On the structure of collision and detachment frequencies in flotation models

New explicit analytical expressions are obtained for both the collision frequency and the bubble/particle detachment frequency which enter flotation separation models. The expression for the collision frequency takes into account both the particle settling velocity and the bubble rise velocity while that for the detachment frequency is motivated by analogous results for floc disruption in a turbulent flow field. In all the cases considered, it is shown that the inclusion of the particle settling velocity increases the collision frequency by a factor of approximately 1.5 and that the most significant factor affecting the collision frequency is the bubble radius.     

Diffusiophoresis of a colloidal sphere in nonelectrolyte gradients parallel to one or two plane walls

The quasisteady diffusiophoretic motion of a spherical particle in a fluid solution of a nonionic solute located between two infinite parallel plane walls is studied theoretically in the absence of fluid inertia and solute convection. The imposed solute concentration gradient is constant and parallel to the two plane walls, which may be either impermeable to the solute molecules or prescribed with the far-field concentration distribution. The particle-solute interaction layer at the particle surface is assumed to be thin relative to the particle radius and to the particle-wall gap widths, but the polarization effect of the diffuse solute in the thin interfacial layer caused by the strong adsorption of the solute is incorporated. The presence of the neighboring walls causes two basic effects on the particle velocity: first, the local solute concentration gradient on the particle surface is enhanced or reduced by the walls, thereby speeding up or slowing down the particle; secondly, the walls increase viscous retardation of the moving particle. To solve the continuity and momentum equations, the general solutions are constructed from the fundamental solutions in both the rectangular and the spherical coordinate systems. The boundary conditions are enforced first at the plane walls by the Fourier transforms and then on the particle surface by a collocation technique. Numerical results for the diffusiophoretic velocity of the particle relative to that under identical conditions in an unbounded fluid solution are presented for various values of the relaxation parameter of the particle as well as the relative separation distances between the particle and the two plates. For the special case of diffusiophoretic motions of a spherical particle parallel to a single plate and on the central plane of a slit, the collocation results agree well with the approximate analytical solutions obtained by using a method of reflections. The presence of the lateral walls can reduce or enhance the particle velocity, depending on the surface properties of the particle, the relative particle-wall separation distances, and the solutal boundary condition at the walls. In general, the boundary effect on diffusiophoresis is quite complicated and relatively weak in comparison with that on sedimentation.     

Spreading of an inviscid drop impacting on a liquid film

The evolution of the deforming liquid surface following the impact of a drop onto a film of the same liquid is analysed numerically using a boundary integral method assuming axisymmetric, inviscid flow. Surface tension and gravity are taken into account. At times comparable to, or larger than the impact time scale (based on initial drop radius and impact velocity), the section of the liquid surface bounded by the radially propagating crown or rim is predicted to approach a single central shape independent of film thickness. At times which are much smaller than the impact time scale, jetting behaviour is obtained in the neck region where the drop meets the film when the Weber number is large enough. The jet is found to move close to the film, and this suggests the possibility of bubble entrapment, confirming a previous report in the literature. The present results suggest the occurrence of a train of bubble rings from repeated near-reconnection events as the neck moves radially outwards under jetting conditions.     

Simulation and experiment of gas–solid flow field in short-contact cyclone reactors

A short-contact cyclone reactor has been designed for the particular case of fluid catalytic cracking. The new type reactor mainly includes two parts: a reaction chamber and a separation chamber. So the cracking reactions and the separations between the products and catalysts could occur respectively and simultaneously. A three dimensional model was used to representing key parts of a laboratory cyclone reactor. The Eulerian–Eulerian computational fluid dynamics model with the kinetic theory of granular flow was adopted to simulate the gas–solid two-phase flow. The particle concentration distribution and pressure drop were measured by a PV-6A particles velocity measure instrument and a U-manometer, respectively. Simulated results show that in the reaction chamber solids can be transformed into a homogeneous dispersed flow, particles’ concentration becomes uniform gradually while catalysts flowing down, the concentration is a little higher near the wall because of boundary effect. After the gas–solid flowing into the separation chamber, the gas phase is separated with solids completely. The new reactor has a good contact and separation effect. Simulated results make a reasonable agreement with the experimental findings.     

Investigation on the effects of fluid intensification based preconditioning process on the decarburization enhancement of fly ash

Fly ash (FA) is a complex and abundant solid waste created by humans, and has caused environmental issues, for which flotation is an effective technique employed before its comprehensive utilization. However, the complex and hydrophilic characteristics of FA particles cannot naturally fulfill the selective separation by common flotation. Therefore, this study aims to provide an insight into fluid intensification effects on flotation to achieve the enhancement of FA surface property and decarburization. The relevant effects and mechanisms are investigated, based on the measurements of zeta potential, infrared spectroscopy, contact/wrap angle, induction time, size distribution and scanning electron microscopy–energy dispersive spectrometry. Experimental results manifested that the maximum unburned carbon recovery (73.25%) and flotation rate (0.2037 s^-1) were achieved with preconditioning energy inputs of 14.23 and 6.57 W·kg^-1 respectively. With increasing preconditioning energy inputs, fluid intensification effects could promote the inter-particle collision/attrition, detachment of hydrophilic existence and collector adsorption on particles. Correspondingly, absorbance of some hydrophobic and hydrophilic functional groups was strengthened and weakened respectively, which accounted for the improved interfacial properties, reflected as the increased contact and wrap angles, together with declined induction time. Overall, this article revealed the positive influences of fluid intensification based preconditioning process on rendering particle surface hydrophobic and improving separation performance.     

Influences of fluid physical properties,solid particles,and operating conditions on the hydrodynamics in slurry reactors

Slurry reactors are popular in many industrial processes, involved with numerous chemical and biological mixtures, solid particles with different concentrations and properties, and a wide range of operating conditions. These factors can significantly affect the hydrodynamic in the slurry reactors, having remarkable effects on the design, scale-up, and operation of the slurry reactors. This article reviews the influences of fluid physical properties, solid particles, and operating conditions on the hydrodynamics in slurry reactors. Firstly, the influence of fluid properties, including the density and viscosity of the individual liquid and gas phases and the interfacial tension, has been reviewed. Secondly, the solid particle properties (i.e., concentration, density, size, wettability, and shape) on the hydrodynamics have been discussed in detail, and some vital but often ignored features, especially the influences of particle wettability and shape, as well as the variation of surface tension because of solid concentration alteration, are highlighted in this work. Thirdly, the variations of physical properties of fluids, hydrodynamics, and bubble behavior resulted from the temperature and pressure variations are also summarized, and the indirect influences of pressure on viscosity and surface tension are addressed systematically. Finally, conclusions and perspectives of these notable influences on the design and scale-up of industrial slurry reactors are presented.     

Liquid re-circulation in turbulent vertical pipe flow behind a cylindrical bluff body and a ventilated cavity attached to a sparger

The turbulent flow field (Re=60024) in the wake of a cylindrical bluff body in a 0.105 m internal diameter pipe with an area blockage ratio of 82% in turbulent single-phase flow was studied using laser Doppler velocimetry (LDV). The results for the time-averaged velocity showed a toroidal vortex below the bluff body. The axial location below the bluff body where both the time-averaged radial and axial velocity components were zero (eye of the vortex) was found at approximately 0.72D. The end of the re-circulation region as defined by a stagnation point on the centreline of the pipe was found at an axial location below the bluff body of approximately 1.3D. These two locations did not change when altering the liquid superficial velocity confirming that the geometry (i.e., size) of the toroidal vortex is not dependent on the superficial liquid velocity or the speed of the vortex.Similar measurements using LDV were taken in the wake of a ventilated cavity in a vertical 0.105 m internal diameter pipe, with an area blockage ratio of 80%. The flow beneath the cavity was turbulent two-phase bubbly flow and the liquid-only flow ahead of the cavity was turbulent (Re=45618). The cavity was attached to a (central) sparger, which is a scale-up of the design used by Bacon (1995). The average gas void fraction in the wake of the cavity was 7%. The results for the time-averaged velocity confirmed the formation of a toroidal vortex remarkably similar to the vortex formed below the bluff body. The eye of the vortex and the end of the re-circulation region were found at an axial location below the ventilated cavity of 0.78 and 1.35D, respectively, i.e., almost identical to the results for the bluff body.The LDV results of the cylindrical bluff body and the ventilated cavity were compared with the fully predictive model of the velocity distribution in the vortex proposed by Thorpe et al. (2001) and good agreement was found in both cases. The model also agreed well with the data of van Hout et al. (2002) for a Taylor bubble rising in stagnant liquid in a 0.025 m internal diameter pipe. The CFX simulations of Thorpe et al. (2001) carried out for a 0.050 m internal diameter pipe, agreed well with the experimental data of the cylindrical bluff body, the ventilated cavity and the data obtained by van Hout et al. (2002) when correlating the results in the appropriate dimensionless form. Our analysis showed that the maximum axial re-circulation velocity in the centre of the vortex ring was directly proportional to the mean velocity in the annulus at the base of the cylindrical bluff body, the ventilated cavity or the Taylor bubble. The proportionality constant for all cases was found to be approximately 0.38 confirming the value proposed by Thorpe et al. (2001).     

Influence of the turbulence model in CFD modeling of wall-to-fluid heat transfer in packed beds

Computational fluid dynamics as a simulation tool allows obtaining a more detailed view of the fluid flow and heat transfer mechanisms in fixed-bed reactors, through the resolution of 3D Reynolds averaged transport equations, together with a turbulence model when needed. In this way, this tool permits obtaining of mean and fluctuating flow and temperature values in any point of the bed. An important problem when modeling a turbulent flow fixed-bed reactor is to decide which turbulence model is the most accurate for this situation. To gain insight into this subject, this study presents a comparison between the performance in flow and heat transfer estimation of five different RANS turbulence models in a fixed bed composed of 44 homogeneous stacked spheres in a maximum space-occupying arrangement in a cylindrical container by solving the 3D Navier-Stokes and energy equations by means of a commercial finite volume code, Fluent 6.0^®. Air is chosen as flowing fluid. Numerical pressure drop, velocity and thermal fields within the bed are obtained. In order to judge the capabilities of these turbulence models, heat transfer parameters (Nu_w, k_r/k_f) are estimated from numerical data and together with the pressure drop are compared to commonly used correlations for parameter estimations in fixed-bed reactors.     

New techniques for measuring and modeling cavern dimensions in a Bingham plastic fluid

A model for predicting the mixing cavern dimensions for Bingham plastic fluids based on the assumption of equal torque is developed. Experimental data has been collected for the purpose of verifying this model, using a novel technique, for both axial and radial flow impellers in a tank of Heinz ketchup. The mixing caverns were found to be the shape of an elliptical torus. The ellipse aspect ratios were determined for both impeller types and are assumed to be constant. The model was able to predict the cavern diameter and cavern height within the experimental uncertainty.