K.P. Galvin

Bubble nucleation from gas cavities : a review

Abstract This review is concerned with the nucleation of bubbles in solutions supersaturated with a gas, in particular the bubble nucleation that occurs at specific sites, as a cycle. A classification system for the kinds of nucleation that occur is defined and discussed in order to place this specific form of nucleation into a better defined context. It is noted that in the absence of pre-existing gas cavities, bubble nucleation requires exceedingly high levels of supersaturation. It is argued that the nucleation observed in most instances, which is often at low levels of supersaturation of 5 or less, is invariably associated with the existence of metastable gas cavities in the walls of the container or the solution bulk, prior to the system being made supersaturated. Here, the nucleation energy barrier for each gas cavity is very much lower than for the classical case, given that less interfacial free energy is needed for the cavity to grow to the critical size when the system is made supersaturated. Once a system contains gas cavities with radii of curvature greater than the critical nucleation radius, bubbles are produced in a steady fashion without the need to scale a nucleation energy barrier. This non-classical form of nucleation is the main focus of the paper. Issues concerning the formation of these gas filled cavities, and their stability are examined.

The effect of surface fog on the transmittance of light

Abstract It is shown theoretically that surface fog can reduce the transmittance of normally incident light through transparent materials from about 90% to nearly 50%. This result is also confirmed experimentally by reflectance measurements. The most important parameter is the contact angle which the droplets make with the surface. For contact angles less than about 40°, there is almost no loss in transmission. For larger contact angles, there is a significant decrease in the transmittance, with the worst case occurring for a contact angle of 90°.

The cycle of bubble production from a gas cavity in a supersaturated solution

Abstract Bubble nucleation, classified according to the review by Jones et al. (Adv. Colloid Interface Sci. 80 (1999) 27–50) as type IV non-classical, was examined in this study. Trains of bubbles were produced in carbonated water solutions at low levels of supersaturation, typically less than about 2, at specific sites on the surface of the vessel in contact with the liquid. Closer examination at a given site revealed a cycle of bubble formation, growth and detachment, defined by the growth time, t g , required for the bubble to grow to its detachment diameter, and the nucleation time, t n , required for a new bubble to appear following detachment. A relationship, representing the cycle of bubble production, was obtained by combining the bubble growth time, calculated using Scrivens model (Scriven, Chem. Eng. Sci. 10(1/2) (1959) 1–13), with the bubble nucleation time. That is, 1 t g = N t n + 1 t g * where N is a dimensionless number characterising the bubble nucleation time, and t g * is the growth time of the last possible bubble. Experiments conducted at a number of sites, and at different temperatures, produced results consistent with the above relationship. Most of the experiments were conducted with the contact angle at 65°, and these generally resulted in a bubble detachment diameter of about 600 μm, and a value of N ∼0.3. It was concluded that the nucleation time was dependent on the diameter of the detaching bubble. This dependence was explained by considering the volume of liquid, partially depleted of carbon dioxide, in the boundary layer of the bubble. Some of this partially depleted liquid should leave with the departing bubble, and the rest should remain above the gas cavity, thus slowing down the rate of bubble growth in the cavity. A consideration of the critical condition for bubble detachment indicated that the bubble remained rooted at the cavity mouth during its growth. It was shown, using the growth time of the last possible bubble, that the critical radius of curvature of the meniscus in the cavity was about 3.3 μm at 16°C. The radius was also found to increase significantly with temperature, suggesting that the position of the meniscus inside the cavity moved when the system temperature was changed, and that the cavity was essentially conical.

Dense medium separation using a teetered bed separator

Abstract A Teetered Bed Separator (TBS) was used autogenously, and with a range of media, to study the dense medium separation of a coal feed slurry, −2.00+0.375 mm in size. The feed slurry consisted of separate portions of a clean coal fraction, and a mineral matter fraction. A series of experiments were conducted using (i) the clean coal only, (ii) the clean coal combined with a portion of the mineral matter, (iii) the clean coal and mineral matter combined with dense media such as magnetite, or sand, or barite. These combinations of feeds provided a basis for assessing the benefits gained from using autogenous dense media, and a range of possible dense media. It was conluded that the TBS performance is improved by increasing the suspension density, and that this is best achieved by operating at the lowest possible water fluidization rate, and using a media with a settling velocity of similar magnitude to the settling velocities of the particles to be separated.

Pilot plant trial of the reflux classifier

Abstract The Ludowici LMPE Reflux Classifier is a new device designed for classifying and separating particles on the basis of size or density. This work presents a series of experimental results obtained from the first pilot scale study of the reflux classifier (RC). The main focus of the investigation was to assess the particle gravity separation and throughput performance of the device. In this study, the classifier was used to separate coal and mineral matter less than 2 mm in size. The experimental results were then compared with the performance data on a teetered bed separator (TBS). It was concluded that the classifier could offer an excellent gravity separation at a remarkably high solids throughput of 47 t / m 2 h more than 3 times higher than for a TBS. The separation performance of the RC was also better, with significantly less variation in the D50 with particle size. A simple theoretical model providing an explanation of the separation performance is also presented.

A generalized empirical description for particle slip velocities in liquid fluidized beds

Abstract An empirical equation for calculating the slip velocity of a species in any homogeneous suspension is proposed. The Richardson and Zaki (1954, Trans. Inst. Chem. Engng, 32, 35–53) and Lockett and Al-Habbooby (1973, Trans. Inst. Chem. Engng 51, 281–292; 1974, Powder Technol., 10, 67–71) equations are special cases of the proposed equation, and arise when all species are of the same density. Therefore, the main value of the proposed equation is in describing the slip velocities of particles in suspensions containing species of different density. In this short note results from one experimental system are presented, and shown to be consistent with the model. The model is also consistent with the explanation used by Moritomi et al. (1982) to account for phase inversion in fluidized beds. The model is appealing in its simplicity, and should find favour in the design and control of process equipment. The new model predicts the strong segregation effects observed in suspensions containing particles of different density, and hence represents an immediate improvement on the Lockett and Al-Habbooby equation. Its application is expected to cover all homogeneous suspensions, in which the particles are all more dense than the suspension. At this stage its validation has been limited to low concentrations of dense particles settling through a fluidized bed of low density particles as occurs in a Teetered Bed Separator, and to phase inversion conditions in fluidized beds. It is hoped that this note might lead to a much more extensive validation of the model by workers using vastly different particle species.

Use of X-rays to determine the distribution of particles in an operating cyclone

Abstract A new technique, based on the use of X-rays, was used to deduce the concentration distribution of particles (magnetite) at three elevations in a small glass cyclone operated at a feed specific gravity of 1.6. Good agreement between the image density profiles of the X-ray photographs and the image density profiles calculated on the basis of the radial concentration distributions was obtained. The average magnetite specific gravity increased as the diameter cross-section decreased, with specific gravities of 1.81, 1.96, and 2.08 at the three cross-section diameters of 29, 22 and 16 mm respectively.

Solid–solid contacts due to surface roughness and their effects on suspension behaviour

Solid–solid contacts due to microscopic surface roughness in viscous fluids were examined by observing the translational and rotational behaviours of a suspended sphere falling past a lighter sphere or down an inclined surface. In both cases, a roll–slip behaviour was observed, with the gravitational forces balanced by not only hydrodynamic forces but also normal and tangential solid–solid contact forces. Moreover, the nominal separation between the surfaces due to microscopic surface roughness elements is not constant but instead varies due to multiple roughness scales. By inverting the system, so that the heavy sphere fell away from the lighter sphere or the plane, it was found that the average nominal separation increases with increasing angle of inclination of the plane or the surface of the lighter sphere from horizontal; the larger asperities lift the sphere up from the opposing surface and then gravity at large angles of inclination is too weak to pull the sphere back down to the opposing surface before another large asperity is encountered. The existence of microscopic surface roughness and solid–solid contacts is shown to modify the rheological properties of suspensions. For example, the presence of compressive, but not tensile, contact forces removes the reversibility of sphere–sphere interactions and breaks the symmetry of the particle trajectories. As a result, suspensions of rough spheres exhibit normal stress differences that are absent for smooth spheres. For the conditions studied, surface roughness reduces the effective viscosity of a suspension by limiting the lubrication resistance during near–contact motion, and it also modifies the suspension microstructure and hydrodynamic diffusivity.

Influence of parallel inclined plates in a liquid fluidized bed system

We investigate the implications of installing a set of parallel inclined plates whitin a liquid fluidized bed, and discuss the benefits of such a design for a range of process systems.

The sliding of sessile and pendent droplets the critical condition

Abstract The critical condition for the sliding of sessile and pendent droplets down a solid substrate has been investigated. For sessile droplets it was found that sin αc scaled with V− 2 3 and that for pendent droplets sin αc scaled with V− where αc is the critical substrate angle and V is the droplet volume. Good agreement between experimental and theoretical values (Dussan Equation) was obtained for sessile droplets. For pendent droplets, however, such agreement was only possible by assuming that the droplet width was independent of the droplet volume.