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Hydrodynamics studies in Semifluidized bed relating to bed pressure drop, height of top packed bed, minimum and maximum semifluidization velocities with regular (spherical glass beads) homogeneous ternary mixtures, have been made in 0.01, 0.025, 0.037, 0.05, and 0.065 m internal diameter Perspex columns, with water as the fluidizing medium. Ternary mixtures of glass beads of different sizes (8+10, 10+12 and 12+14 BSS) have been used as the semifluidized solids. Experimental studies relate to establish the effect of system parameters viz. column diameter, average particle size of semifluidized solid and initial static bed height and operating parameters viz. superficial liquid velocity and bed expansion ratio on the above mentioned system variables. Empirical and semiempirical models have been developed using dimensional as well as statistical analyses. The calculated values from the predicted models have been compared with their experimental counterparts and fairly good agreement has been obtained. The results have also been compared with those available in the literature for irregular homogenous ternary mixtures.
Keywords 
Semifluidization; Liquidsolid system; Homogeneous ternary mixtures; Regular particles; Hydrodynamics; Mathematical modeling 
Nomenclature 
BSS British Standard Sieve 
D,d Diameter, m 
G Mass velocity, kg/m^{2}s 
H,h Height, m 
P Pressure, N/m^{2} 
R Bed expansion ratio 
U Velocity, m/s 
Greek letters 
μ Viscosity, kg/m.s 
Δ Difference 
Subscripts 
av average 
c column 
f fluid 
l liquid 
mf minimum fluidization 
msf maximum semifluidization 
osf onset of semifluidization 
p particle 
pa top packed bed 
s static/superficial 
sf semifluidization 
w water 
Introduction 
Semifluidization is a novel technique of fluidsolid contacting which is a stage between fluidization and pneumatic conveyance. Semifluidization begins when the expanded bed of fluidization is restricted at certain height by means of a restraint which only allows the fluid to pass. A semifluidized bed is thus obtained by increasing the fluid velocity beyond minimum fluidization velocity and thereafter arresting the movement of the solid particles with a restraint fixed at a suitable height towards the top of the conduit. This results in the formation of packed bed below the top restraint. The velocity at which the first particle of solid touches the top restraint is called minimum semifluidization velocity (U_{osf}). Similarly when all the bed materials form a packed bed below the top restraint, the corresponding fluid velocity is called the maximum semifluidization velocity (U_{msf}) [1]. The pioneering work as regards the concept and application of a semifluidized bed started by Fan et al. [2]. Hydrodynamic study on single size particle in solidliquid system was highlighted by Fan and Wen [3]. Investigations relating to various aspects of semifluidized bed behavior involving different systems are available in literature. Considerable work on hydrodynamic studies in semifluidized bed has been reported by Roy et al. [46] and Ho et al. [7]. Murthy and Roy reviewed the various studies on semifluidization [8]. Of late, hydrodynamic investigations relating to mixtures (binary/ternary) of homogenous or heterogeneous nature has become essential in view of their potential applications in slurry and gassolid reactions. A few articles on hydrodynamic characteristics of liquidsolid binary homogenous and heterogeneous mixtures in semifluidization have been reported [1,5,9,10]. The use of mixtures have the 
advantages in semifluidization as with less pressure drop both fluidized and the packed bed condition can be achieved compared to a particle [1]. The maiden investigations relating to hydrodynamics of liquidsolid semifluidized bed with irregular homogenous ternary mixtures have been reported by present author [1]. The correlations developed from dimensional analysis approach are as under: 
For the bed pressure drop, 
ΔP_{sf}/ΔP_{mf}=2×10^{7}(ρ_{sav}/ρ_{f})^{1.675}(D_{c}/d_{pav})^{3.338}(G_{sf}/G_{mf})^{3.094}(H_{s}/D_{c})^{0.424}R^{0.938} (1) 
For the top packed bed formation, 
H_{pa}/H_{s}=1×10^{5}(ρ_{sav}/ρ_{f})^{3.155}(D_{c}/d_{pav})^{1.510}(G_{sf}/G_{mf})^{2.426}(H_{s}/D_{c})^{0.524}R^{1.676} (2) 
For minimum semifluidization velocity, 
U_{osf}/U_{mf}=296.5(ρ_{sav}/ρ_{f})^{0.451}(D_{c}/d_{pav})^{1.343}(H_{s}/D_{c})^{0.228}R^{0.755} (3) 
For maximum semifluidization velocity, 
U_{msf}/U_{mf}=0.001(ρ_{sav}/ρ_{f})^{0.680}(D_{c}/d_{pav})^{2.430}(H_{s}/D_{c})^{0.613}R^{0.633} (4) 
Investigation relating to liquidsolid semifluidization regular homogenous ternary mixtures is almost absent. The objective of the present work is to study the hydrodynamics of liquidsolid semifluidization viz. the bed pressure drop, height of the top packed bed, minimum and maximum semifluidization velocities using homogenous ternary mixture of spherical glass beads. In addition the current study includes investigations carried out in five different column diameters with five different ternary mixtures of spherical glass beads of diameter 0.001854, 0.001504,0.001303 m. The experimental data have been correlated with the system parameters by two different approaches viz. the dimensional analysis and the statistical analyses. 
Materials and Methods 
Schematic representation of the experimental setup is shown in Figure 1. The details of the experimental set up and its components are given elsewhere [1]. The scope of the experiment is presented in Table 1. Accurately weighed amount of material was fed into the column, fluidized and defluidized slowly and adjusted for a specific reproducible initial static bed height. Liquid was then pumped to the fluidizer through a rotameter and the temperature was maintained at 25 ± 5°C. At least two minutes were allowed to attain a steady state and then the readings of the manometers and the top packed bed height for each liquid flow rate were noted. The procedure was repeated for different values of initial static bed height, column diameter, the average particle size and the bed expansion ratio. In this work dimensional and statistical analyses approach have been used for predicting dimensionless responses like semifluidized bed pressure drop (ΔP_{sf}/ ΔP_{mf}), height of top packed bed (H_{pa}/H_{s}), and minimum and maximum semifluidization velocities (U_{osf}/U_{mf} and U_{msf}/U_{mf}) as functions of the dimensionless parameters viz. H_{s}/D_{c}, D_{c}/H_{s}, d_{pav}/D_{c}, G_{sf}/G_{mf}, and R. For statistical analysis, Central Composite Design (CCD) [1113] has been used to develop correlations for responses for the four dependent variables in dimensionless form. The complete experimental range and the levels of the independent variables are given in Table 2. The design of the experiment is given in Table 3 (dimensional analysis) and Tables 4a and 4b (statistical analysis). For statistical analysis, a statistical software package DesignExpert8.0.7.1, StatEase, Inc., Minneapolis, USA, has been used for regression analysis of the semifluidized bed responses. 
Results and Discussions 
The minimum and maximum semifluidization velocities are determined by the extrapolation of H_{pa}/H_{sto} 1 on H_{pa}/H_{svs} U_{sf} plot which also used in present investigation. During the present investigation it has been found that maximum contribution for the semifluidized bed pressure drop is due to the top packed bed. Also it has been observed that due to the presence of fines in mixture though bulk density of bed increases, but the fines move faster to form top packed bed. The experimental investigations has established that the semi fluidized bed responses viz. ΔP_{sf}, H_{pa}, U_{osf}, and U_{msf} not only depend on fluid velocity and the material properties, but also on other system parameters like initial static bed height, column diameter and bed expansion ratio. The detailed results on individual parameters and the correlations developed are presented below. 
Semifluidized bed Pressure drop (ΔP_{sf}) 
Figure 2 shows the variation of semifluidized bed pressure drop with respect to the superficial liquid velocity for different values of initial static bed height for average particle diameter of 0.001509 m at constant bed expansion ratio (R=2) in the 0.05 m internal diameter column. From Figure 2, it has been observed that with increase in initial static bed height, the bed pressure drop increases. This is due to the increase in the bed weight and therefore an increase in the top packed bed formation with all the other variables remaining constant. Effect of fines in the mixture is shown in Figure 3 shows the variation of semifluidized bed pressure drop with superficial liquid velocity for different average particle diameter with constant bed expansion ratio (R=2), initial static bed height (H_{s}=0.08m) in 0.05 m internal diameter column. Increase of fines results in a relatively fast formation of top packed bed leading to higher values of semifluidized bed pressure drop, which is evident from Figure 3. Figure 4 shows the variation of pressure drop with superficial liquid velocity for different bed expansion ratio for an initial static bed height of 0.08 m, with a mixture of average particle diameter of 0.001457 m in 0.05 m internal diameter column. From Figure 4, it is clearly observed that with increase in bed expansion ratio the pressure drop decreases. This is due to the fact that, relatively less amount of particles reach the top restraint to form the top packed bed, which has also been observed in other systems. Figure 5 shows the variation of bed pressure drop with superficial liquid flow rate for different column diameters for average particle diameter of 0.01509 m with 0.08 m initial static bed height and a bed expansion ratio of 2.5. The superficial liquid velocity decreases as the column diameter increases for a constant liquid flow rate. Decrease in velocity results in 
lesser transport of bed solids to the top with slower formation of top packed bed and thereby lower values of bed pressure drop. 
Formation of Top packed bed (Hpa) 
Formation of the top packed bed in a semifluidized bed is controlled not only by the superficial liquid velocity but also by other variables like bed expansion ratio, initial static bed height, column diameter and average particle diameter. Figure 6 shows the variation of the height of top packed bed in semifluidized bed with respect to the superficial liquid velocity for different values of initial static bed height for average particle diameter of 0.001509 m at constant bed expansion ratio (R=2) in 0.05 m internal diameter column. From Figure 6, it has been observed that with increase in initial static bed height, the height of top packed bed increases. This is because of the increase in fines in the increased bed which help rapid formation of the top packed bed when the other variables remaining constant. Figure 7 shows the variation of height of top packed bed in semifluidized bed with superficial liquid velocity for different average particle size at constant bed expansion ratio (R=2) in 0.05 m internal diameter column. Increase of fines result in a relatively fast formation of top packed bed, which is evident from Figure 7. Figure 8 depicts the variation of height of top packed bed with superficial liquid velocity for different bed expansion ratio for an initial static bed height of 0.08 m, with a mixture of average particle diameter of 0.001457 m in 0.05 m internal diameter column. From Figure 8, it is clearly observed that with increase in bed expansion ratio the height of top packed bed decreases. This is due to the fact that the buoyancy force is insufficient to lift the particles when the restraint is placed a higher distance in the column with superficial liquid velocity remaining unchanged. The effect of column diameter is shown in Figure 9 where the variation of dimensionless height of top packed bed with superficial liquid flow rate for different diameter columns for an average particle diameter of 0.01509 m, 0.08 m initial static bed height and a bed expansion ratio of 2.5. Increase in column diameter decreases the superficial liquid velocity and thereby relatively fewer amounts of solids are transported to the top. 
Development of correlations by dimensional analysis 
The dimensionless semifluidized bed pressure drop and top packed bed height are found to be dependent on five different variables viz. H_{s}, D_{c}, d_{pav}, G_{sf} and R while dimensionless minimum and maximum semifluidization velocities are functions of H_{s}, D_{c}, d_{pav}, G_{sf} and R. The values of the parameters and responses for the developing correlations are given in Table 3 and the developed correlations are represented as Eqs. (5)  (8). 
For dimensionless semifluidized bed pressure drop, 
ΔP_{sf}/ΔP_{mf}=2.73×10^{5}(H_{s}/D_{c})^{0.087}(D_{c}/H_{s})^{0.404}(d_{pav}/D_{c})^{2.712}(G_{sf}/G_{mf})^{2.995}R^{0.649} (5) 
For dimensionless top packed bed height, 
H_{pa}/H_{s}=2.6×10^{8}(H_{s}/D_{c})^{0.135}(D_{c}/H_{s})^{0.467}(d_{pav}/D_{c})^{4.688}(G_{sf}/G_{mf})^{1.447}R^{0.623} (6) 
For dimensionless minimum semifluidization velocity, 
U_{osf}/U_{mf}=7.74(H_{s}/D_{c})^{0.070}(D_{c}/H_{s})^{0.410}(d_{pav}/D_{c})^{0.485}R^{1.038} (7) 
For dimensionless maximum semifluidization velocity, 
U_{msf}/U_{mf}=1×10^{8}(H^{s}/D^{c})^{0.141}(D_{c}/H_{s})^{0.356}(d_{pav}/D_{c})^{5.304}R^{0.626} (8) 
Figure 10 shows the comparison between the experimental and calculated values (Eq. (1) and Eq.(5)) of Δ_{Psf}/Δ_{Pmf}. The standard deviations and coefficients of correlation are 0.39 and 0.662 for Eq. (1) and 0.94 and 0.982 for Eq. (5) respectively. Figure 11 shows the comparison between the experimental and calculated values (Eq. (2) and Eq. (6)) of H_{pa}/H_{s}. The standard deviations and coefficients of correlation are 0.06 and 0.703 for Eq. (2), 0.043 and 0.967 for Eq.(6) respectively. Figure 12 shows the comparison between the experimental and calculated values (Eq.(3) and Eq. (7)) of U_{osf}/U_{mf}, which shows standard deviations and coefficients of correlation of0.64 and 0.792 for Eq.(3) and 0.13 and 0.984 for Eq. (7) respectively. Figure 13 shows the comparison between the experimental and calculated values (Eq. (4) and Eq. (8)) of U_{msf}/U_{mf}, which shows standard deviations and coefficients of correlation of 0.60 and 0.460 for Eq. (4) and0.32 and 0.973 for Eq. (8) respectively. 
Development of correlations by Statistical analysis 
The method of experimentation is based on statistical design of experiments (Factorial Design Analysis) in order to bring out the interaction effects of variables, which would not otherwise be found by conventional experimentation and to explicitly find out the effect of each of the variables quantitatively on the response. In addition, the number of experiments required is far less compared to the conventional experiments [1].The equations developed by the statistical analysis approach are: 
For dimensionless semifluidized bed pressure drop: 
ΔP_{sf}/ΔP_{mf}=16.990.41×X_{1}2.58×X_{2}0.74×X_{3}+4.09×X_{4}2.51×X_{5}+0.068×X_{1}×X_{2}+0.028×X_{1}×X_{3}0.086×X_{1}×X_{4} +0.048×X_{1}×X_{5}+ 0.11×X_{2}×X_{3}0.53×X_{2}×X_{4}+0.301.50×X_{2}×X_{5}0.14×X_{3}×X_{4} +0.081×X_{3}×X_{5}0.56×X_{4}×X_{5}+0.034×X_{1}^{2}+0.74×X_{2}^{2}0.014×X_{3}^{2}+0.28×X_{4}^{2}+ 0.43×X_{5}^{2} (9) 
In Figure 14, the experimental values of Δ_{Psf}/Δ_{Pmf} have been compared with the calculated values obtained from Eq. (9). The values of standard deviation and correlation coefficient are 0.55 and 0.993. 
For dimensionless top packed bed height: 
H_{pa}/H_{s}=0.620.022×X_{1}0.100×X_{2}0.045×X_{3}+0.072×X_{4}0.087×X_{5}+6.25×10^{4}×X_{1}×X_{2}1.250×10^{3}×X_{1}×X_{3}+0.000×X_{1}×X_{4} +1.250×10^{3} ×X_{1}×X_{5}+3.75×10^{3}×X_{2}×X_{3}7.500×10^{3}×X_{2}×X_{4}+0.011×X_{2}×X_{5}1.875×10^{3}×X_{3}×X_{4}+4.375×10^{3}×X_{3}×X_{5} 8.125×10^{3}×X_{4}×X_{5}+5.510×10^{3}×X_{1}2+0.021× X_{2}2+3.413×10^{3}×X_{3}2+1.974×10^{3}×X_{4}2+0.018×X_{5}2 (10) 
In Figure 15, the experimental values of H_{pa}/H_{s} have been compared with the calculated values obtained from Eq. (10). The values of standard deviation and correlation coefficient are 0.013and 0.995. 
For dimensionless minimum semifluidization velocity: 
U_{osf}/U_{mf}=3.33+0.077 × X_{1}+0.53×X_{2}+0.027×X_{3}+0.82×X_{5}+8.75×10^{3}×X_{1}×X_{2} +6.25×10^{3}×X_{1}×X_{3}+0.014×X_{1}×X_{5}+7.50×10^{3}×X_{2}×X_{3}+ 0.13×X_{2}×X_{5}+7.5×10^{ 3}×X_{3}×X_{5}7.083×10^{3}×X_{1} 20.062×X_{2}2+4.167×10^{3}×X_{3}2+6.667×10^{3}×X_{5}2 (11) 
In Figure 16, the experimental values of U_{osf}/U_{mf} have been compared with the calculated values obtained from Eq. (11). The values of standard deviation and correlation coefficient are 0.023and 0.999. 
For dimensionless maximum semifluidization velocity: 
U_{msf}/U_{mf}=7.55+0.32×X_{1}+1.03×X_{2}+0.7×X_{3}+1.14×X_{5}+0.035×X_{1}×X_{2}+0.034×X_{1}×X_{3} +0.047×X_{1}×X_{5}+0.095×X_{2}×X_{3} +0.15×X_{2}×X_{5}+0.097×X_{3}×X_{5}0.041×X_{1}20.14×X_{2}2+0.039×X_{3}20.046×X_{5}2 (12) 
In Figure 17, the experimental values of U_{msf}/U_{mf} have been compared with the calculated values obtained from Eq. (12). The values of standard deviation and correlation coefficient are 0.091and 0.998. 
The coefficient of correlations for statistical analysis is more than that of dimensional analysis. 
Conclusion 
Hydrodynamic parameters for the liquidsolid semifluidization using homogenous regular ternary mixture viz. the minimum and maximum semifluidization velocities, semifluidized bed pressure drop, height of top packed bed have the importance for knowing the limits of operational parameters when the semifluidized beds are in use. In the current study, investigations have been carried out to study the behavior of homogenous ternary mixtures of regular glass beads with the superficial liquid velocity in a liquidsolid semifluidized bed. To get the advantages of a semifluidized bed, the fines in the mixture have a great role as those help the fast formation of top packed bed, which is desirable. For small and large scale operations, conduits of different sizes are required. The effects of column diameter and the fines have been studied along with other process variables. Correlations for the calculation of semifluidized bed pressure drop, height of top packed bed, minimum and maximum semifluidization velocities have been proposed. The values calculated from the developed correlations have been compared with the experimental ones. The values of coefficients of correlation are found to be greater than0.96, thus emphasizing the validity of the developed correlations over the range of the operating parameters investigated. The statistical analysis approach can suitably be used for the development of model equations as it expresses the individual, interaction and cubic effects. Apart from this the requirement of number of experimental data is less as compared to the conventional method. 
The hydrodynamics study conducted and the correlations developed thereof can find potential applications in physical and chemical processing. In the present investigation, the wide range in experimental parameters involved especially with respect to the mixture compositions and the column diameter makes it amenable to logical scaleup while considering design of liquidsolid semifluidization systems, involving ternary mixtures of homogenous particles. 
Acknowledgements 
The authors gratefully acknowledge the support and encouragement received from GIET, Gunupur, Odisha, India765022. 
References 

Table 1  Table 2  Table 3  Table 4a  Table 4b 
Figure 1  Figure 2  Figure 3  Figure 4  Figure 5 
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Figure 16  Figure 17 