Effect of particle characteristics on particle pickup velocity

Particle entrainment is investigated by measuring the velocity required to pick up particles from rest, also known as pickup velocity. Pickup velocity is a function of individual particle characteristics and interparticle forces. Although 5-200 μm particles are investigated, the work presented here focuses on the pickup of particles in a pile in the size range of 5-35 μm. These smaller particle sizes are more typical for pharmaceutical and biomedical applications, such as dry powder inhalers (DPIs). Pickup velocities varied from 3.9 to 16.9 m/s for the range of particle sizes investigated.There is a strong correlation between particle size and the dominating forces that determine the magnitude of the pickup velocity. Preliminary data investigating pickup velocity as a function of particle size indicate the existence of a minimum pickup velocity. For larger particle sizes, the mass of the particle demands a greater fluid velocity for entrainment, and for smaller particle sizes, greater fluid velocities are required to overcome particle-particle interactions. Pickup velocity remains relatively constant at very small particle diameters, specifically, less than 10 μm for glass spheres and 20 μm for nonspherical alumina powder. This can be attributed to the negligible changes in London-van der Waals forces due to a hypothesized decrease in interparticle spacing. At intermediate particle diameters, electrostatic forces are dominant.     

COMPARISON OF THE VELOCITIES AND THE WALL EFFECT BETWEEN SPHERES AND CUBES IN THE ACCELERATING REGION

The velocities and the wall effect for spheres and cubes in the accelerating region were compared experimentally for very high Reynolds number (18000 < N _Re  < 77000 for spheres and 12000 < N _Re  < 49000 for cubes). Experiments were conducted with 0.012, 0.015, 0.018, 0.021, 0.025, and 0.03175 m spheres and their respective cubes of equal volume falling in water inside cylinders of diameters equal to 0.034, 0.049, 0.07, 0.10, 0.14, and 0.19 m. The velocities of the spheres were always greater than the velocities for the respective cubes of equal volume. The wall effect increases with the particle size and fall distance. The relative wall effect between the spheres and the cubes varies with the fall distance and the ratio of the particle to tube diameter. The wall factor as a function of particle-to-tube ratio for the spheres is described well by the Munroe equation (5.7% absolute error), while for the cubes the points are more dispersed.     

Low-Reynolds-number motion of a heavy sphere between two parallel plane walls

A novel boundary-integral algorithm [Staben, M.E., Zinchenko, A.Z., Davis, R.H., 2003. Motion of a particle between two parallel plane walls in low-Reynolds-number Poiseuille flow. Physics of Fluids 15, 1711-1733; Erratum: Phys. Fluids 16, 4206] is used to obtain O(1)-nonsingular terms that are combined with two-wall lubrication asymptotic terms to give resistance coefficients for near-contact or contact motion of a heavy sphere translating and rotating between two parallel plane walls in a Poiseuille flow. These resistance coefficients are used to describe the sphere's motion for two cases: a heavy sphere driven by a Poiseuille flow in a horizontal channel and a heavy sphere settling due to gravity through a quiescent fluid in an inclined channel. When the heavy sphere contacts a wall in either system, which occurs when the gap between the sphere and the wall becomes equal to the surface roughness of the sphere (or plane), a contact-force model using the two-wall resistance coefficients is employed. For a heavy sphere in a Poiseuille flow, experiments were performed using polystyrene particles with diameters 10%-60% of the channel depth, driven through a glass microchannel using a syringe pump. The measured translational velocities for these particles show good agreement with theoretical results. The predicted translational velocity increases for increasing particle diameter, as the spheres extend further into the Poiseuille flow, except for particles that are so large (diameters of 80%-85% of the channel depth) that the upper wall has a dominant influence on the particle velocity. For a heavy sphere settling in a quiescent fluid in an inclined channel, the transition from the no-slip regime to slipping motion occurs for a larger inclination angle of the channel with respect to the horizontal for an increase in particle diameter, since the larger particles are more slowed by the second wall. Limited experiments were performed for Teflon spheres with diameters 64%-95% of the channel depth settling in a very viscous fluid along the lower wall of an inclined acrylic channel. The measured translational velocities, which are only about 15%-25% of the tangential component of the undisturbed Stokes settling velocity, are in close agreement with theory using physical parameters obtained from similar experiments with a single wall [Galvin, K.P., Zhao, Y., Davis, R.H., 2001. Time-averaged hydrodynamic roughness of a noncolloidal sphere in low Reynolds number motion down an inclined plane. Physics of Fluids 13, 3108-3119].     

Fluid velocity profiles near the wall of liquid-fluidized beds

A direct, non-disturbing flash photolysis dye technique has been used to measure liquid velocities in 2.465-in. beds of 0.1248, 0.233 and 0.368-in. diameter lucite spheres at porosities of 0.8 and 0.9. Aggregative fluidization, including layering, was observed in all beds, and increased in magnitude with the larger spheres. Distinct velocity maxima were found from 0.5 to 2 particle diameters from the wall and distinct minima at from 0.6 to 1.2 particle diameters for the more particulately fluidized beds. Variations in velocity greater than the mean were observed. Conservatively estimated wall shear stresses were 2 to 5 times times larger than in the open pipe.     

不同圆球复合无序堆积床内流动传热数值分析

圆球堆积床内孔隙分布影响其内部流场及温度场分布, 且小管径-球径比堆积床由于壁面限制, 内部孔隙率变化剧烈, 其内部流动和传热不均匀现象明显。针对D/d_p为3的圆球无序堆积床构建了3种非等直径圆球复合堆积结构:径向分层复合堆积、轴向分层复合堆积以及随机复合堆积结构, 并采用DEM-CFD方法建模计算, 从径向及整体角度分析比较不同复合堆积床内流动换热特性及其流场和温度场分布的均匀性。结果表明:孔隙率及孔隙大小分布共同影响堆积床内流场和温度场分布;相对于单一等直径圆球堆积, 采用复合堆积结构能使堆积床内部孔隙率分布更均匀, 其内部流场和温度场分布也更为均匀;对于D/d_p为3的堆积通道, 径向分层堆积结构对于提高整体流动换热性能及改善内部流动换热均匀性都有显著效果。     

Packing of multi-sized mixtures of wet coarse spheres

The effect of water addition on the packing of multi-sized coarse spheres has been experimentally investigated under standard poured packing conditions. The results indicate that porosity is strongly affected by particle characteristics such as particle sizes and their distribution, in addition to water content. The packing features in the relationship between porosity and moisture content for wet multi-sized spheres are found to be similar to those for wet mono-sized spheres, implying that the same governing mechanisms apply. The comparison between the dry and wet packing systems confirms that there is a similarity between them, suggesting that the packing of wet particles can be predicted within the framework of a packing model developed for dry coarse particles. Future work in this direction is also discussed.     

Synthesis and catalytic properties of sulfonic acid-functionalized monodispersed mesoporous silica spheres

A new type of sulfonic acid-functionalized monodispersed mesoporous silica spheres (MMSS) were synthesized directly by co-condensation and subsequent oxidation. By changing the methanol ratio, sulfonic acid-functionalized MMSS with different particle diameters (390–830 nm) and the same mesopore sizes were successfully synthesized. TEM observations revealed that the mesopores were aligned radially from the center towards the outside of the spheres, even in the sulfonic acid-functionalized MMSS. The catalytic activities of the sulfonic acid-functionalized MMSS were studied in condensation reactions between 2-methylfuran and acetone, and it was found that their catalytic activities are highly dependent on the particle diameters. In addition, the catalytic activity of MMSS was much higher than that of other forms of mesoporous silica due to its radially-aligned mesopores.     

Packed bed structure: Evaluation of radial particle distribution

A model describing the radial distribution of monosized spheres in randomly packed beds up to distances of about two particle diameters from the vessel wall is presented here. The model is based on the existence of a highly ordered layer of particles adjacent to the wall followed by a more diffuse, but still identifiable, second layer. Expressions generated from simple geometrical concepts (intersection between a cylindrical surface and a sphere) straightforwardly allow calculating the radial voidage profile given the radial distribution of particle centers and vice versa. These expressions are employed to fit the model to measures of voidage profiles within a wide range of aspect ratios, a = (R_T/R_P). The model can be used to accurately predict radial voidage profiles, but it is stressed that the identification of particle distribution constitutes more valuable information than an empirical expression for describing voidage variations.     

Periodic pressure fluctuations in fluidized beds

In shallow gas fluidized beds harmonic oscillations of the pressure around its equilibrium value can be observed. Three aspects of these vibrations have been analysed: the frequency, the critical bed height and the damping. The frequency decreases with the inverse of the square root of the bed height for values below the critical height.For bed heights larger than the critical height the fluctuations cease to be harmonic, the bed breaks up and voids are formed leading to the formation of bubbles or slugs. The critical bed height can be calculated from the frequency and the wave velocity. The maximum value of the critical bed height is a few hundred particle diameters, thus most beds will fluidize heterogeneously. Damping of the oscillations is governed by the ratio of the fluid- to solids-density; the lower this values the higher the damping. The damping is liquid fluidized beds is such that oscillations are prevented.     

Impact of Pulsed Electric Fields on the Dehydration and Physical Properties of Apple and Potato Slices

Abstract

The effect of pulsed electric fields (PEF) on drying and some physical properties of apple and potato was evaluated. Pulsed electric field intensities from 0.75 to 1.5 kV/cm with pulse duration within 100 and 300 μs were studied. The number of pulses applied was up to 120. Measurement of porosity and density were conducted using a mercury porosimeter. The drying process was carried out in a convective air oven at 70°C. The compressive strength of apples was reduced between 21 and 47% after treatment. The results show potential advantage for PEF enhanced juice extraction from the tissues even at moderate PEF treatment. PEF treatment increased porosity and particle density but decreased bulk density. Treating the apple samples with PEF resulted in generation of more pores of sizes in the order of cell wall thickness. Thus electric field application affected not only cell membranes but also cell wall integrity. PEF treatment enhanced drying rates of potato samples. Diffusion coefficients of PEF pretreated potato samples increased by up to 40%.     

Online Nanoparticle Mass Measurement by Combined Aerosol Particle Mass Analyzer and Differential Mobility Analyzer: Comparison of Theory and Measurements

A combination of a differential mobility analyzer (DMA) and aerosol particle mass analyzer (APM) is used to measure the mass of NIST Standard Reference Materials (SRM®) PSL spheres with 60 and 100 nm nominal diameter, and NIST traceable 300 nm PSL spheres. The calibration PSL spheres were previously characterized by modal diameter and spread in particle size. We used the DMA to separate the particles with modal diameter in a narrow mobility diameter range. The mass of the separated particles is measured using the APM. The measured mass is converted to diameter using a specific density of 1.05. We found that there was good agreement between our measurements and calibration modal diameter. The measured average modal diameters are 59.23 and 101.2 nm for nominal diameters of 60 and 100 nm (calibration modal diameter: 60.39 and 100.7 nm) PSL spheres, respectively. The repeatability uncertainty of these measurements is reported. For 300 nm, the measured diameter was 305.5 nm, which is an agreement with calibration diameter within 1.8%.

The effect of spread in particle size on the APM transfer function is investigated. Two sources of the spread in “mono-dispersed” particle size distributions are discussed: (a) spread due to the triangular DMA transfer function, and (b) spread in the calibration particle size. The APM response function is calculated numerically with parabolic flow through the APM and diffusion broadening. As expected from theory, the calculated APM response function and measured data followed a similar trend with respect to APM voltage. However, the theoretical APM transfer function is narrower than the measured APM response.     

Oscillatory flow and axial dispersion in packed beds of spheres

The effect of oscillations in the bulk flow on the axial dispersion coefficient in packed beds of spherical particles has been studied using the imperfect pulse tracer method with two probes located within the bed. Three bed sizes with diameters in the range 25-47.3 mm have been used with oscillation frequencies and amplitudes in the range 0-2.4 Hz and 0-3.5 mm, respectively. In the absence of oscillations, the axial dispersion coefficient increases linearly with interstitial velocity. For a given bulk velocity and oscillation frequency, the axial dispersion coefficient-amplitude relationship shows a minimum. Over the ranges of conditions studied, the best reduction (up to 50%) in the axial dispersion coefficient from the non-oscillation base case occurred at the highest frequency studied and when the wall effect was the greatest, i.e. when the column-to-particle size was the smallest. The axial dispersion coefficient was fitted to a mathematical model, which takes into account the diameters of both the column and the packing, the fluid velocity, and the oscillation intensity (frequency and amplitude). The model was adapted from those developed by Göebel et al. (1986) and Mak et al. (1991) so as to need no a priori assumptions about the relationship between oscillation parameters and the axial dispersion coefficient. The model provides near-perfect fits to the experimental data for the higher frequencies studied.     

A study of the area porosity profiles in a bed of equal-diameter spheres confined by a plane

Profiles have been measured of area porosity in random beds of equal-diameter spheres confined by a plane surface. The results have been interpreted in terms of a proposed stratified model of the random bed. The assumptions made in the formulation of the model seem to be justified in view of the generality of results obtained with spheres of different diameter and the good agreement of the experimental and predicted porosity profiles.The model has been tested also for describing porosity oscillations near the top of beds compressed by a plane surface and beds prepared by charging the spheres by portions while compressing simultaneously each portion added.     

ON THE PREDICTION OF POROSITY OF BEDS COMPOSED OF MIXTURES OF SPHERICAL PARTICLES†

A semi-theoretical study of porosity of particulate beds composed of mixtures of various size spherical particles has been performed. A model for mixtures of only two particle sizes is developed and is used to identify several dimensionless parameters which are correlated by comparing predictions with the data. The model is then extended to evaluate porosity of mixtures of a large number of particle sizes and distributions. The predictions from the model are found to compare quite well with the data taken in this work and the existing data in the literature when unavailability of a certain fraction of pores formed of largest size particles in the mixture is accounted for.     

Near-wall porosity characteristics of fixed beds packed with wood chips

Packed beds of fuel wood chips are commonly found in thermal conversion processes such as combustion or gasification. Wood chips in particular are mostly used as fuel for small-scale domestic heating boilers but also for commercial-scale combustion units. The characterization of spatial voidage distribution inside the wood chip beds is of great importance for flow and reactor modelling. This study focuses on the radial porosity variations of cylindrical beds of three different types of commercially available wood chips including chips classified as G30 size class. The conventional technique of consolidating packed beds with a resin was chosen as the experimental procedure. The radial voidage distribution in different cylindrical beds is determined by image analysis of sections of the solidified packings. Additionally, a packing of monosized spheres was investigated in order to assess the selected procedure in comparison with widely available literature data for spheres. The results are discussed and summarized in a mathematical expression correlating the radial voidage distribution depending on average wood chip size, packing core porosity and dimensionless distance from the tube wall.     

Velocity and temperature profiles in compressible turbulent wall jets

The results of an experimental study on compressible turbulent wall jets resulting from a normally impinging round jet are presented. A finite difference technique was used for the calculation of velocity and temperature profiles. The eddy transfer coefficients used were functions of the distance from the plate throughout the flow field of the wall jet. The nozzle exit Mach number ranged up to 0.85. The nozzle exit temperature to the ambient temperature ratio ranged up to 2.92. The applicability of the calculational method has been thoroughly checked for a region of flow extending up to 12 nozzle diameters from the axis of symmetry. Using the empirical eddy transfer coefficients presented in this paper only starting profiles are needed to generate the solution for any point in the wall jet flow field which is described by a system of parabolic (boundary layer) equations.     

Kinetic modeling of miniemulsion nitroxide mediated polymerization of styrene: Effect of particle diameter and nitroxide partitioning up to high conversion

The miniemulsion polymerization of styrene mediated by N-(2-methyl-2-propyl)-N-(1-diethylphosphono-2,2-dimethylpropyl)-N-oxyl (SG1) at 396 K is modeled up to high conversion as a function of the targeted chain length (TCL) and particle diameter. Thermal self-initiation and diffusional limitations are explicitly accounted for. The importance of the compartmentalization of nitroxide, initiator and macroradicals and of nitroxide partitioning is assessed using 3-dimensional Smith-Ewart equations. Diffusional limitations on termination are important for higher particle diameters only (>～70 nm). The influence of diffusional limitations on deactivation, however, can be significant even for intermediate particles diameters (～40 nm). For a TCL of 300, low particle diameters (<～20 nm) provide theoretically both a better livingness and control over chain length compared to the bulk case at the expense of a significant reduction of the polymerization rate. For a sufficiently high particle diameter (～30 nm), a rate acceleration can be obtained accompanied by an improved livingness but with a somewhat reduced control over chain length. For TCLs higher than 300, better overall average polymer properties can be achieved up to particle diameters of ～ 50 nm. Nitroxide partitioning is shown to lead on average to a limited increase of the polymerization rate without significantly affecting the average polymer properties.     

Euler/Lagrange computations of pneumatic conveying in a horizontal channel with different wall roughness

The present study is related to the particle behaviour and the pressure drop in a particle-laden six meter long horizontal channel with rectangular cross-section from both experimental and numerical perspectives. Experiments and calculations are carried out for different spherical glass beads with diameters between 60 and 625 μm and mass loadings up to 1.0 (kg particles/kg gas). Additionally, stainless steel walls with different wall roughness are considered. In all experiments the air volume flow rate is constant in order to maintain a fixed gas average velocity of 20 m/s. As a result, the pressure drop in the channel is strongly influenced by wall roughness. Higher wall roughness implies higher pressure drop because of the increase in wall collision frequency, whereby momentum is extracted from the fluid due to two-way coupling. The numerical computations were performed by the Euler/Lagrange approach accounting for two-way and four-way coupling. For the calculation of the particle motion all relevant forces (i.e. drag, transverse lift and gravity), inter-particle collisions and wall collisions with wall roughness were considered. The agreement of the computations with the experiments was found to be very good for the gas and particle velocities as well as the pressure drop.     

Simultaneous Elemental Composition and Size Distributions of Submicron Particles in Real Time Using Laser Atomization Ionization Mass Spectrometry

Composition and size of individual submicron particles have been measured using a laser atomization ionization mass spectrometry technique, the Particle Blaster. Individual particles are quantitatively converted to atomic cations, providing information on both their complete elemental composition and particle size. Measured average atomic ratios for 100 nm particles of sodium chloride is 1.12 +- 0.36 (Cl:Na), for 50 nm particles of silica is 1.93 +- 0.52 (O:Si), and for 64 nm polystyrene latex spheres (PSL) is 1.13 +- 0.19 (H:C), in excellent agreement with the empirical formulae. Calculated particle sizes agree well with electrostatic classifier or TEM measurements in the size range of 17-900 nm diameter for particles of sodium chloride, silicon, and PSL. Size distributions are also obtain able, giving narrower distributions than are measured with an electrostatic classifier, for particles of alumina, silica, sodium chloride, and PSL spheres. Comparison with TEM data shows comparable primary particle sizes, but numerous particle aggregates are detected by the Particle Blaster which are unreported by the TEM measurements.     

On the relationship between porosity and interparticle forces

This paper presents an attempt to quantify the relationship between porosity and interparticle forces for mono-sized spheres. Two systems are considered: the packing of wet coarse spheres where the dominant interparticle force is the capillary force, and the packing of dry fine spheres where the dominant force is the van der Waals force. The interrelationships between porosity, capillary force and liquid content are first discussed based on the well-established theories and experimental observations. The resultant relationship between porosity and capillary force is then applied to the packing of fine particles to quantify the van der Waals force in a packing. A generalised relationship between porosity and interparticle forces results as an extension of this analysis. The usefulness of this relationship is finally demonstrated in depicting the fundamentals governing the relationship between porosity and particle size.