Radial Concentration Profiles Research Articles

Development of solid—liquid mixing models using tomographic techniques

The need for tomographic technology to assist in the development of reliable correlations for scale-up of slurry mixing processes is described. In situ measurements of the axial and radial solid concentration profiles and vector velocities of particulates are required which indicate the effect of mixing impeller geometry, mixing speed, solid concentration and size distribution of solids on mixing performance. The current status of tomographic techniques that could be suited for the applications is assessed. Recent results obtained using the two methods of electrical resistance tomography (ERT) and positron emission tomography (PET) are described together with complementary measurements performed using an invasive single point conductivity probe. The effect of particle size on the “just suspension speed” N js, as determined from conductivity measurements, was compared with the Zweitering correlation (Th. N. Zweitering, Chem. Eng. Sci., 8 (1958) 244-253). Good agreement was obtained. The principle of using data derived from conventional probes and three-dimensional tomograms to yield mixing indices for control decision making is described.

Electron diffusion in the fast-axial-flow CO2 laser

It is pointed out that the electron diffusion driven by collisions between electrons and neutral molecules cannot explain the radial profiles of electron concentrations observed in the fast-axial-flow continuous wave industrial CO2 laser plasma. Based on the approximations of the k- epsilon turbulence model, a simplified model of the turbulent electron diffusion is developed. Predicted radial profiles of electron concentration in the laser cavity and experimentally observed profiles are shown to be in reasonable agreement if we assume that the electron density at the boundary is equal to about 0.6 of the maximum electron density.

Large-scale measurements of the physical characteristics of round vertical bubble plumes in liquids

The hydrodynamics of air/water plumes in a large-scale model of a metallurgical ladle were investigated. The dimensions of the cylindrical vessel were 1600-mm ID and 2250-mm total height. The air was injected through a centered nozzle. Axial and radial profiles of gas concentration, bubble frequency, and liquid and gas velocities were measured using electrical resistivity probes and a propeller flowmeter. It was found that the bubble plume is not at a fixed position but wanders away from the vertical vessel axis. This causes difficulties in the measurements, and special methods have to be designed to define and deduce reproducible values for the characteristic plume quantities. In the analysis of the data, the various physical characteristics were related toz 0, the distance from the nozzle where the axial gas concentration is 50 Pct. The maximum values of the radial profiles are presented in nondimensional correlations.

Shear‐induced particle migration in suspensions of rods

Shear‐induced migration of particles occurs in suspensions of neutrally buoyant spheres in Newtonian fluids undergoing shear in the annular space between two rotating, coaxial cylinders (a wide‐gap Couette), even when the suspension is in creeping flow. Previous studies have shown that the rate of migration of spherical particles from the high‐shear‐rate region near the inner (rotating) cylinder to the low‐shear‐rate region near the outer (stationary) cylinder increases rapidly with increasing sphere size. To determine the effect of particle shape, the migration of rods suspended in Newtonian fluids was recently measured. The behavior of several suspensions was studied. Each suspension contained well‐characterized, uniform rods with aspect ratios ranging from 2 to 18 at either 0.30 or 0.40 volume fraction. At the same volume fraction of solids, the steady‐state, radial concentration profiles for rods were independent of aspect ratio and were indistinguishable from those obtained from suspended spheres. Only minor differences near the walls (attributable to the finite size of the rods relative to the curvature of the walls) appeared to differentiate the profiles. Data taken during the transition from a well‐mixed suspension to the final steady state show that the rate of migration increased as the volume of the individual rods increased.

Shape of the solid-liquid interface and dopant distribution of Bridgman grown Ge:Ga

The influence of process parameters and convections on grown crystals during Bridgman-Stockbarger crystal growth is analysed experimentally. It is shown that the shape of the solid-liquid interface depends mainly on thermal boundary conditions of the growth system. In the thermally stabilized Bridgman configuration, convections in the semiconductor melt with low Prandtl number have negligible effect on the shape of the interface. The axial and in particular the radial dopant concentration profiles allow conclusions on influence and type of bouyant convection in the melt to be made.

Uncoupling the effects of convection and diffusion on refractive index gradient detection in high-temperature liquid chromatography

A model based on Poiseuille flow is expanded upon to describe the coupled effects of diffusion and convection on the sensitivity of the radial refractive index gradient (RIG) measurement with the Z-configuration flow cell for high-performance liquid chromatography (HPLC) detection. Diffusion and convection are shown to affect the radial concentration profile probed by RIG measurements

Turbulence measurements in axisymmetric jets of air and helium. Part 2. Helium jet

A turbulent round jet of helium was studied experimentally using a composite probe consisting of an interference probe of the Way–Libby type and an × -probe. Simultaneous measurements of two velocity components and helium mass fraction concentration were made in the x/d range 50–120. These measurements are compared with measurements in an air jet of the same momentum flux reported in Part 1. The jet discharge Froude number was 14000 and the measurement range was in the intermediate region between the non-buoyant jet region and the plume region. The measurements are consistent with earlier studies on helium jets. The mass flux of helium across the jet is within ±10% of the nozzle input. The mean velocity field along the axis of the jet is consistent with the scaling expressed by the effective diameter but the mean concentration decay constant exhibits a density-ratio dependence. The radial profiles of mean velocity and mean concentration agree with earlier measurements, with the half-widths indicating a turbulent Schmidt number of 0.7. Significantly higher intensities of axial velocity fluctuations are observed in comparison with the air jet, while the intensities of radial and azimuthal velocity fluctuations are virtually identical with the air jet when scaled with the half-widths. Approximate budgets for the turbulent kinetic energy, scalar variance and scalar fluxes are presented. The ratio of mechanical to scalar timescales is found to be close to 1.5 across most of the jet. Current models for triple moments involving scalar fluctuations are compared with measurements. As was observed with the velocity triple moments in Part 1, the performance of the Full model that includes all terms except advection was found to be very good in the fully turbulent region of the jet.

Flow of dilute gas‐particle suspensions

AbstractA semi‐empirical model of the radial segregation of solids in upward flow of dilute gas‐particle suspensions in riser systems is presented on the basis of a reduced form of the fundamental two‐phase flow governing equations and experimental evidence concerning the solids concentration at the wall. The following simple expression for the radial solids concentration profile is obtained: and is in agreement with experimental data over a wide range of operating conditions: superficial gas velocity from 1.4 to 15.3 m/s, riser diameter from 0.032 to 0.40 m, imposed solids flux from 6.60 to 207 kg/m2·s, mean particle size from 32 to 120 μm and particle density from 1,000 to 3,500 kg/m3.The model confirms the existence of the core‐annulus flow structure in gas‐particle suspensions reported in riser reactors, circulating fluidized beds, and the freeboard of bubbling fluidized beds.

Catalytic cracking in riser reactors: core-annulus and elbow effects.

The results of a simple model of vacuum gasoil cracking are presented:the radial profiles of superficial gas velocity, solid concentrations and axial profiles of conversion and yields are predicted by a plug flow model with a gas velocity profile and a radial dispersion coefficient. The catalyst to gas slip coefficient is fitted to industrial results. The core annulus structure of the bed results in a substantial reduction of gasoline yield.

Hydrodynamics of cocurrent downflow circulating fluidized bed (CDCFB)

This paper presents an experimental study on the hydrodynamics of cocurrent downflow gas—solid suspension in a 140 mm i.d. Circulating Fluidized Bed (CDCFB) reactor. The influence of gas velocity and solid circulating rate on axial pressure drop, radial profiles of solid concentration and particle velocity has been examined. It is shown that solid flow in CDCFB is much more uniform than that in the riser.

HUMAN HAIR ANALYSIS BY PIXE

Hair is the unique biological material which, because of its growth, reflects the biomedical and environmental history of the subject. Because of convenience in handling and sampling and relatively high concentrations of metals, trace-element analysis of human hair has been applied widely for different purposes. Although even the measurements of the bulk trace element levels contain some information, the real meaning is contained in longitudinal and radial concentration profiles. This is best achievable by X-ray emission spectroscopy measurements.

Numerical Simulation of the Scalar Fluctuation Field by the Two-Particle Stochastic Process Model.

A three-dimensional Lagrangian stochastic process model of a particle pair has been suggested for prediction of concentration fluctuations by a point-source plume in a low Reynolds number grid turbulence. The velocity correlation function between two particles at a given instant has been taken as the Eulerian velocity correlation, which obeys the continuity conditions. Moreover, the model explicitly contains the effect of molecular diffusivity. Simulation of two types of source (a plain Gaussian source and a uniform concentration circular plain source) has been made and compared with the experimental data. The main results are as follows : (1) the radial profiles of the mean concentration, rms value and intermittency coefficient by simulation are in good agreement with the experimental profiles in both the sources ; (2) the simulated downstream variation of the rms value in the case of the plain Gaussian source agrees well with the data. However, the mean concentration shows a slightly faster downstream decay than the experiments.

Experimental observations of particle migration in concentrated suspensions: Couette flow

Nuclear magnetic resonance (NMR) imaging was used to observe the evolution of radial concentration and velocity profiles of initially well‐mixed concentrated suspensions of spheres in viscous Newtonian liquids undergoing flow between rotating concentric cylinders (wide‐gap, annular Couette flow). In Couette flow, particles migrate from the high shear‐rate region near the inner rotating cylinder to the low shear‐rate region at the outer wall. The particle concentration near the outer wall approaches maximum packing for randomly distributed spheres at steady state, and velocity profiles reveal that the suspension is almost stagnant in these regions. For unimodal suspensions of spheres, the shear‐induced migration of large particles results in concentric two‐dimensional, circular sheets of particles arranged in hexagonal close‐packed arrangements extending inward from the outer wall. This paper examines the functional dependence of particle migration in concentrated suspensions undergoing shear flow in a wid...

Effective diffusivity measurement in porous media via NMR radial imaging

Diffusion of 2H 2O into a water-saturated porous cylinder of zirconia is studied using nuclear magnetic resonance imaging (NMRI or MRI). Typically, NMRI experiments require 1 to 100 min per image, which precludes its use for the study of transport processes with short time constants. However, by employing a fast radial imaging scheme, radial concentration profiles in the pellet at different times were obtained with spatial resolution of < 200 μm in less than 1 min. Since the reservoir of fluid around the pellet was not agitated, the effect of external mass transfer was accounted for by using the measured surface concentration as a function of time. From these measurements, the effective diffusivity was found to be 6.5 × 10 −6 cm 2/s, yielding a tortousity value of 1.98 which is in good agreement with the value calculated from 1/ε(τ = 1.90).

Flame structure of an axisymmetric hydrogen-air diffusion flame

A detailed model including a full scheme of combustion reactions and the governing equations of fluid mechanics was designed for two-dimensional hydrogen burning systems, and applied to a Burke-Schumann type hydrogen-air diffusion flame to elucidate its flame structure and combustion reaction mechanism. The same flame was also experimentally investigated and radial profiles of OH radical concentration and rotational temperature through the flame were determined by a conveniently improved line-of-sight absorption method. Simulation suggested that a well-developed diffusion flame occurs from heights about 5 mm from the burner mouth, in very good agreement with the experimental results. At each horizontal section of the well-developed diffusion region, the calculated rates of the chemical reactions showed considerable values within an annular zone about 5 mm thick, in which there is a point where H2 and O2 are simultaneously exhausted, and in whose vicinity the temperature becomes maximum. This result confirmed one of the Burke-Schumann's predictions, but radial displacements of about 1 mm between the peeks of the rates of different reactions and also between the maximum OH radical concentration and the maximum temperature were found in both experiments and calculation, showing that the reactions do not occur in an infinitely thin region, contradicting one of the Burke-Schumann's assumptions. At the lowest part of the flame, below the burner tip, the issuing air and the H2 diffusing downward meet and react like premixed gas mixtures; the whole flame was found to be held at the burner rim by large heat release rates at that region. The experimental results, in very good agreement with the simulation, showed that the maximum OH concentration through the flame occurs at a height around 2 mm, confirming the premixed-like intense combustion reactions taking place at the lower part of the flame.

Multiple steady states in a radio frequency chlorine glow discharge

Multiple steady states have been observed in a 13.56 MHz chlorine glow discharge in a parallel plate radial flow reactor. Measurements of the flux and energy distribution of positive ions bombarding the electrode are reported along with radial profiles of atomic chlorine (Cl) concentration and etch rate of polysilicon for different states of the plasma. At the same operating conditions the plasma may exist in one of two states. In one state the plasma appeared radially uniform, resulting in relatively uniform radial Cl concentration profiles and etch rate. In the other state the plasma appeared radially nonuniform with a higher intensity central region (‘‘plasmoid’’). The etch rate and Cl concentration profiles were nonuniform in the presence of the plasmoid. The plasmoid generally appeared under conditions of high power and pressure and could be eliminated by adding noble gases and/or decreasing the electrode spacing. The multiple states may be a result of the strongly electronegative nature of the chlorine discharge.

Distribution of solid particles in a mixed vessel

The aim of our research was to study the axial, radial and tangential solid phase concentration profiles in a mixed vessel. The conductivity method was used for the concentration measurement. We accomplished the measurement in eleven points in five heights above the vessel bottom. The points were situated on three vertical planes passing through the vessel axis and on five values of radii. It was determined by means of statistic test of variance if it was possible to measure the concentration only in one point in each distance from the vessel bottom and neglect the radial and tangential concentration differences.

Gas‐particle flow in a vertical pipe with particle‐particle interactions

AbstractA theory is presented for the fully‐developed flow of gas and particles in a vertical pipe. The relation between gas pressure gradient and the flow rates of the two phases is predicted, over the whole range of cocurrent and countercurrent flows, together with velocity profiles for both phases and the radial concentration profile for the particles. The gas and the particles interact through a drag force depending on their relative velocity, and there are mutual interactions between pairs of particles through inelastic collisions. This model is shown to account for marked segregation of gas and particles in the radial direction, and the predicted relation between the pressure gradient and the flow rates of the two phases is surprisingly complex.

Transport of electrolytes in charged pores: Analysis using the method of spatial averaging

The method of spatial averaging is used to analyze the equations for electrolyte transport across charged cylindrical pores. Using this approach, an analytical expression for the radial potential profile is obtained which is valid when the radial deviations of the electrical potential from the area-averaged potential are small. This expression can be integrated analytically, thus eliminating the need for much of the computational effort required in the usual space-charge models. Furthermore, it is shown that this analytical expression for the radial potential profile leads to model predictions for membrane permeability, osmotic flow, conductivity, streaming potential, and concentration potential in solutions of binary electrolytes which match the predictions from the space-charge model using a numerical solution to the Poisson-Boltzmann equation when the radial deviation of the potential is as high as 50 mV. Unlike most previous models of electrolyte transport in charged capillaries, this approach allows one to easily model systems of three or more ions while still taking into account the effects of the radial profiles of potential, concentration, and velocity.

Recent developments for plasma edge diagnostics using atomic beams

Li-atom beams with velocities of 1.5 × 10 5 cm/s and 1× 10 6 cm/s have been used to measure n e profiles in the density range 10 11–10 13 cm −3 from the Li line emission with a spatial resolution of about 1 mm. Injecting in addition a different type of atoms, the ionization rate of which shows a strong dependance on the electron temperature in the interesting range of 5–100 eV (e.g. carbon and helium), also radial T e profiles are obtained. A high intensity 30 keV Li beam is employed to measure radial profiles of impurity ion concentrations (e.g. He, C, 0) by charge exchange recombination spectroscopy. For the different purposes several types of injectors have been developed: thermal beams using ovens, suprathermal beams using laser ablation techniques, and a high energy beam using a plasma ion source in combination with a charge exchange cell. They are located at different poloidal and toroidal positions. The spatial line emission profiles of the beams are recorded either by Si diode array cameras or by a photomultiplier in combination with a scanning mirror so that a spatial resolution better than 2 mm is achieved. The combination of all these systems delivers information about the structure of the TEXTOR boundary layer in poloidal and toroidal direction.