MOTION OF AND MASS TRANSFER FROM AN ASSEMBLAGE OF SOLID SPHERES MOVING IN A NON-NEWTONIAN FLUID AT HIGH REYNOLDS NUMBERS

An approximate solution for the motion of an assemblage of solid spheres moving in a power-law fluid in the high Reynolds number region is obtained using a combination of Happel's free-surface cell model and the boundary layer theory. It is theoretically predicted that the drag coefficient will decrease with the increase of the shear-thinning anomaly. The results of the present analysis are in reasonably good agreement with the available experimental data for fixed and fluidized beds. The influence of the non-Newtonian behavior on the mass transfer rate from an assemblage of solid spheres is also discussed.     

SEDIMENTATION OF PARTICLES IN NON-NEWTONIAN FLUIDS

The influence of non-Newtonian flow behavior on sedimentation velocity of particles is investigated using an approximate solution for the motion of an assemblage of solid spheres presented previously by the authors. It is theoretically predicted that the pseudoplaslicity decreases the sedimentation velocity and its reduction is pronounced at large voidage. The present theory is discussed using the available empirical correlations.     

SEDIMENTATION OF PARTICLES IN NON-NEWTONIAN FLUIDS

The influence of non-Newtonian flow behavior on sedimentation velocity of particles is investigated using an approximate solution for the motion of an assemblage of solid spheres presented previously by the authors. It is theoretically predicted that the pseudoplaslicity decreases the sedimentation velocity and its reduction is pronounced at large voidage. The present theory is discussed using the available empirical correlations.     

Drag and mass transfer in non-newtonian flows through multi-particle systems at low reynolds numbers

An approximate solution for the motion of an assemblage of solid spheres moving through a power-law fluid at low Reynolds numbers is obtained using HapThe theoretical predictions based on Kuwabara's zero-vorticity cell model are very similar to those based on Happel's model. An approximation technique     

DRAG AND MASS TRANSFER IN SLOW NON-NEWTONIAN FLOWS OVER AN ENSEMBLE OF NEWTONIAN SPHERICAL DROPS OR BUBBLES

An approximate solution for the slow motion of an ensemble of spherical drops through a power law fluid is obtained using Happel's free-surface cell model. It is shown that the drag coefficient decreases with decrease of the flow index and that this reduction is more significant at low voidage and large viscosity ratio parameter. The effect of the pseudoplastic anomaly on the mass transfer rate is more pronounced at low voidage for large values of viscosity ratio parameter, unlike the case of a single spherical drop

The present analysis covers the whole range of values of viscosity ratio parameter from infinity (an assemblage of solid spheres) to zero (a swarm of bubbles) and reduces to the solutions for those cases already known

The results for the motion of an ensemble of spherical drops also provide the basis for proposing a tentative expression for the expansion of liquid-liquid fluidized bed at low Reynolds number.     

CONJUGATE HEAT AND MASS TRANSFER IN CONVECTIVE DRYING OF MULTIPARTICLE SYSTEMS. PART I: THEORETICAL CONSIDERATIONS

This is the first of two papers concerning conjugate transport in convective drying of multiparticle systems. In this study, a methodology for the solution of conjugate transport problems is proposed. The theoretical aspects and relevant assumptions are briefly discussed and the results for convective heat and mass transfer in assemblages of spheres are presented. It is shown that both heat and mass transfer rates for an assemblage of two spheres in tandem arragement are significantly different from those of a single sphere case, and that care should be taken when modeling multiparticle systems by means of single-particle analysis.     

A STUDY OF SPINLINE DYNAMICS USING ORTHOGONAL COLLOCATION

Previous work on slow flow of non-Newtonian fluids past particles assemblages has been reviewed. Using a combination of Happel's free surface model and variational principles, bounds on the drag have been obtained for the creeping flow of a Carreau Model fluid past an assemblage of rigid spheres. The bounds are related to friction factor for flow through fixed beds of spherical particles. Numerical results covering a wide range of model parameters and bed voidages are presented.

Theoretical predictions are validated by comparing with experimental results reported in the literature that involve viscoelastic fluids. Arithmetic averages of the two bounds compare well for 182 data points with an average error of 12%. It is demonstrated that the present analysis, though based on a purely viscous model, can predict creeping flow behaviour in rigid particles assemblage for both inelastic and viscoelastic fluids.     

SLOW NON-NEWTONIAN FLOW PAST AN ASSEMBLAGE OF RIGID SPHERES

Previous work on slow flow of non-Newtonian fluids past particles assemblages has been reviewed. Using a combination of Happel's free surface model and variational principles, bounds on the drag have been obtained for the creeping flow of a Carreau Model fluid past an assemblage of rigid spheres. The bounds are related to friction factor for flow through fixed beds of spherical particles. Numerical results covering a wide range of model parameters and bed voidages are presented.

Theoretical predictions are validated by comparing with experimental results reported in the literature that involve viscoelastic fluids. Arithmetic averages of the two bounds compare well for 182 data points with an average error of 12%. It is demonstrated that the present analysis, though based on a purely viscous model, can predict creeping flow behaviour in rigid particles assemblage for both inelastic and viscoelastic fluids.     

CONJUGATE HEAT AND MASS TRANSFER IN CONVECTIVE DRYING OF MULTIPARTICLE SYSTEMS. PART I: THEORETICAL CONSIDERATIONS

Abstract

This is the first of two papers concerning conjugate transport in convective drying of multiparticle systems. In this study, a methodology for the solution of conjugate transport problems is proposed. The theoretical aspects and relevant assumptions are briefly discussed and the results for convective heat and mass transfer in assemblages of spheres are presented. It is shown that both heat and mass transfer rates for an assemblage of two spheres in tandem arragement are significantly different from those of a single sphere case, and that care should be taken when modeling multiparticle systems by means of single-particle analysis.     

OPTICAL MEASUREMENT OF THE MOTION OF SMALL PARTICLES CLOSE TO THE FLUID-SOLID INTERFACE

A novel and versatile optical method, based on the phenomenon of total internal reflection and useful for studying the motion of small particles in a moving fluid very close to the interface between a fluid and an optically flat solid, is described. Initial tests using 0.2 to 1 micron silica particles and 3.2 micron polystyrene spheres have demonstrated the effectiveness of the method and provide a basis for several extensions, which are discussed.     

OPTICAL MEASUREMENT OF THE MOTION OF SMALL PARTICLES CLOSE TO THE FLUID-SOLID INTERFACE

A novel and versatile optical method, based on the phenomenon of total internal reflection and useful for studying the motion of small particles in a moving fluid very close to the interface between a fluid and an optically flat solid, is described. Initial tests using 0.2 to 1 micron silica particles and 3.2 micron polystyrene spheres have demonstrated the effectiveness of the method and provide a basis for several extensions, which are discussed.     

Gas‐Solid Drag Coefficient for Ordered Arrays of Monodisperse Microspheres in Slip Flow Regime

Numerous analytical and numerical correlations for the drag force of particles in packed arrays are not applicable to microspheres because of the invalidity of the no‐slip assumption at a solid wall. The slip flow through assemblages of spheres is investigated by the lattice Boltzmann method (LBM). Three periodic arrays of static and monodisperse particles, i.e., a simple cubic, a body‐centered cubic, and a face‐centered cubic array, each with a relatively wide range of solid volume fraction, are considered. The LBM is validated for the slip flow over a single unbounded sphere and the continuum flow through spheres in a simple cubic array. The LBM results agree well with the experimental and numerical data in the literature. Simulations of slip flow through the three ordered arrays of spheres are performed. The effects of solid volume fraction and slip are both quantified within the developed drag laws.     

木素磺酸盐在固体颗粒表面的吸附性能

引　言木素磺酸盐是亚硫酸法生产纸浆或纤维浆的副产物 ,来源于可再生资源 ,具有吸附分散性、黏结性、流变性和胶体性质等表面物化特性 ,广泛应用在染料、涂料、石油工业和建筑业等领域 .木素磺酸盐是具有C3～C6 疏水骨架和以磺酸根为主的亲水性基团的阴离子表面活性剂 ,具有强     

Preparation of Spherical Yttria-Stabilized Zirconia Powders by Reactive-Spray Atomization

A new inorganic sol–gel process of zirconia (yttri-stabilized) spherical powders production has been developed. The process is based on spraying zirconia sol into an ammoniawater solution, followed by drying of the gel precipitate and calcination. The gel particles preserve the spherical shape of sprayed droplets, because of a thin solid film that forms on the drop surface via its contact with gaseous ammonia before the impact with the ammonia solution. Being dried and calcined, the gel spheres transform to free–flowing powders composed of the solid, not hollow smooth spheres of zirconia–yttria solid solutions. The particle composition, morphology, and microstructure have been investigated in detail versus the process conditions.     

Settling and fluidization of tall cylinders in solid-liquid suspensions

We numerically study how rigid solid cylinders with a length over diameter aspect ratio of 10 settle through suspensions consisting of uniformly sized solid spheres and Newtonian liquid. We identify regimes with preference for horizontal settling and vertical settling of the cylinders dependent on the overall solids volume fraction (in the range of 0–0.58) and the Archimedes number of the cylinders. These insights we use to interpret the behavior of fluidized suspensions consisting of mixtures of spheres and cylinders with an emphasis on cylinder orientation distributions and slip velocities between solids and liquid phase. The three-dimensional and time-dependent simulations explicitly resolve the solid-liquid interfaces by applying an immersed boundary method contained in a lattice-Boltzmann flow solver.     

SETTLING VELOCITIES OF TWO EQUAL-SIZED SPHERES FOLLOWING EACH OTHER IN VISCOUS FLUIDS CONTAINED IN CYLINDERS

Experimental data are presented for two equal-sized spheres falling along the axis of a cylinder. The two spheres settle with the same velocity as that of a single falling sphere as long as their separation distance is larger than a critical value. When the distance is smaller than the critical value, the two spheres fall faster than a single sphere. The drag on the two spheres is less affected when two spheres fall in a cylinder in comparison to the situation when two spheres fall in an unbounded medium. The data are correlated and shown to agree with numerical calculations.     

Internal Nucleation of Highly Undercooled Magnesium Metasilicate Melts

Crystallization and vitrification in undercooled, fine magnesium silicate droplets, with compositions ranging from 34.5 ≤ wt% MgO ≤ 39.9, were examined following containerless drop tube processing. From an initial phase assemblage of a mixture of the metasilicate (MgSiO₃) polymorphs orthoenstatite and clinoenstatite, three morphological powder types were observed following processing: unmelted shards, glass spheres, and melted/recrystallized spheres. The primary phase in the powders processed at a maximum temperature of ∼1650°C is the high-temperature metasilicate polymorph protoenstatite, with metastable forsterite (Mg₂SiO₄) also appearing. The melted/recrystallized spheres have the uniform, submicrometer texture of a glass ceramic, decisively different from the surface crystallization textures normally seen for melts/glasses of these compositions. Transmission electron microscopy results indicate that the glass-ceramic texture occurs because the process technique allows a liquid-phase immiscibility to precede crystallization. The phases and textures developed during containerless solidification processing of these metsilicate compositions are analyzed thermodynamically; the minimum amount of undercooling required for amorphous phase separation is evaluated using the metastable extensions of the forsterite + liquid and the silica-rich, twoliquid miscibility phase boundaries. The application of metastable phase diagram analysis is demonstrated as an effective guide for identifying potential compositions for development of novel glass-ceramics.     

Dissolution-regrowth synthesis of SiO2 nanoplates and embedment into two carbon shells for enhanced lithium-ion storage

In this work, SiO_2 nanoplates with opened macroporous structure on carbon layer(C-mSiO_2) have been obtained by dissolving and subsequent regrowing the outer solid SiO_2 layer of the aerosol-based C-SiO_2 double-shell hollow spheres. Subsequently, triple-shell C-mSiO_2-C hollow spheres were successfully prepared after coating the Cm SiO_2 templates by the carbon layer from the carbonization of sucrose. When being applied as the anode material for lithium-ion batteries, the C-mSiO_2-C triple-shell hollow spheres deliver a high capacity of 501 mA ·h·g~(-1) after100 cycles at 500 m A·g~(-1)(based on the total mass of silica and the two carbon shells), which is higher than those of C-mSiO-12(391 m A·h·g~(-1)) spheres with an outer porous SiO_2 layer, C-SiO_2-C(370 m A·h·g) hollow spheres with a middle solid SiO_2 layer, and C-SiO_2(319.8 m A·h·g~(-1)) spheres with an outer solid SiO_2 layer. In addition,the battery still delivers a high capacity of 403 m A·h·g~(-1) at a current density of 1000 m A·g~(-1) after 400 cycles.The good electrochemical performance can be attributed to the high surface area(246.7 m~2·g~(-1)) and pore volume(0.441 cm~3·g~(-1)) of the anode materials, as well as the unique structure of the outer and inner carbon layer which not only enhances electrical conductivity, structural stability, but buffers volume change of the intermediate SiO_2 layer during repeated charge–discharge processes. Furthermore, the SiO_2 nanoplates with opened macroporous structure facilitate the electrolyte transport and electrochemical reaction.     

Eddy motions between fluid spheres in a stokes flow

In the axisymmetric Stokes streaming flow past two fluid spheres it is shown that, in contrast to when the spheres are solid, no separation from the surfaces of the spheres occurs. However, for oil droplets in water, free toroidal eddies are predicted for a certain range of proximities and for a ratio of radii up to about 7. The limit in which one sphere becomes a half space is discussed.     

Motion of a solid sphere in a horizontally oscillating liquid

The behaviour of a single dense sphere in a horizontal tube containing an oscillating liquid has been studied experimentally and theoretically. The experiments were carried out using steel, glass and nylon spheres in water or dilute glucose solutions in a 5·08 cm diameter horizontal tube, at oscillation frequencies of 0·4 to 1·3 Hz. The measured amplitude of oscillation of the spheres agreed fairly well with predictions from the equation of motion of the spheres. It was necessary to allow for the rotational inertia of the rolling spheres and quasi-steady drag behaviour was assumed. Solid—solid friction and boundary layer effects were not included in the analysis and were responsible for some deviations between observation and prediction.