongated conglomerates of spheres. From these measurements, a new and accurate empirical correlation for the drag coefficient, C_D, of variously shaped particles has been developed. This correlation has been formulated in terms of the Reynolds number based on the particle nominal diameter, Re, the ratio of the surface-equivalent-sphere to the nominal diameters, d_A/d_n, and the particle circularity, c. The predictions have been tested against both the experimental data for C_D collected in this study and the ones reported in previous works for cubes, rectangular parallelepipeds, tetrahedrons, cylinders and other shapes. A good agreement has been observed for the variously shaped agglomerates of spheres as well as for the regularly shape particles, over the ranges 0.15<Re<1500, 0.80<d_A/d_n<1.50 and 0.4<c<1.0.     

Encapsulation of irregularly shaped solid forms of proteins in a high-pressure fluidized bed

By combining the advantages of a high-pressure fluidized bed with the adjuvant properties of a supercritical fluid, namely RESS-process, solid proteins could be encapsulated by paraffin. Two different irregular shaped proteins, a model protein (bovine serum albumin, BSA) and a pharmaceutical protein (insulin) were investigated. Mixing the highly non-spherical protein particles with lactose allows its usage as bed material despite the unfavourable shape properties. The paraffin encapsulation of respective bed mixtures with BSA was successful with paraffin loadings up to 9.1 g/100 g_bed and yields up to nearly 100%, depending on process parameters. During the encapsulation process, breakage of the bed material occurred, resulting in mean sauter diameters of even less than 35 μm. Dissolution tests pointed out, that 100% dissolution after more than 180 min could be achieved. Thus, the particle breakage induced by the nozzle jet during the coating process seems to support the encapsulation of fines. A principle application of the process for insulin encapsulation for a selected set of process parameters has been demonstrated.     

Breakage rates of lignite particles during hydraulic transport

Experiments conducted with recirculating test loops show that the rate equations for rod and ball mill grinding can be applied to the changes induced by pumping. Selection rate constants in the range considered were found to be rather insensitive to particle size but strongly time dependent. This time dependence can be attributed to changes in particle shape dominating over fracture as a degradation mechanism. Pump construction and speed appeared to be of considerable importance in determining breakage rates.     

Effective packing of 3-dimensional voxel-based arbitrarily shaped particles

In many research areas including medicine and paper coating, packing of particles together with numerical simulation is used for understanding important material functionalities such as optical and mass transfer properties. Computational packing of particles allows for analysing those problems not possible or difficult to approach experimentally, e.g., the influence of various shapes and size distributions of particles. In this paper a voxel-based algorithm by Jia et al. [X. Jia, R.A. Williams, A packing algorithm for particles of arbitrary shapes, Powder Technology 2001, vol. 120, pp. 175-186.] enabling the packing of arbitrarily shaped particles, is memory- and speed-optimised to allow for simulating significantly larger problems than before. Algorithmic optimisation is carried out using particle shell area reduction decreasing the amount of time spent on collision detection, fast rotation routines including lookup tables, and a bit packing algorithm to utilise memory effectively. Presently several hundreds of thousands of complex arbitrarily shaped particles can be simulated on a desktop machine in a simulation box consisting of more than 10⁹ voxels.     

Drag coefficients of variously shaped solid particles,drops, and bubbles

This article, which is largely a review, deals with the drag force and drag coefficient for rigid spherical and deformable particles in ordinary and non-Newtonian fluids. The most important theoretical formulas for small Reynolds numbers of Re ≪ 1 and semiempirical formulas for the drag coefficient in a wide Re range up to 10⁶ are presented. The deformation of drops and bubbles and its effect on the drag coefficient are considered.     

Experimental investigation of pressure drop in packed beds of irregular shaped wood particles

The knowledge of the pressure drop across a packed bed of irregular shaped wood particles is of great importance for achieving optimal control and maximum efficiency in many applications, such as wood drying, pyrolysis, gasification and combustion. In this work the effect of porosity, average particle size and main particle orientation on the pressure drop in a packed bed is investigated. To this end, particle size distributions and porosities are determined experimentally.Based on the experimental results obtained in this study, the form coefficient C and the permeability K of the Forcheimer equation are calculated for different packed beds. The Ergun equation requires an average equivalent particle diameter that is derived from the measured particle size distribution. This equivalent diameter and the corresponding bed porosity are used in the well known Ergun equation in order to derive adapted shape factors A and B.Since a change in bed porosity and particle size, caused by the degradation of the wood particles and gravity, can be expected in a reacting packed bed, a set of shape factors for use with the Ergun equation is determined that are independent of porosity and particle diameter and fit the experimental data very well.     

Breakage model development and application with CFD for predicting breakage of whey protein precipitate particles

Particle breakage due to fluid flow through various geometries can have a major influence on the performance of particle/fluid processes and on the product quality characteristics of particle/fluid products. In this study, whey protein precipitate dispersions were used as a case study to investigate the effect of flow intensity and exposure time on the breakage of these precipitate particles. Computational fluid dynamic (CFD) simulations were performed to evaluate the turbulent eddy dissipation rate (TED) and associated exposure time along various flow geometries. The focus of this work is on the predictive modelling of particle breakage in particle/fluid systems. A number of breakage models were developed to relate TED and exposure time to particle breakage. The suitability of these breakage models was evaluated for their ability to predict the experimentally determined breakage of the whey protein precipitate particles. A “power-law threshold” breakage model was found to provide a satisfactory capability for predicting the breakage of the whey protein precipitate particles. The whey protein precipitate dispersions were propelled through a number of different geometries such as bends, tees and elbows, and the model accurately predicted the mean particle size attained after flow through these geometries.     

Determination of Breakage Parameters in Turbulent Fluid‐Fluid Breakage

Numerous sets of single‐particle breakage experiments are required in order to provide a sufficient database for improving the modeling of fluid particle breakage mechanisms. This work focuses on the interpretation of the physical breakage events captured on video. In order to extract the necessary information required for modeling the mechanisms of the fluid particle breakage events in turbulent flows, a well‐defined image analysis procedure is necessary. Two breakage event definitions are considered, namely, initial breakup and cascade breakup. The reported breakage time, the number of daughter particles created, and the daughter size distribution are significantly affected by the definition used. For each breakage event definition, an image analysis procedure is presented.     

Calculation of the settling velocity of particles for the hindered sedimentation of polydisperse mixtures of arbitrarily shaped solid particles in a Newtonian liquid

The method developed earlier for calculating the hindered settling velocity of arbitrarily shaped particles is generalized for polydisperse particle-size distributions. The calculated results are in satisfactory agreement with the experimental data on the sedimentation of bi-and trimodal mixtures of spherical glass particles.     

Breakage patterns of agglomerates

The experimental information available in the literature regarding the patterns of breakage of agglomerate materials is scarce, particularly in dynamic loading. The primary objective of this paper is to present our findings on the breakage patterns of the agglomerates and the interparticle bond. A high-speed digital video imaging technique is used here to gain an insight into the impact behaviour of individual agglomerates against a target plate. Several breakage patterns are observed. Agglomerates may suffer localised damage only, with the disintegration of the damaged zone into very fine debris, or localised damage combined with fracture. The frequency of occurrence of these patterns depends on the impact velocity and agglomerate structure. The pattern of breakage affects significantly the size distribution of the impact product. An investigation of the breakage of individual interparticle bonds is also presented. Two forms of failure are observed, internal (cohesive) and interfacial (adhesive) failure. The morphology of the fractured surface depends greatly on the type of breakage. Internal breakage shows irregular surfaces due to crack jumping, whereas interfacial failure produces clean, smooth fracture surfaces. These observations should provide the necessary foundation for the development of a fundamental model of agglomerate breakage.     

液-液水力旋流器中的液滴破碎

在总结前人研究成果的基础上,分析了液-液水力旋流嚣中液滴破碎产生的原因,指出流场的湍流特性是产生液滴破碎的主要原因。对水力旋流器中的湍流度、雷诺切应力及颗粒的湍动能进行了分析,给出了水力旋流器中液滴破碎可能性较大的几个部位,并对旋流器边壁液滴破碎的可能性进行了讨论。分析了水力旋流器中液滴破碎的机理,阐明了液滴破碎判据——临界Weber数的表达式,并对理想球形液滴的破碎进行了分析。     

Breakage behaviour of spherical granulates by compression

This paper describes the deformation and breakage behaviour of granulates in single particle compression test. Three industrial spherical granulates—γ-Al₂O₃, the synthetic zeolite Köstrolith^® and sodium benzoate (C₆H₅COONa) were used as model materials to study the mechanical behaviour from elastic to plastic range. The elastic compression behaviour of granulates is described by means of force-displacement curves, by application of Hertz-Huber contact theory and continuum mechanics. An elastic-plastic contact model was proposed to describe the deformation behaviour of elastic-plastic granules. The effects of granulate size and stressing velocity on the breakage force and contact stiffness during elastic and elastic-plastic displacement are examined. It is shown that the zeolite granulates with elastic-plastic behaviour have viscous properties as well. Breakage mechanisms of granulates during elastic, elastic-plastic and plastic deformation are also explained. The breakage probability is approximated by Weibull distribution function. The behaviour of the granulate during compression under the repeated loading-unloading conditions was investigated.     

Breakage of waste concrete by free fall

For producing high-quality recycled aggregates from waste concrete, the characteristics of waste concrete when subjected to breakage by impact were investigated under free-fall conditions at various heights. In general, a lump of waste concrete did not disintegrate by a single impact, but underwent abrasion and occasional chipping before eventually breaking into several pieces. Further, when the sample was pretreated by heat, the number of free falls required for disintegrative fracture reduced markedly. Moreover, the resulting recycled aggregates had less adherent cement mortar due to weakening of the bonding strength between the aggregates and the cement mortar. Therefore, the energy penalty resulting from preheating the sample could be partially compensated for by the production of high-quality recycled aggregates. These results suggest that preheating followed by gentle breakage through free fall is an efficient technique to produce high-quality recycled aggregates from waste concrete.     

Rheological behaviour of suspensions prepared from plate‐shaped titanium dioxide particles in (hydroxypropyl) methylcellulose aqueous solution

Suspensions were prepared by homogeneously mixing titanium dioxide particles in (hydroxypropyl) methylcellulose (HPMC) aqueous solutions. Thin plate‐shaped particles were made from balloon materials crushed to pieces. The other three types of particles used as references were plate‐shaped samples surface‐modified with alumina, and two types of spherical particles of anatase and rutile forms. Plateau adsorption amounts of HPMC onto particles depended on their surface properties. Comparisons of rheological behaviour were carried out among the residual three samples except for the sample having the rutile form. Within the concentration range used, the viscosity values of suspensions were rather lower than that of HPMC aqueous solutions. The reason for such low values was attributed to the decrease of entanglements in the semi‐dilute regime and also to steric stabilization resulting from the formation of the HPMC adsorbed layer. The change of structural viscosity and its recovery were evaluated by observation of the decrease of viscosity and its recovery as an indicator. It was confirmed that suspensions of thin plate‐shaped particles had superior structural recovery performance. © 2002 Society of Chemical Industry     

Breakage in granulation: A review

The study of breakage in granulation is important from a process and from a product quality perspective. Breakage is considered an important rate process in granulation, and plays roles in granule homogeneity and strength. Understanding this rate process has important implications in the design and control of the granulation process. From a product perspective, the study of breakage has important implications for the subsequent processing, transport, handling and final use of granular products. Breakage behaviour of granules can be a strong signature of the consistency of properties between nominally identical granular products. This paper reviews the study of breakage from the process scale down to the single granule and sub-granule scale, discussing largely experimental results complemented with some modelling results.     

Breakage Probability of Granules by Repeated Stressing

The breakage behavior of γ‐Al₂O₃ granules was investigated by repeated stressing with double impact and compression test. Regarding to the stressing point of particle surface, the experiment was established in two treatment conditions – fixed and rotated treatment. In the case of double impact test a hardening factor was introduced into the breakage probability model. The result described the breakage probability for both fixed and rotated granules during repeated stressing.