Studies on Axial Turbulent Diffusion Coefficient in Water-Fluidized Beds

Abstract
The mixing characteristics of the fluid flowing through reactors are industrially important for the purpose of designing reactors and estimating the yield of the product. Recently several studies have been made on the mixing characteristics of the homogeneous and heterogeneous reactors. These mixing characteristics usually cover the field of turbulent diffusion whose coefficient is obtained on the assumption that the turbulent mass diffusion is superimposed on the convective flow with the uniform velocity. Studies on fluid mixing in the fluidized bed were made by Wilhelm et al for the liquid-solid system and by Gilliland et al for the gas-solid system. Wilhelm et al4) measured the turbulent diffusion coefficient by measuring the spreading of the methylene blue dye from a point source in water-fluidized bed of glass beads. Gilliland et al carried out the diffusion experiment on helium gas from a point source2), and employed the technique of the residence time curve3) for the fluidized bed of gas-solid system. The present authors have obtained the axial turbulent diffusion coefficients by measuring axial concentration gradients in the water-fluidized beds of β-naphthol cylindrical particles. When the concentration in the bed is very small as compared with the saturation concentration, the dissolution rate approximates to the zero-order reaction as expressed by Equation (1'). By using the boundary conditions at the inlet and outlet of the bed, that is by using Equations (2) and (3), Equation (4) can be derived from Equation (I'). The experimental apparatus used for this work is shown in Figure 1. The inside diameter of the column is 52.1mm. City water is used as the fluid. The water, before entering the fluidized bed, passes through the calming section of fixed bed packed with glass beads. The water in the fluidized bed is slowly taken out by means of the injectors thrust along the tube wall at intervals of 5cm. The concentration of this water is measured by the spectrophotometer at the wave length of 2, 735 A and 2, 850 A. From the measured concentration gradients, the axial diffusion coefficient Ez is calculated with the help of Equation (4) at three points: η≡l/L=1/4, 1/2, 3/4. The results derived are presented in Table I, Figures 2 and 3. Figure 2 shows the relative axial Peclet number (Pe=Dpμ0/Ez) plotted against fractional void ε, and the relative Pe vs. Rep is shown in Figure 3. From these figures we know that the turbulent diffusion coefficient Ez increases with the increase of fractional void and reaches the maximum value of about 70cmcm2/sec in this system.