Fractal analysis of fluidized particle behavior in liquid‐solid fluidized beds

Abstract

Liquid-solid fluidized beds have been adopted widely for catalytic liquid-phase reactions, separation and recovery of materials with ion exchange resin, adsorption, sedimentation, and wastewater treatment. Recent works on multiphase flow systems have indicated that the concept of fractional Brownian motion (fBm), which can be characterized by the Hurst exponent, H, may be applicable to the analysis of liquid-solid fluidized beds. The model based on this concept has been proposed by Mandelbrot and van Ness to identify the long-term correlation in a time series, which is self-affine. It has been postulated that the rescaled range (R/S) analysis can be a means of estimating H for a given time series. In this work, pressure fluctuations in a liquid-solid fluidized bed have been examined by resorting to the R/S analysis; the effects of fluidized particle size, axial position, and liquid flow rate on the Hurst exponent, H, or the local fractal dimension, d[sub FL], have been examined. The results have revealed that the pressure fluctuations in the bed, exhibiting long-term correlation, essentially reflect the behavior of fluidized particles, and thus, these particles can be considered to undergo fractional Brownian motion.