Granular temperature in a liquid fluidized bed as revealed by diffusing wave spectroscopy

Abstract

We report granular temperature and solid fraction fields for a thin rectangular bed (20×200 mm crosssection and 500 mm high) of glass particles (mean diameter of 165 m and density of 2500 kg/m 3 ) fluidized by water for superficial velocities ranging from 0.05U t , which is approximately double the minimum fluidization velocity, to 0.49U t , where U t is the particle terminal velocity estimated by fitting the Richardson-Zaki correlation to the bed expansion data. At superficial velocities below 0.336U t , the solid fraction and granular temperature are uniform throughout the bed. At higher superficial velocities, the solid fraction tends to decrease with height above the distributor, whilst the granular temperature first increases to a maximum before decaying towards the top of the bed. Correlation of the mean granular temperature with the mean solid fraction and the local granular temperature with the local solid fraction both suggest that the granular temperature in the liquid fluidized bed can be described solely in terms of the solid fraction. The granular temperature increases monotonically with solid fraction to a maximum at ≈ 0.18 where it then decreases monotonically as approaches the close-packed limit.

Granular pressure in a liquid‐fluidized bed as revealed by diffusing wave spectroscopy

“…A second decay in the IACF was observed at time scales of order 0.1 s (see, e.g., Figure 5a in Zivkovic et al18), which is consistent with the frequency of density waves in homogeneous fluidization (i.e., 4–8 Hz31). As this timescale is far greater than that associated with the granular temperature determination (i.e., 1–10 μs),18 the granular temperature measured here is unrelated to the oscillatory motion associated with the density waves.…”

“…A detailed description of the method used to determine the granular temperature in the liquid‐fluidized bed using DWS is provided in Zivkovic et al18 We provide here, however, a brief overview. IACFs were obtained by collecting and correlating 10 blocks of data of 30 s each.…”

“…Equation 3 requires knowledge of the transport mean free path, l *, or step size in the random walk of photons, and the diffusive absorption path length, l a , which accounts for light absorption, at the positions and conditions considered. They were determined using the method of static transmission21, 30 as a function of solid volume fraction and height above the distributor 18…”

“…We report here the granular pressure data for a thin, rectangular bed of small glass particles fluidized by water across a wide range of superficial velocities and, hence, bed solids fraction. The granular pressure was determined by using the granular temperature data obtained from diffusing wave spectroscopy (DWS)18 in expressions for the pressure derived from the kinetic theory of granular flow 19, 20. We first outline the experimental details, including an overview of DWS and details pertaining to the apparatus and the particulate material, and the experimental procedure used.…”

Scaling of granular temperature in a vibrated granular bed

“…The measurements were done at only one position, as our previous experiments found that the granular temperature varied very little with spatial position in the bed [20]. Measurements near the wall, and the top and bottom of the bed where variations may be expected were impossible due to experimental constraints [20,22]. Before each measurement the system was vibrated for at least 10 min, allowing the bed to reach a stationary state.…”