Velocity solids, determination

In a recent study of the transport of coarse solids in a horizontal pipeline of 38 mrrt diameter, pressure drop, as a function not only of mixture velocity (determined by an electromagnetic flowmeter) but also of in-line concentration of solids and liquid velocity. The solids concentration was determined using a y-ray absorption technique, which depends on the difference in the attenuation of y-rays by solid and liquid. The liquid velocity was determined by a sail injection method,1"1 in which a pulse of salt solution was injected into the flowing mixture, and the time taken for the pulse to travel between two electrode pairs a fixed distance apart was measured, It was then possible, using equation 5.17, to calculate the relative velocity of the liquid to the solids. This relative velocity was found to increase with particle size and to be of the same order as the terminal falling velocity of the particles in the liquid. 

The data of Fig. 20 also point out an interesting phenomenon—while the heat transfer coefficients at bed wall and bed centerline both correlate with suspension density, their correlations are quantitatively different. This strongly suggests that the cross-sectional solid concentration is an important, but not primary parameter. Dou et al. speculated that the difference may be attributed to variations in the local solid concentration across the diameter of the fast fluidized bed. They show that when the cross-sectional averaged density is modified by an empirical radial distribution to obtain local suspension densities, the heat transfer coefficient indeed than correlates as a single function with local suspension density. This is shown in Fig. 21 where the two sets of data for different radial positions now correlate as a single function with local mixture density. The conclusion is That the convective heat transfer coefficient for surfaces in a fast fluidized bed is determined primarily by the local two-phase mixture density (solid concentration) at the location of that surface, for any given type of particle. The early observed parametric effects of elevation, gas velocity, solid mass flux, and radial position are all secondary to this primary functional dependence. 

The velocity is therefore determined by two fundamental physical properties of a material its elastic modulus and density. The less dense a material or the more resistant it is to deformation the faster an ultrasonic wave propagates. Usually, differences in the moduli of materials are greater than those in density and so the ultrasonic velocity is determined more by the elastic moduli than by the density. This explains why the ultrasonic velocity of solids is greater than that of fluids, even though fluids are less dense [1],... 

These values are not absolute velocity constants since transfer to alkyl-aluminum occurs during the reaction. However, the transfer reactions will be proportional to the concentration of active centers. Hence, at similar conversions the fractions of active alkylmetal bonds are likely to be approximately the same, and the constants will be proportional to the true velocity constants. Determining relative propagation velocity constants is complicated by the participation of a termination reaction. At low temperatures the polymer is insoluble and the catalyst is embedded in a semi-solid mass, resulting in very slow rates of polymerization. At temperatures of 41°-60° C. reasonably good first-order reactions with respect to monomer are found, but at higher temperatures there is a rapid fall-off in reaction rate with time (Figure 4). The velocity constants in Table III were calculated from the linear portion of the rate-time curve, and no account was taken of termination reactions. 

The same apparatus was used to measure the kinetics of emulsion crystallization under shear. McClements and co-workers (20) showed that supercooled liquid n-hexadecane droplets crystallize more rapidly when a population of solid n-hexa-decane droplets are present. They hypothesized that a collision between a solid and liquid droplet could be sufficient to act as a nucleation event in the liquid. The frequency of collisions increases with the intensity of applied shear field, and hence shearing should increase the crystallization rate. A 50 50 mixture of solid and liquid n-hexadecane emulsion droplets was stored at 6 -0.01 °C in a water bath (i.e., between the melting points and freezing points of emulsified n-hexadecane). A constant shear rate (0-200 s ) was applied to the emulsion in the shear cell, and ultrasonic velocities were determined as a function of time. The change in speed of sound was used to calculate the percentage solids in the system (Fig. 7). Surprisingly, there was no clear effect of increased shear rate. This could either be because increase in collision rate was relatively modest for the small particles used (in the order of 30% at the fastest rate) or because the time the interacting droplets remain in proximity is not affected by the applied shear. 

Kariyasaki [70] studied bubbles, drops, and solid particles in linear shear flow experimentally, and showed that the lift force on a deformable particle is opposite to that on a rigid sphere. For particle Reynolds numbers between 10 and 8 the drag coefficient could be estimated by Stokes law. The terminal velocity was determined to be equal to that of a particle moving in a quiescent... 

Fig. 9.10. Drift velocity field determined from Eqs.(9.43), (9.42), (9.48) for (a) dp/A = 0.45, (b) dp/X = 1.0. Thin solid lines represent lines of fixed points that satisfy Eq. (9.49) (compare text). Thick solid lines depict trajectories of the spiral center computed for the Oregonator model (9.1) with fc/ , = 0.02 and t = 0 [53].

Particle velocity was determined by the cross-correlation technique. Figure 6.34 shows typical cross-correlation functions that were obtained from the velocity electrodes. For a solids feed rate of 3.2 lb/s, the cross-correlation functions show well-defined peaks, from which particle velocities can be... 

A model for the atomization and spray formation by splash plate nozzles is developed by Sarchami et al. [30]. This model is based on the liquid sheet formation theory due to an oblique impingement of a liquid jet on a solid surface. The continuous liquid sheet formed by the jet impingement is replaced with a set of dispersed droplets. The initial droplet sizes and velocities are determined based on theoretically predicted liquid sheet thickness and velocity. A Lagrangian spray code is used to model the spray dynamics and droplet size distribution further downstream of the nozzle. 

Most of gravity sedimentation techniques use an initially homogeneous suspension in which particles are allowed to settle under the influence of gravity. Two basic modes of operation can be found in practice the fraction of particles which have a given settling velocity is determined from either the concentration measurements at a certain depth below the surface in a sedimentation cell (incremental techniques) or from measurements of the total mass of solids accumulated at the bottom (cumulative techniques). 

The reflectance signal, in the upper part of Fig.3, indicates the onset of the high reflectivity phase and its duration. Comparison of experimental data with calculation is shown in Fig.4, where the voltage data are converted into melt depth through a detailed analysis. The solid-liauid interface velocity as determined by the slopes of the curves agrees quite well with the estimated values. 

Fig. 18.63 Determination of penetration region and partial penettatitm regitni at different atomizer operation condititnis based on comparison of particle-droplet relative velocity and critical penetration velocity (/ ) solid-liquid contact angle 0 = 90° (right) solid-liquid contact angle...

Of these factors, the size, density, and shape of a particle are the most important determinants of settling velocity. Solids concentration and turbulence indirectly affect settling velocity by influencing formation of floes, while sediment bed roughness is a factor in deposition. Floe formation is also strongly influenced by particle and surface chemistry. Chemical properties which factor into the process of floe formation include... 

When consistent units are used, the particle size will either be in meters or feet. The equation contains effects of cyclone size, velocity, viscosity, and density of solids. In practice, a design curve as given in Fig. 17-39 uses Dptk the size at which 50 percent of sohds of a given size are collected by the cyclone. The material entering the cyclone is divided into fractional sizes, and the collecdion efficiency for each size is determined. The total efficiency of coUection is the sum of the col-lecdion efficiencies of the cuts. 

Many times solids are present in one or more phases of a solid-hquid system. They add a certain level of complexity in the process, especially if they tend to be a part of both phases, as they normally will do. Approximate methods need to be worked out to estimate the density of the emulsion and determine the overall velocity of the flow pattern so that proper evaluation of the suspension requirements can be made. In general, the solids will behave as though they were a fluid of a particular average density and viscosity and won t care much that there is a two-phase dispersion going on in the system. However, if solids are being dissolved or precipitated by participating in one phase and not the other, then they will be affected by which phase is dispersed or continuous, and the process will behave somewhat differently than if the solids migrate independently between the two phases within the process. 

FIG. 18-85 Depth correction factorto he applied to unit areas determined with Wilhelm-Naide and direct methods. Velocity ratio calculated using tangents to settling cun e at a particular settled solids concentration and at start of test. 

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