The sintering behavior of ellipsoidal particles

The sintering behavior of ellipsoidally shaped particles, particularly spheroids, was studied using a numerical kinetic Monte Carlo model for solid-state sintering. Compact packings of spheroids with five different aspect ratios from 0.5 to 2.0, thus comprising oblate, spherical, and prolate particles, were generated by simulating the pouring of such particles into a cubic container. For each spheroid particle aspect ratio, five different packings were generated to provide statistics on the sintering properties. The sintering behavior was quantified by the densification rate, relative density, anisotropic strain, grain size, and grain coordination number, as determined from the kinetic Monte Carlo model. The spherical particles were found to sinter to a relative density of 0.87 before grain growth occurs, whereas the oblate and prolate particles reach a relative density of 0.91 before grain growth sets in, with the prolate particles sintering slightly better compared to oblate particles. The more extreme the particle aspect ratio, the more anisotropic the strain is. Finally, the oblate and prolate spheroids have a slightly higher mean grain coordination number and a slightly higher initial relative density compared to the spherical particles.     

Microstructural Shape Factors: Relation of Random Planar Sections to Three-Dimensional Microstructures

The relation of random planar sections of anisometric microstructures to the actual three-dimensional anisometry is considered for oblate and prolate spheroids and cylinders. Simple formulae are obtained relating the two-dimensional (2-D) to three-dimensional (3-D) aspect ratios; for oblate systems with large aspect ratios, the area-weighted average 2-D aspect ratio varies linearly with the actual aspect ratio, whereas for prolate systems of large aspect ratio, the 2-D aspect ratio varies logarithmically with actual aspect ratio. Extension to polydisperse systems yields a shape factor, R , which gives greatest weight to grains (or particles) having the highest volume fraction. This not only preserves the linear and logarithmic functionalities found in monodisperse systems, but favorably affects the sensitivity of R to visually apparent differences among microstructures.     

Mass transfer around oblate spheroidal drops at low Reynolds numbers

Steady and unsteady mass transfer in the continuous phase around slightly deformed oblate spheroidal drops at low (but not zero) Reynolds numbers was investigated theoretically. Asymptotic analytical solutions for short and long times, at large Peclet numbers, were obtained by the useful equations derived by Lochiel and Calderbank and by Favelukis and Mudunuri for axisymmetric drops of revolution, with the only requirements being the shape of the drop and the tangential velocity at the surface of the drop. As expected, the result, although complicated, represents a small correction to the classical problem of mass transfer around a spherical drop under creeping flow conditions, since the physical problem presented here requires both the Reynolds and the Weber number to be much smaller than one.     

Conductivity of porous materials with spheroidal pores

Models predicting the conductivity of porous materials with spheroidal insulating pores are summarized and a new model, based on our exponential relation, is proposed. Using the well-known single-inclusion solution for spheroids, Maxwell coefficients (“intrinsic conductivities”) are calculated in dependence of the pore aspect ratio for isotropic microstructures with randomly oriented spheroidal pores, and implemented into the three traditional effective medium approximations (Maxwell-type, self-consistent, differential) and our exponential relation. As expected, all models predict that prolate pore shape has a very small influence on the porosity dependence, while oblate pores affect the porosity dependence of conductivity significantly. However, the self-consistent predictions are linear and imply spurious percolation thresholds, whereas Maxwell-type and differential models (power-law relations) are known to provide predictions that are unrealistically high for the special case of spherical pore shape. Thus, our exponential relation seems to be currently the most suitable relation for implementing the single-inclusion solution for spheroids.     

The relation between rheological and mechanical properties of PA6 nano- and micro-composites

A series of nanocomposites was prepared with two different methods leading to different levels of exfoliation, and the dynamic properties were measured in the solid state and the melt. The results were compared with micro-composites containing various shapes of glass filler. The higher modulus of nanocomposites at higher concentrations is accompanied by an increase in melt viscosity and the occurrence of a yield stress in the melt. The modulus at room temperature and the melt viscosity are influenced by the aspect ratio and the concentration of the filler particles. These results were used to calculate the aspect ratios of the reinforcement using the Halpin-Tsai composite model and several modified Einstein viscosity models. The experiments showed that the Simha theory for oblate and prolate spheroids predicts platelet aspect ratios from melt viscosity data that are close to the results from the Halpin-Tsai composite model and from TEM observations. The results of the analysis show the advantages and disadvantages of the various shapes and sizes of fillers and the level of exfoliation, both from a processing and a mechanical properties point of view.     

Cross-Flow Microfiltration of Industrial Oily Wastewater: Experimental and Theoretical Consideration

Microfiltration of industrial oily wastewater was performed using polyamide membrane. A rectangular cross flow membrane cell was used for the experiments. Effects of different operating parameters such as transmembrane pressure drop and Reynolds numbers on the steady state permeate flux and oil rejection was investigated in detail. Initial oil concentration in the industrial oil-water emulsion was found to be 192 mg/L with average oil droplet range size 0.01 to 47 µm. The treated industrial oily water was characterized in terms of electrical conductivity, total dissolved solids (TDS), and chemical oxygen demand (COD). It was observed that the steady state permeate flux increased with transmembrane pressure drop and Reynolds numbers. The oil concentration in permeate was found to be around 4.5 mg/L, after treatment, which was lower than the permissible discharge limit. The results showed that microfiltration was an efficient and ecologically suited technology for the treatment of industrial oily wastewater. The cross flow velocity was considered in both laminar and turbulent regimes. A model was proposed by combining of Brownian diffusion and shear-induced diffusion to predict the steady state permeate flux data at different Reynolds numbers and different transmembrane pressure drops.     

Particle Shape and Aspect Ratio Effect of Al2O3–Water Nanofluid on Natural Convective Heat Transfer Enhancement in Differentially Heated Square Enclosures

The present numerical investigation, based on the finite volume method, deals with the characterization of flow and thermal fields inside differentially heated square enclosures filled with Al₂O₃–water nanofluid. The study focuses on the effect of shapes and aspect ratios of nanoparticles (NPs), depicted by Rayleigh number (Ra), solid volume fraction (?), and enclosure on both flow and heat transfer enhancement. Streamlines, isotherms contours, and velocity profiles as well as the average Nusselt number are considered. Results found show that the heat transfer rate increases with Rayleigh number as well as with nanofluid volume fraction. For the six different examined cases of NPs’ aspect ratios, nanofluid with oblate spheroids NPs (d_p = 0.13) was found to engender a significant enhancement in the overall heat transfer. In addition, heat transfer rate was more pronounced at great values of aspect ratios of NPs for prolate spheroids. Results also showed that heat transfer enhancement decreases as the Rayleigh number increases independently of the considered enclosure, shapes, and aspect ratios of NPs.     

In situ visualization of drop deformation,erosion, and breakup in high viscosity ratio polymeric systems under high shearing stress conditions

In this paper, deformation and breakup under simple shear of single molten polymer drops in a polymer matrix were investigated. Flow visualization was carried out in a Couette‐Flow apparatus under relatively high shear rates and temperatures up to 230°C. Drop/Matrix combinations were composed of polystyrene drops of 0.5–0.6 mm in diameter in polyethylene matrix, and ethylene–propylene copolymer drops of approximately the same size in polypropylene matrix. The deformation and breakup processes were studied under steady state and time‐dependent shearing conditions. Either for steady state or time‐dependant shearing conditions, drop elasticity generated at relatively high shear rates helped the drops to align perpendicular to the flow direction, i.e., parallel to vorticity axis. Also, the most striking non‐Newtonian effects for the high viscosity ratio systems were the surface erosion and the drop splitting mechanisms. The particles eroded off the main droplet surface were very fine, in the range of 10–50 μm, and led to a significant reduction in main drop size before its final breakup. © 2006 Wiley Periodicals, Inc. J Appl Polym Sci 100: 2582–2591, 2006     

Unsteady mass transfer in the continuous phase around axisymmetric drops of revolution

Unsteady mass transfer in the continuous phase around any axisymmetric drop of revolution at high Peclet numbers has been theoretically studied. General equations for the concentration profile, the molar flux, the concentration boundary layer thickness, and the time to reach steady state have been obtained using a similarity transformation and by the method of characteristics. Solutions for large number of problems can be immediately obtained, with the only requirements being the shape of the drop and the tangential velocity at the surface of the drop.     

Thermophoretic motion of slightly deformed aerosol spheres

The thermophoretic motion of a slightly deformed aerosol sphere in a uniformly prescribed but arbitrarily oriented temperature gradient is analyzed in the steady limit of negligible Peclet and Reynolds numbers. The Knudsen number is assumed to be small so that the fluid flow is described by a continuum model with a temperature jump, a thermal slip, and a frictional slip at the surface of the particle. The energy and momentum equations governing the system are solved asymptotically using a method of perturbed expansions. To the second order in the small parameter characterizing the deformation of the aerosol particle from the spherical shape, the thermal and hydrodynamic problems are formulated for the general case, and explicit expressions for the thermophoretic velocity of the particle are obtained for the special cases of prolate and oblate spheroids. The agreement between our asymptotic results for a thermophoretic spheroid and the relevant exact or numerical solutions in the literature is quite good, even if the particle deformation from the spherical shape is not very small. Depending on the values of the relative thermal and surface properties of the aerosol spheroid, its thermophoretic mobility normalized by the corresponding value for a spherical particle with equal equatorial radius is not necessarily a monotonic function of the aspect ratio of the spheroid.     

溶液初始pH值对2,4-D臭氧直接反应动力学的影响

引言 目前,农药被大量研制及施用,由此带来的农药污染越来越受到人们的重视.含氯苯氧梭酸类除草剂2,4-D(2,4-二氯苯氧乙酸)是一种使用较广、应用较早的除草剂.2,4-D自然降解较慢,由于具有非挥发性和可溶性,易导致地下水或地表水污染,水体中已经可以检测到2,4-D的存在.     

Thermophoresis of Aerosol Spheroids

An analytical study is presented for the thermophoretic motion of a freely suspended aerosol spheroid in a uniform prescribed temperature gradient that is oriented arbitrarily with respect to its axis of revolution. The Knudsen number is assumed to be small so that the fluid flow is described by a continuum model with a thermal slip at the particle surface. In the limit of small Peclet and Reynolds numbers, the appropriate energy and momentum equations are solved in the quasisteady situation using the bifocal-coordinate transformations. Explicit expressions for the thermophoretic velocity and force are obtained for various cases of prolate and oblate spheroidal particles. The average thermophoretic velocity and force for an ensemble of identical, noninteracting spheroids with random orientation distribution are also determined. The results indicate that the shape and relative thermal conductivity of a spheroidal particle and its orientation with the thermal gradient can have significant effects on its thermophoretic behavior.     

Direct numerical simulation of moderate-Reynolds-number flow past arrays of ellipsoids

Through particle-resolved direct numerical simulations of flow past arrays of ellipsoids, the hydrodynamic force on ellipsoids depends on the particle orientation, aspect ratio, particle Reynolds number, and solid volume fraction is revealed at moderate Reynolds numbers. The results show that the mean drag force on arrays of prolate/oblate ellipsoids decreases/increases as the Hermans orientation factor increases when flows are in the reference direction defined by the average symmetric axis of particles. The individual drag force on a prolate/oblate ellipsoid increases/decreases with the increase of incidence angle, and it is also affected by the orientation of surrounding particles. The individual lift force is also significant when the aspect ratio is away from unity at large particle Reynolds numbers. Based on simulation results, correlations for the hydrodynamic force on ellipsoids at arbitrary particle Reynolds numbers, solid volume fractions, Hermans orientation factors, incidence angles, and aspect ratios are formulated.     

Identical Feed Drops in a Flow Vessel May not Always Be Desirable

In this paper, the effect of feed size and daughter drop size distributions on the steady‐state drop size distribution in a continuous flow vessel is discussed. For identical sizes of feed drops, a new criterion has been proposed to ensure the complete breakage of the feed drops giving rise to smooth continuous drop size distributions. This has been predicted on the basis of two competing time scales, namely, breakage and residence times.     

Numerical simulation of a falling droplet surrounding by air under electric field using VOF method: A CFD study

This is a numerical study of a falling droplet surrounding by air under the electric field modeled with finite volume method by means of CFD. The VOF method has been employed to model the two-phase flow of the present study. Various capillary numbers are investigated to analyze the effects of electric field intensity on the falling droplet deformation. Also, the effects of electric potential on the heat transfer coefficient have been examined. The obtained results showed that by applying the electric field at a capillary number of 0.2 the droplet tends to retain its primitive shape as time goes by, with a subtle deformation to an oblate form. Intensifying the electric field to a capillary number of 0.8 droplet deformation is almost insignificant with time progressing; however, further enhancement in capillary number to 2 causes the droplet to deform as a prolate shape and higher values of this number intensify the prolate form deformation of the droplet and result in pinch-off phenomenon. Ultimately, it is showed that as the electric potential augments the heat transfer coefficient increases in which for electric potential values higher than 2400 V the heat transfer coefficient enhances significantly.     

Numerical simulation of a falling droplet surrounding by air under electric field using VOF method: A CFD study

This is a numerical study of a falling droplet surrounding by air under the electric field modeled with finite volume method by means of CFD. The VOF method has been employed to model the two-phase flow of the present study. Various capillary numbers are investigated to analyze the effects of electric field intensity on the falling droplet deformation. Also, the effects of electric potential on the heat transfer coefficient have been examined. The obtained results showed that by applying the electric field at a capillary number of 0.2 the droplet tends to retain its primitive shape as time goes by, with a subtle deformation to an oblate form. Intensifying the electric field to a capillary number of 0.8 droplet deformation is almost insignificant with time progressing; however, further enhancement in capillary number to 2 causes the droplet to deform as a prolate shape and higher values of this number intensify the prolate form deformation of the droplet and result in pinch-off phenomenon. Ultimately, it is showed that as the electric potential augments the heat transfer coefficient increases in which for electric potential values higher than 2400 V the heat transfer coefficient enhances significantly.     

Sedimentation of two prolate spheroids in close proximity

Experiments concerned with the rate of fall of two prolate spheroids (needle-like objects) in close proximity to each other are described in this paper. Quantitative agreement with S. Wakiya's theoretical predictions is obtained for the case in which two prolate spheroids are settling, one above the other, in the direction perpendicular to their axis of symmetry and for the case in which two prolate spheroids are settling end to end in the same horizontal plane in the direction perpendicular to their axis of symmetry. These experiments and this theoretical treatment apply only in the creeping motion region. At higher velocities, inertial effects would become significant.     

Mass transfer around prolate spheroidal drops in an extensional flow

Mass transfer in the continuous phase around a small eccentricity prolate spheroidal drop in an axisymmetric extensional creeping flow and at large Peclet numbers was investigated theoretically. The results show that, at very short times, the total quantity of solute transferred to or from the drop represents, at O(Ca¹), mass transfer by diffusion only around a sphere. For long times, or at steady‐state, the total quantity of solute transferred is, at O(Ca¹), slightly smaller than that of a spherical drop, and it decreases with an increase of the capillary number or the viscosity ratio. © 2012 Canadian Society for Chemical Engineering     

Influence of elasticity on dispersed‐phase droplet size in immiscible polymer blends in simple shearing flow

The influence of elasticity of the blend constituent components on the size and size distribution of dispersed‐phase droplets is investigated for blends of polystyrene and high density polyethylene in a simple shearing flow. The elasticities of the blend components are characterized by their first normal stress differences. The role played by the ratio of drop to matrix elasticity at fixed viscosity ratio was examined by using high molecular weight polymer melts, high density polyethylene and polystyrene, at temperatures at which the viscosity ratios roughly equaled each of three different values: 0.5, 1, and 2. The experiments were conducted by using a cone‐and‐plate rheometer, and the steady‐state number and volume‐mean averages of droplet diameters were determined by optical microscopy. After steady‐state shearing, the viscoelastic drops were larger than the Newtonian drops at the same shearing stress. From the steady‐state dispersed‐phase droplet diameters, the steady‐state capillary number, Ca, defined as the ratio of the viscous shearing stress over the interfacial tension stress, was calculated as a function of the ratio of the first normal stress differences in the droplet and matrix phases. For the blend systems with viscosity ratio 0.5, 1 and 2, the values of steady‐state capillary number were found to increase with the first normal stress difference ratio and followed a power law with scaling exponents between 1.7 and 1.9.     

Characteristic intervals in suspension polymerisation reactors: An experimental and modelling study

Suspension polymerisation of methyl methacrylate was carried out as a model to elaborate on the evolution of particle size average and distribution in the course of polymerisation. Four characteristic intervals in the evolution of particle size were identified as: transition, quasi-steady-state, growth, and identification stages. The effects of stabiliser and initiator concentrations, monomer hold up, reaction temperature, and agitation speed on the characteristic intervals, as well as the kinetics of polymerisation, were examined. The transition stage, which has been totally ignored in the literature, was found to have significant effect on the evolution of particle size. The transition stage is shortened by increasing the rate of polymerisation in the drops (either by increasing initiator concentration or using a higher reaction temperature). Increasing the impeller speed and stabiliser concentration will also lead to a shorter transition period. However, the delayed adsorption of the stabiliser on the surface of drops will prolong the transition stage. It is shown that the occurrence of the quasi-steady state depends on the polymerisation conditions. The quasi-steady state occurs only if the balance between drop break up and coalescence can be maintained. This requires a high rate of drop break up within a period of time during polymerisation (i.e., a low rate of polymerisation in the drops by using a low initiator concentration and reaction temperature, a high agitation speed and a high stabiliser concentration). The mechanisms underlying the growth stage are explained in terms of the overall rates of drop break up and coalescence in the course of polymerisation reactions. It is also shown that the onset of growth stage cannot be defined in terms of a critical conversation or viscosity, and it depends on the polymerisation conditions including mixing. The growth stage occurs if drops are not sufficiently stable against both break up and coalescence. The onset of the growth stage is advanced with a decrease in the rate of drop break up (e.g., decreasing agitation speed and stabiliser concentration). The growth stage can be totally eliminated from a polymerisation process if dispersions with a static steady state can be formed. That requires a high concentration of stabiliser, or a low concentration of monomer, to be used. A population balance model, which included the transition stage and the delayed adsorption of the stabiliser, was developed that is capable of predicting the evolution of drop size in the suspension polymerisation.