Characteristics of large two-dimensional air bubbles in liquids and in three-phase fluidised beds
Abstract
The rising velocity, included angle and wake size of large single air bubbles have been measured in a two-dimensional column, 39.5 cm wide and 112 cm high, which contained a liquid or three-phase fluidised bed. The liquids used were water, 82% w/w aqueous glycerol, 90% w/w aqueous glycerol and methanol The fluidised beds consisted of glass beads with diameters 0.2 mm, 1 mm and 3 mm, fluidised by water. Bed porosities varied between 0.5 and 0.75. In all the liquids and fluidised beds, except 3 mm fluidised particles, bubble velocities werefound to be proportional to the square root of the radius of curvature of the circular cap. The included angle of the cap increased as the viscosity of the liquid increased.
Bubble shapes were used to estimate an apparent viscosity for the fluidised beds which varied from 0.12 to 3.1O P.
References (19)
- G.R. Rigby
Chem. Eng. Sci.
(1970) - J.R. Grace et al.
Chem. Eng. Sci.
(1967) - P.S.B. Stewart et al.
Chem. Eng. Sci.
(1964) - K. Østergaard
Chem. Eng. Sci.
(1965) - I. Slaughter et al.
Chem. Eng. Sci.
(1968) - R. Collins
Chem. Eng. Sci.
(1965) - J.F. Davidson et al.(1963)
- L. Massimilla
Brit. Chem. Eng.
(1961) - R.M. Davies et al.
Proc. Roy. Soc. A
(1950)
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Bubble formation and dynamics in gas-liquid-solid fluidization-A review
2007, Chemical Engineering ScienceCurrent worldwide commercial activities in converting natural gas to fuels and chemicals, or gas-to-liquids technology use slurry bubble column reactors with column sizes considerable larger than those currently in practice. Such commercial activities have prompted further fundamental research interest in fluid and bubble dynamics, transport phenomena and the scale up effects of three-phase fluidization systems. The fundamental behavior of particular relevance to these activities is associated with the elevated temperature and pressure conditions.
This review attempts to summarize the salient characteristics of liquid, bubbles, and particles and their interactive behavior and dynamics in the process of bubble formation and bubble rising in gas–liquid–solid fluidization systems. Measurement techniques including both intrusive techniques such as the probes, and non-intrusive techniques such as tomography, that are used to study fluid and bubble properties in gas–liquid and gas–liquid–solid systems, are illustrated. Governing mechanisms of bubble–particle collision and bubble breakup are discussed. The state-of-the-art computational techniques, that consider both the discrete and the continuum approaches for movement of the particle and bubble phases along with the discrete simulation results, are presented. Of particular emphasis is the effect of pressure and temperature on the fluid and bubble dynamics in three-phase fluidization.
Numerical studies of bubble and particle dynamics in a three-phase fluidized bed at elevated pressures
2000, Powder TechnologyA discrete phase simulation is conducted to study the bubble and particle dynamics in a three-phase fluidized bed at high pressures. The Eulerian volume-averaged method, the Lagrangian dispersed particle method, and the volume of fluid (VOF) method are employed to describe, respectively, the motion of liquid, solid particles, and gas bubbles. A bubble-induced force model, a continuum surface force (CSF) model, and Newton's third law are applied to illustrate, respectively, the coupling effect of particle–bubble, gas–liquid, and particle–liquid interactions. A close-distance interaction (CDI) model is included in the particle–particle collision analysis, which considers the liquid interstitial effect on colliding particles. Effects of the pressure and solids holdup on the bubble rise characteristics such as the bubble rise velocity, bubble shape and trajectory are examined. Simulations of the bubble rise velocity at various solids holdups and pressures are conducted along with the maximum stable bubble size and the particle–bubble interactions. The simulated results compare favorably with the experimental data and calculation from a mechanistic model.
On the rise velocity of bubbles in liquid-solid suspensions at elevated pressure and temperature
1997, Chemical Engineering ScienceExperiments are conducted to measure the rise velocity of single bubbles in liquid-solid suspensions at pressures up to 17 MPa and temperatures up to 88°C over the bubble size range from 1 to 20 mm. It is found that the bubble rise velocity decreases with increasing pressure and with decreasing temperature. The decrease of bubble rise velocity is due mainly to the variations of gas density and liquid viscosity with pressure and temperature. The presence of solid particles also reduces the rise velocity; the extent of reduction can be examined in terms of an increase in the apparent suspension viscosity by applying the homogeneous, Newtonian analogy. A mechanistic model is developed which considers a balance of forces acting on a single bubble, including the impact force due to solid particles, as well as buoyancy, gravity and liquid drag forces. Comparisons between the model predictions and the experimental data on the bubble rise velocity in liquid-solid fluidized beds are shown to be satisfactory.
Suspension viscosity and bubble rise velocity in liquid-solid fluidized beds
1997, Chemical Engineering ScienceThe effective viscosity which characterizes the pseudo-homogeneous property of the liquid-solid suspension in gas-liquid-solid fluidization is examined in light of the velocity of single bubbles rising through the suspension. Experiments conducted in this study cover a wide range of bubble diameters (2–23 mm) under high solids holdup (0.48 – 0.57) conditions. The study reveals that the liquid-solid medium exhibits a homogeneous, Newtonian property at any given solids holdup when the bubble diameters are greater than 12–17 mm. The effective viscosities obtained in this study based on equivalency of the single bubble rise velocity in Newtonian media as well as those reported in the literature are found to follow the Mooney-type relationship for solids holdup dependence. The two parameters underlying this relationship can be correlated as a function of the particle terminal velocity, particle shape and packed solids holdup. When the bubble diameters are smaller than 12–17 mm, the effective viscosity of the liquid-solid medium deviates from the viscosity of the corresponding Newtonian liquid. The deviation which marks the reduction in the bubble rise velocity reflects a significant close-range interaction between particles. In this bubble size range, the liquid-solid medium exhibits a non-Newtonian property characterized by shear-thinning behavior with flow .
Effect of solid particles on gas holdup in flotation columns-II. Investigation of mechanisms of gas holdup reduction in presence of solids
1995, Chemical Engineering SciencePart I showed that the presence of solids decreased gas holdup under conditions typical of flotation in columns. Four mechanisms which might explain this effect are evaluated here: bubble coalescence, slurry density and viscosity changes, changes in radial gas holdup and flow profiles, and bubble wake effects. The first two cannot explain the holdup decrease but the second two can. It was shown experimentally that solids do not cause bubbles to coalesce in flotation columns. Using the drift flux model, changes in density and viscosity of the slurry due to the presence of solids could not account for the observed reduction in gas holdup. A drift flux analysis for the gas-slurry system suggested both that the holdup and flow were not distributed uniformly and that the bubbles rose more rapidly in the presence of solids. Two gas holdup and flow profiles were postulated which could account for the lower gas holdup. These profiles had an upward flow in the center of the collumn and an annular downward flow near the wall. The bubble wake mechanism postulates that wake stability is increased in the presence of solids due to increased viscosity. This, in turn, increases the probability of in line bubble-bubble interaction where the wake velocity of the leading bubble increases the rise velocity of the trailing bubble. The resulting higher rise velocity reduces the gas holdup. It is proposed that the effect of solids on reducing gas holdup is a combination of an increase in the rise velocity of bubbles due to stabilization of the bubble wake and a change in the holdup and flow profiles from flat to non-uniform.
The effects of solids density and void fraction on the bubble rise velocity in a liquid-solid fluidized bed
1992, Chemical Engineering ScienceThe effects of solids density and void fraction on the bubble rise velocity of distorted spherical and circular-cap bubbles in two- and three-dimensional liquid-solid fluidized beds have been examined. Specific gravities of the solid phase ranged from 1.02 to 2.50, and the equivalent bubble diameter varied from 0.07 to 2.0 cm. Bubble rise velocities were found to decrease with increasing solids fraction and density and to increase with bubble size. The reduction in the bubble rise velocity due to the presence of the solid phase was semi-empirically modeled for bubble diameters greater than 0.20 cm using a virial expansion in the solids fraction. Smaller bubbles seemed to be influenced by local liquid flow patterns. The bubble rise velocity model was found to fit experimental results and literature values for solids fractions up to 0.43.