Terminal Settling Velocity Research Articles

Settling properties of digested sludge particle aggregates

A multi-exposure photographic method and an image analysis system were used to measure the terminal settling velocities and some geometric characteristics of digested sludge particle aggregates larger than 35 μm (>90% of the sludge mass). It was found that the aggregates larger than 150 μm showed low settling shape factor values, indicating their irregular structure. The density of the aggregates decreased with the increase in their size and was calculated by neglecting or accepting the irregularity of their structure. The terminal settling velocities of the aggregates, in a settling medium of filtered supernatant diluted 1:2 with tap water, were proportional to their diameter rising to the power of 0.67. A correction factor, incorporating the settling shape factor, was formulated for the determination of the hydrodynamic properties of the aggregates studied. Their solid volume fraction was expressed by a three-parameter empirical model.

Particle recycling in the TAG hydrothermal plume

Analysis of Th isotope distributions in the TAG hydrothermal plume yields evidence for pronounced 234Th/ 230Th isotope fractionation. This fractionation can be attributed to a combination of four processes: (1) particle ageing; (2) differential scavenging of 234Th and 230Th; (3) differential focusing of 234Th and 230Th and (4) recycling of old particles. We present arguments for the importance of the last of these processes, particle recycling. Particles in the TAG hydrothermal plume exhibit grain sizes which fall in the range 1–10 μm. Applying the range of densities reported for amorphous iron oxyhydroxide and iron oxide mineral phases, Stokes' Law predicts that these particles should achieve terminal settling velocities ranging between 4 and 8 m d −1 for coarse-grained (5 μm radius) particles and 0.2–0.3 m d −1 for fine-grained particles (1 μm radius). These velocities have been used in a physical model of re-entrainment and recycling in neutrally buoyant plumes. Our results indicate that particle recycling and re-entrainment in hydrothermal plumes may be important over length scales of 1–10 km. The model predicts that the proportion of particles re-entrained is independent of particle size but increases with plume strength. For plumes with volumetric fluxes greater than 10 3 m 3 s −1, the proportion of particles re-entrained exceeds 50%, in agreement with previous calculations based upon 230Th distributions. Sampling strategies in the past have typically concentrated upon processes operating within ⩽ 1 km of active vent fields and will need to be revised accordingly in the future.

Translation and rotation of spheres settling in square and circular conduits: Experiments and numerical predictions

The terminal settling velocities and rotation rates of spherical particles settling in circular and square conduits were investigated experimentally and numerically with the aim to benchmark the numerical predictions using the boundary element method. Spheres were allowed to settle in viscous Newtonian fluid under conditions such that only hydrodynamic forces exerted an appreciable effect. The terminal settling velocities and the rotation rates were measured as a function of the size and density of the falling sphere, the drop position of the sphere in the conduit and the dimensions and geometry of the containing vessel or conduit. The experimental measurements were subjected to an exacting error analysis and compared with fully three-dimensional boundary element calculations. We found that the results of the experiments and numerical simulations showed remarkable agreement within the bounds of experimental error.

Fluidization and Sedimentation of Carrier Material in a Pilot-Scale Airlift Internal-Loop Reactor

Balsalt (ρ=2760 kg.m−3, d=0.245 mm) was used as the solid carrier in a pilot-scale airlift internal-loop reactor for wastewater treatment (AILRW), which was filled with tap water in this study, to investigate the regimes of fluidization and sedimentation. Solid sediment was observed even when the liquid velocity in the riser was much higher than the terminal settling velocity of the particles. Circulation cannot be maintained if the superficial liquid velocity in the downcomer ud. is below a definite value (blocking velocity ub) . In a dimensionless model, ub is related to the bulk volume of carrier solids added (Vt), the available space at the bottom (Va) and the gap size at the bottom (a0) according to ub2/(a0.g) = 0.04(Vt/Va) −0.036.

Double step compaction of multi-level parts with electric drive CNC press

Agarose–nickel nanoporous composite matrices with a series of densities, named Ag–Ni, were prepared herein for expanded bed adsorption of nanobioproduct/bioproduct by a water-in-oil emulsification method. The optical microscope (OM), scanning electronic microscope (SEM) and particle size analyzer (PSA) were utilized in order to characterize the structure and morphology of the agarose–nickel composite. The results indicated that the matrices prepared had a spherical appearance, appropriate wet density of 1.73–2.56 g/ml, water content of 32.2–58.5% and porosity of 79.4–96.37% and pore size of about 100–150 nm. All the Ag–Ni beads follow logarithmic normal size distribution with the range of 60–230 μm and average diameter of 133.68–148.4 μm. One of the useful properties of the Ag–Ni particles is the high wet density up to 2.56 g/ml, which shows a potential for the operation in an expanded bed at high flow rate. The impact of nickel powder addition on the physical and hydrodynamic properties was also investigated. In addition, the fluidization behavior of the Ag–Ni particles under various conditions was characterized by the measurement of bed expansion and axial dispersion coefficients for the liquid phase when operated in a standard fluidized bed contactor. It was observed that the expansion factors were decreased with the increasing matrix density under the same velocity. The bed expansion and fluid velocity were correlated with Richardson–Zaki equation for all particles prepared and the correlation parameters (the terminal settling velocity Ut and expansion index n) were investigated. Using measurements of residence time distributions, hydrodynamic properties in the expanded beds were investigated and were compared with reported matrices in other literatures. In addition, the impact of the flow velocity, bed expansion degree and density of adsorbent on hydrodynamic properties in the expanded beds were investigated. The results indicated that the expansion factor showed little effect on the hydrodynamic properties while the fluid velocity was the most essential factor on this regard. Furthermore, the results indicated that the heavy matrices of Ag–Ni-3, Ag–Ni-4 and Ag–Ni-5, were more suited for high operation fluid velocity. In addition, even the light matrices, i.e. Ag–Ni-1 and Ag–Ni-2, seem to be superior to other matrices in hydrodynamic properties, which made them promising adsorbents for further use in EBA processes.

Behaviour and removal of fine particles in a liquid‐solid spouted bed consisting of binary mixtures

AbstractIn a liquid‐solid spouted bed system containing coarse and fine particles, the entrainment and elutriation of the separated fines were investigated with reference to variations in the pressure drop through the bed. The effect of operating parameters on the velocity corresponding to the beginning of entrainment of fines (Ube) was examined and a dimensionless correlation was proposed.The effect of operating parameters on the elutriation rate coefficient of fines at liquid velocities larger than their terminal settling velocity (Ul) also was studied. An empirical equation was proposed for a column height above TDH, the height of freeboard at which the elutriation rate becomes constant. It was recognized that the elutriation phenomenon was closely related to the length of the stratified particle transport bed when the ascending velocity of the elutriable particles at the top of bed becomes constant.

Spherical particle terminal settling velocity and drag in Bingham liquids

Graphical relations have been developed from data on the fall of spherical particles in Bingham fluids available in literature for predicting terminal settling velocity and drag coefficient. It has been found that the relations fit the data extremely well.

Collision efficiency for fine mineral particles with single bubble in a countercurrent flow regime

The collision of fine mineral particles with a bubble in a countercurrent flow regime has been modeled to predict the collision efficiency between fine mineral particles and a single bubble in a flotation column. Surface forces (DLVO forces as well as non-DLVO forces) are ignored in the collision process. The complete Navier-Stokes equations are resolved to achieve a finer angular grid for the numerical solution of a collision angle which is a function of the density of the particles represented by the Galileo number ( Ga) and of the Reynolds number of bubbles in a countercurrent flow regime ( Re). The collision efficiency given is a function of the diameters of both the particles and the bubble, and to both Ga and Re, and to the bubble slip velocity and terminal settling velocity of the particles. The value of the collision efficiency has been determined experimentally: the agreement between the theoretical predictions and the measured values is good.

ＰＳＬ粒子への微小粒子のヘテロ凝集による湿式コーティング

A fundamental experimental study of the alternation and modification of particle characteristics has been carried out by the use of a small scale vessel with a stirrer for a suspension of polystyrene latex (PSL) particles (2μm in diameter) as the carrier and magnetite particles (0.23μm in diameter) as a coating material. The qualitative maps of the progressive coating on the carrier surface by fines have been depicted along the variation of operational conditions, such as concentrations and the concentration ratio of each component in the suspension, pH, stirring speed, and agitation period among others. The number distribution of fines coated on a carrier has been correlated through sedimentation velocity data and by the equations which give the relationship between the terminal settling velocity and the composition of the component particles in each coated particle. The results show that the number of fines coated on a carrier is about 114 and has a rather narrow distribution.

The Effect of Particle Size on the Evaluation of Aerosol-Derived Effective Airway Dimension (EAD)

Human airway dimensions of ten healthy subjects were investigated by means of monodisperse aerosols as function of the volumetric lung depth (VLD). A non-invasive single breath aerosol inhalation technique was used (Heyder, 1989) with two different particle sizes (0.8 μm and 1.5 μm). The method is based upon measurements of gravitational losses of the inhaled particles in the respiratory tract during respiratory pauses. From the loss rate of the particles at different VLDs during breath-holding and their known terminal settling velocity (vs), EADs can be calculated. EAD-values have been determined by holding the breath at a lung volume of 1000 cm3 above functional residual volume (FRC). Highly significant (p < 0.005) differences were found between the EADs obtained with the two particle sizes. These differences can be explained by a mixing mechanism during the breathholding period caused by cardiogenic flow oscillations.

Pollen Morphology and Ultrastructure of the Cabombaceae: Correlations with Pollination Biology

Of all species comprising the two genera of the Cabombaceae, only Brasenia schreberi J. F. Gmel. and Cabomba caroliniana Gray have been critically investigated with regard to their pollination biology. Brasenia schreberi has been shown to be anemophilous, while C. caroliniana has an entomophilous (myophilous) pollination syndrome. In the present paper, a number of pollen and pollen-related characters, including pollen size, shape, quantity, terminal settling velocity, pollen-ovule ratios, and overall exine architecture of B. schreberi and C. caroliniana are evaluated. Pollen from both species is elliptic, monosulcate, and has a tectate-columellate sporoderm with supratectal surface ornamentation. Grains of B. schreberi are small, produced in copious amounts, and settle relatively slowly. Flowers of this species have large pollen-ovule ratios. The exine of B. schreberi pollen is scabrate, relatively thin, has a uniformly thick sexine composed of a two-zoned (homogeneous/granular) tectum and distinct columellae, and a homogeneous nexine. Pollen of C. caroliniana is relatively large, produced in small quantities, and has a rapid terminal settling velocity. Flowers exhibit small pollen-ovule ratios. Exine organization of C. caroliniana pollen is typically two times thicker than that of B. schreberi; ornamentation is striate. Nonapertural sexine regions have a thick tectum and well-defined columellae, with both sexine components traversed by a dense system of channels. The nexine is relatively thin. All of the palynological characters examined correlate well with the anemophilous and entomophilous syndromes of B. schreberi and C. caroliniana, respectively. Moreover, several other parameters of exine ultrastructure from each species exhibit positive correlations with the respective pollination mechanisms, including: tectum thickness, columellae diameter, tectum-nexine ratios, and the consistency, distribution, and total amount of pollenkitt present. Overall exine ultrastructure is also discussed from a historical perspective as well as with respect to its phylogenetic significance.

POLLEN MORPHOLOGY AND ULTRASTRUCTURE OF THE CABOMBACEAE: CORRELATIONS WITH POLLINATION BIOLOGY

Of all species comprising the two genera of the Cabombaceae, only Brasenia schreberi J. F. Gmel. and Cabomba caroliniana Gray have been critically investigated with regard to their pollination biology. Brasenia schreberi has been shown to be anemophilous, while C. caroliniana has an entomophilous (myophilous) pollination syndrome. In the present paper, a number of pollen and pollen‐related characters, including pollen size, shape, quantity, terminal settling velocity, pollen‐ovule ratios, and overall exine architecture of B. schreberi and C. caroliniana are evaluated. Pollen from both species is elliptic, monosulcate, and has a tectate‐columellate sporoderm with supratectal surface ornamentation. Grains of B. schreberi are small, produced in copious amounts, and settle relatively slowly. Flowers of this species have large pollen‐ovule ratios. The exine of B. schreberi pollen is scabrate, relatively thin, has a uniformly thick sexine composed of a two‐zoned (homogeneous/granular) tectum and distinct columellae, and a homogeneous nexine. Pollen of C. caroliniana is relatively large, produced in small quantities, and has a rapid terminal settling velocity. Flowers exhibit small pollen‐ovule ratios. Exine organization of C. caroliniana pollen is typically two times thicker than that of B. schreberi; ornamentation is striate. Nonapertural sexine regions have a thick tectum and well‐defined columellae, with both sexine components traversed by a dense system of channels. The nexine is relatively thin. All of the palynological characters examined correlate well with the anemophilous and entomophilous syndromes of B. schreberi and C. caroliniana, respectively. Moreover, several other parameters of exine ultrastructure from each species exhibit positive correlations with the respective pollination mechanisms, including: tectum thickness, columellae diameter, tectum‐nexine ratios, and the consistency, distribution, and total amount of pollenkitt present. Overall exine ultrastructure is also discussed from a historical perspective as well as with respect to its phylogenetic significance.

A RISE IN SOLID HOLDUP IN AN ASCENDING FLOW TYPE GAS-SOLID CONTACTOR WITH THE USE OF INERTIAL GAS-SOLID SEPARATOR

A new internal-circulation gas-solid contactor has been developed to improve and simplify the operation and the structure of the existing circulating fluidized bed (CFB). The contactor consists of a column in which an ascending-flow-type inertial gas-solid separator is equipped to return the solids to the column. To keep gas-solid contact effective, the contactor is operated at a gas velocity above the terminal settling velocity of solid panicles (like the existing CFB). Characteristics of the separator and the rise in holdup in the contactor are described.

On the prediction of terminal settling velocity of solids in liquid-solid systems

The settling velocity of solids has been determined experimentally in a fluidizing column. The bed expansion characteristics of monodispersed (single component) systems have been noted using water as the fluid. The experimentally determined bed voidages have been plotted against particle Reynolds number, Re p on a log-log graph paper. The settling velocity, u t, has been obtained by extrapolating the resulting straight line to ϵ=1.0. Close-cut size fractions of coal, graphite, sand, limestone, chalcopyrite and magnetite have been used as different solids. Water has been used as the fluidizing fluid throughout the experiment. The experimental values of Re t have been empirically correlated with the relevant system properties, e.g., particle diameter, its shape, density of liquid and solid, liquid viscosity—all of these being represented by Archimedes number and shape factor, φ s. The correlation proposed is: Re t=0.103(Ar 0.804( φ s) 0.745 The standard deviation of the proposed correlation has been calculated to be ±15.2%. The ranges of Ar and φ s are: 53≤ Ar≤3761; 0.5000≤ φ s≤0.9740 The present correlation has been compared with existing equations for monodispersed systems whereby a fair agreement is obtained. This is also found to be reasonably accurate for polydispersed systems when the calculated u t values, based on average bed properties, are compared with those calculated theoretically after being multiplied with the Pettyjohn-Christiansen sphericity correction factor.

Inhalability of Large Particles into the Human Nasal Passage: In Vivo Studies in Still Air

The aspiration of large particles (18–30.5 μm) in the human nose was studied to determine the inhalation efficiency as a function of particle size, and to evaluate the upper size cutoff for inhalable particles in still air. Under these conditions, the ability of a particle to be inhaled is dependent on the inhalation velocity entering the nose and the particle terminal settling velocity. Nasal inhalation of radiolabeled pollen and wood dust aerosols was measured in four subjects at normal resting breathing rates. The efficiency of nasal aspiration was found to decrease as the square of the particle size. The upper size cutoff for inhalability was estimated to be approximately 39 μm in still air.

An experimental study of the settling velocities of single particles in non-Newtonian fluids

Therminal settling velocities of single particles, both spherical and non-spherical, were measured in various non-Newtonian fluids. The shear rheology of each fluid was determined using a Weissenberg rheogoniometer. The spherical particles varied in radius and density, and the non-spherical particles were marble chippings selected such that their volume was within the range of sphere volumes. Terminal settling velocities were analysed using a method for determining the drag force on a sphere falling in a power law fluid. A particle falling through a fluid generates a localised shear rate in the fluid surrounding it. The analysis for the drag force was limited to the region bounded by slow particle settling, generating a shear rate within the first Newtonian region, and a rapid particle settling giving rise to inertial affects with Reynolds numbers greater than 0.1. Within the bounds of these constraints it was found to be difficult to obtain a polymer fluid which behaved as a power law fluid at the shear rates generated by the falling spheres. The sensitivity of a falling particle to a fluids shear history, and thus to a viscosity regime governed by an “effective shear rate” which itself generates, was demonstrated using a thixotropic fluid. The results indicate that the settling velocities of particles of irregular shape could be approximated by that of a sphere of equivalent volume and density.

Determination of the free settling parameters of spherical particles in power law fluids

A new generalized method for rapid determination of the terminal free settling parameters of spherical particles in shear-thinning power law fluids has been proposed. On the basis of experimental data published elsewhere and the authors' own results, general plots have been obtained. These plots, together with the equations presented, permit the computation of the unknown parameters, such as the terminal free settling velocity or settling diameter, which characterize the steady motion of spherical particles in the power law fluids.

不規則形状粒子群の干渉終速度

The type of slurry flow behavior attained in a given pipe diameter is largely determined by the settling velocity of solid particles in a fluid. However, it varies as a function of slurry concentration C, particle diameter, and particle shape. Since the slurry are composed of irregular shaped materials in most slurry pipeline application, design requires an accurate knowledge of the effect of a shape factor used for evaluating the particle shape on terminal settling velocity Vt and on hindered settling velocity VεThe object of this paper is to find the method of estimating Vε of irregular shaped particles in a fluid bounded by rigid wall. It is well known that a sedimenting suspension and a fluidized bed are similar hydrodynamically, therefore experimentswith a variety of materials were carried out in batch fluidized systems, covering the particle Reynolds number range 180 to 1400.Based on the experimental results we discussed the modified Richardson's equation which could be describedby: Vε/Vt=Ko (1-C) nThe index n is a function of the particle Reynolds number and of the dimensionless number depending upon the configulationof suspended particles, while the factor Ko represents the wall effect and increases with area index of particles. Experimental data were analysed taking into account the particle segeregation and the types of behavior of fluidized systems. Moreover, the generalized equation of Vε was derived, and then the quantity ψ(ε) representing the mutual interferenceof particles was determined by experiments.

堆積層上の粒子群の流動について

Contrary to the most investigators' opinions that the deposit regime is uneconomical, some papers have reported this regime to be not necessarily uneconomic since the power requirement may decrease for velocities below the limit deposit velocity. Also, it is said that in all applications of industrial significance the system should be designed to prevent occurrence of this unsafe region because there is imminent danger of pipe blockage. Nevertheless, for the slurry pipeline system transporting coarse solid particles and involving difficulties in controling operational variables rigorously such as hydraulic dredging or hydraulic conveying of run-of-mine coal, it is inevitable for some or all of solids to deposit temporarily on the bottom of the pipe.On these bases there is an immediate need for relationships to use in estimating both the bed thicknesses and the hydraulic gradients under the flow conditions in the deposit regime.This paper presents results of investigations of design methods in this regime. Experiments were conducted to support the theoretical modeling effort for the particle size range 1.71-3.10 mm using a 25.9mm (ID) transparent plastic pipeline, with total length of approximately 10 m, mounted on the frame horizontally.The correlation of experimental data has shown that the ratio hr of the bed thickness to the pipe diameter D and the hydraulic gradient im of slurry flow may be determined from following equations if the functions of f1 (Cv) and f2 (Cv) are given experimentally:_??_in which: Va=apparent mean velocity of slurry flow; g=gravitational constant; Cv=delivered volumetric concentration of solids; v=kinematic viscosity of water; R, R0=hydraulic radii of the free flow section above the bed and of the pipe; Vt=terminal settling velocity of single particle;δ=specific gravity of solids.

A shape-modified size correction for terminal settling velocity in the intermediate region

The terminal velocity of arbitrarily shaped sand particles was experimentally studied in the intermediate (or transition) Reynolds number region (2 < Re < 500). The equation relating terminal velocity and drag coefficients of spheres has been modified to correct for the deviation from roundness by including a shape-modified size term using the morphological descriptor for radial variance called not-roundness. The advantage of this correlation is that all experimental data for non-spherical particles can be correlated by a single drag coefficient curve for spheres.