Velocity experiment curves, particle

Figure 4. Particle settling velocity experiment curves for the effluents mentioned in Table IV.

Figure 2 shows the mean cascading velocity versus distance down the granular cascade for experiments run at the same tangential velocity. Despite a nearly fourfold difference in diameter, the velocity data all fall on nearly the same curve over the first 3 cm down the flowing layer. This agreement indicates that initial particle accelerations may be nearly equivalent, regardless of vessel size. Scatter in the experimental data shown in Figure 2 precludes direct calculation of accelerations, so least-square polynomials were fit to the experimental data. By differentiating the polynomial fit, we obtain an estimate of the downstream acceleration, shown in Figure 3. Over the initial upper third [0 to ( )F of the flowing layer, the acceleration profiles for all cylinders are nearly identical, with only mi-...

The second step was to examine the effect of particle size on the calibration curve. This step was not possible by sedimentation, because coarser particles have higher settling velocities. Therefore, a liquid-solid fluidized bed was used. A fluidization column was constructed with a 5-cm acrylic pipe. Weighed quantities of solids were used, and solids concentration was varied by changing the liquid flow rate. Measurements for these experiments included voltage, bed height, and temperature. To allow a precise determination of concentration from bed height, narrow sizes of particles were used. 

For drying of wet material, experimental and calculated mass loss curves of the water for different gas temperatures are shown In Fig.7. To avoid intaraction with the pyrolysis process, a gas temperature of 150 C has been chosen for the drying of wood. At this tempo-ature the drying velocity is low, thus wood in the expo-iments contained only a small amount of water. Because pyrolysis of wood starts at temp atures of about 200 C, wet slate particles have b n used for drying experiments at higher temperatures. 

Figure 3.13 CompEirison of experiment and theory for the deposition of monodisperse latex particles on a free-slanding wafer 4 in. in diameter. The air mainstream velocity normal to the wafer was 30 cm/sec, typical of microelectronics clean room operations. The diffu-sion equation wa.s solved numerically using calculated velocity and temperature distributions. The curves show that a small increase in surface temperature eHeelivcly suppresses deposition over a wide intermediate particle size range. Larger particles deposit by sedimentation smaller ones break through the thermal barrier by Brownian diffusion. (After Ye et aL, 1991.)...

Diffusion of a solute through immobile water to a reaction site also is affected by interstitial water velocity. If the diffusion rate is slow compared to the interstitial velocity, physical nonequilibrium occurs (5-7). The immobile water can be a layer on the grain surface (film diffusion), in dead-end pores between tightly packed grains (pore diffusion), or within crevices or pits on the grain surfaces (particle diffusion). Calcium and chloride breakthrough curves from column experiments done by James and Rubin (8) indicate that nonequilibrium transport occurs unless interstitial velocities are decreased so that the hydrodynamic-dispersion coefficient is of the same order of magnitude as the molecular-diffusion coefficient. 

The curve fitting procedure used (7, has one other adjustable parameter, pulse input, or number of pore volumes for which the contaminant was fed. As column pore volume was known from independently measurements, pulse input was fixed rather than fit. That is, particle and bulk density of the packing were known from prior measurements, pore volume was determined for each column by weighing dry versus wet, and flow velocity was measured for each experiment. Further, fitted conservative-tracer breakthrough curves gave R = I, suggesting that pulse input and pore volume measurements were consistent. 

The exact shape of the breakthrough curve and the value of tb are hard to predict. Therefore, the design of large units is usually based on experience or tests with a small column. If the particle size and liquid velocity are kept constant, and care is taken to ensure uniform distribution of the feed, the LUB should not change in going to a larger column. 

In spiral, rectangular channels, cells and particles experience Dean drag forces in addition to inertial lift forces. The first conclusive research to analyze flow in curved channels was done by Dean in 1927 [10]. He showed that in curved channels/pipes, the plane Poiseuille flow is disturbed by the presence of centrifugal force (Fcf), and in this condition, the maximum point of velocity distribution shifts from the center of the channel toward the concave wall of the channel (Fig. 2a). This shift causes a sharp velocity gradient to develop near the concave wall between the point of maximum velocity and the outer concave channel wall where the velocity is zero. This causes decrease in the centrifugal force on the fluid near the concave wall which leads to... 

Figure 2. Comparison of the mean square of particle fluctuation velocity (curve) with experiments in reference [42] (dots).

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