Interceptional and gravitational collision efficiencies for single collectors at intermediate Reynolds numbers

Water-to-Air Transfer of Nano/Microsized Particulates: Enrichment Effect in Bubble Bursting Jet Drops

Bubbles dispersed in liquids are widely present in many natural and industrial processes and play a key role in mediating mass transfer during their lifetime from formation to rising to bursting. In particular, nano/microsized particulates and organisms present in the bulk water can be highly enriched in the jet drops ejected during bubble bursting, impacting global climate and public health. However, the detailed mechanism of this enrichment remains obscure with the enrichment factor being difficult to predict. Here, we experimentally investigate the enrichment of nano/microsized particles in bubble bursting jet drops and highlight the underlying hydrodynamic mechanism, combining the effects of bubble scavenge and bursting on the transport of particles. Scaling laws for the enrichment factor are subsequently proposed that describe both our and prior experimental results reasonably well. Our study may provide new insights for water-to-air transfer of bulk particulates such as microbes related to bubble bursting.

Recent Developments in Generation, Detection and Application of Nanobubbles in Flotation

This paper reviews recent developments in the fundamental understating of ultrafine (nano) bubbles (NBs) and presents technological advances and reagent types used for their generation in flotation. The generation of NBs using various approaches including ultrasonication, solvent exchange, temperature change, hydrodynamic cavitation, and electrolysis was assessed. Most importantly, restrictions and opportunities with respect to the detection of NBs were comprehensively reviewed, focusing on various characterization techniques such as the laser particle size analyzer (LPSA), nanoparticle tracking (NTA), dynamic light scattering (DLS), zeta-phase light scattering (ZPALS), and zeta sizer. As a key feature, types and possible mechanisms of surfactants applied to stabilize NBs were also explored. Furthermore, flotation-assisted nano-bubbles was reported as an efficient method for recovering minerals, with a special focus on flotation kinetics. It was found that most researchers reported the existence and formation of NBs by different techniques, but there is not enough information on an accurate measurement of their size distribution and their commonly used reagents. It was also recognized that a suitable method for generating NBs, at a high rate and with a low cost, remains a technical challenge in flotation. The application of hydrodynamic cavitation based on a venturi tube and using the LPSA and NTA in laboratory scales were identified as the most predominant approaches for the generation and detection of NBs, respectively. In this regard, neither pilot- nor industrial-scale case studies were found in the literature; they were only highlighted as future works. Although the NB-stabilizing effects of electrolytes have been well-explored, the mechanisms related to surfactants remain the issue of further investigation. The effectiveness of the NB-assisted flotation processes has been mostly addressed for single minerals, and only a few works have been reported for bulk materials. Finally, we believe that the current review paves the way for an appropriate selection of generating and detecting ultrafine bubbles and shines the light on a profound understanding of its effectiveness.

Effect of Bubble Surface Properties on Bubble–Particle Collision Efficiency in Froth Flotation

In research on the particle–bubble collision process, due to the adsorption of surfactants and impurities (such as mineral particles, slime, etc.), most studies consider the bubble surface environment to be immobile. However, in the real situation of froth flotation, the nature of the bubble surface (degree of slip) is unknown. Mobile surface bubbles increase the critical thickness of the hydration film rupture between particles and bubbles, and enhance the collision between particles and bubbles. Sam (1996) showed that when the diameter of the bubble is large enough, a part of the surface of the bubble can be transformed into a mobile state. When the bubble rises in a surfactant solution, the surface pollutants are swept to the end of the bubble, so when the bubble reaches terminal velocity, the upper surface of the bubble is changed into a mobile surface. This paper analyzes the collision efficiency and fluid flow pattern of bubbles with mobile and immobile surfaces, and expounds the influence of surface properties on collision efficiency.

Computer simulations of particle-bubble interactions and particle sliding using Discrete Element Method

Three dimensional Discrete Element Method (DEM) computer simulations have been carried out to analyse the kinetics of collision of multiple particles against a stationary bubble and the sliding of the particles over the bubble surface. This is the first time that a computational analysis of the sliding time and particle packing arrangements of multiple particles on the surface of a bubble has been carried out. The collision kinetics of monodisperse (33 μm in radius) and polydisperse (12-33 μm in radius) particle systems have been analysed in terms of the time taken by 10%, 50% and 100% of the particles to collide against the bubble. The dependencies of these collision times on the strength of hydrophobic interactions follow relationships close to power laws. However, minimal sensitivity of the collision times to particle size was found when linear and square relationships of the hydrophobic force with particles radius were considered. The sliding time for single particles has corroborated published theoretical expressions. Finally, a good qualitative comparison with experiments has been observed with respect to the particle packing at the bottom of the bubble after sliding demonstrating the usefulness of computer simulations in the studies of particle-bubble systems.

Dynamic aspects of small bubble and hydrophilic solid encounters

The capture of solid particles suspended in aqueous solution by rising gas bubbles involves hydrodynamic and physicochemical processes that are central to colloid science. Of the collision, attachment and aggregate stability aspects to the bubble-particle interaction, the crucial attachment process is least understood. This is especially true of hydrophilic solids. We review the current literature regarding each component of the bubble-particle attachment process, from the free-rise of a small, clean single bubble, to the collision, film drainage and interactions which dominate the attachment rate. There is a particular focus on recent studies which employ single, very small bubbles as analysis probes, enabling the dynamic bubble-hydrophilic particle interaction to be investigated, avoiding complications which arise from fluid inertia, deformation of the liquid-vapour interface and the possibility of surfactant contamination.

Entrapment efficiencies of hydrodynamic boundary layers on rising bubbles

Flotation and separation practice shows that fine hydrophilic solids are often drawn into the froth product. The occurrence of this unwanted event in the classical froth flotation has led to the idea of using it for the separation by size of ground materials. Thus, a method for the extraction of hydrophilic fines by foaming of a suspension was proposed. The aim of the present study is to relate this phenomenon to the residence time of the particles in the vicinities of the rising bubbles. Dynamic interactions of fine solids with rising bubbles cause perturbations in the background flow field. A procedure for the mathematical modeling of these disturbance effects is proposed. The initial idea is that the particles lag behind the background bubble-driven flows. A key point is the possibility of classifying fine entities according to a general criterion, containing only parameters of the outer flow. The basic result is that there exists a range of particle and bubble dimensions for which this entrapment is optimal. The proposed model investigation gives a concise explanation for the observed capture of fine solids in many flotation and separation processes.

Effect of surface mobility on the particle sliding along a bubble or a solid sphere

The sliding velocity of glass beads on a spherical surface, made either of an air bubble or of a glass sphere held stationary, is measured to investigate the effect of surface mobility on the particle sliding velocity. The sliding process is recorded with a digital camera and analyzed frame by frame. The sliding glass bead was found to accelerate with increasing angular position on the collector's surface. It reaches a maximum velocity at an angular position of about 100 degrees and then, under certain conditions, the glass bead leaves the surface of the collector. The sliding velocity of the glass bead depends strongly on the surface mobility of a bubble, decreasing with decreasing surface mobility. By a mobile surface we mean one which cannot set up resistive forces to an applied stress on the surface. The sliding velocity on a rigid surface, such as a glass sphere, is much lower than that on a mobile bubble surface. The sliding velocity can be described through a modified Stokes equation. A numerical factor in the modified Stokes equation is determined by fitting the experimental data and is found to increase with decreasing surface mobility. Hydrophobic glass beads sliding on a hydrophobic glass sphere were found to stick at the point of impact without sliding if the initial angular position of the impact is less than some specific angle, which is defined as the critical sticking angle. The sticking of the glass beads can be attributed to the capillary contracting force created by the formation of a cavity due to spontaneous receding of the nonwetting liquid from the contact zone. The relationship between the critical sticking angle and the particle size is established based on the Yushchenko [J. Colloid Interface Sci. 96 (1983) 307] analysis.

Studies on oxygen mass transfer in stirred bioreactors 2: Suspensions of bacteria, yeasts and fungis

The aim of these experiments is to study the oxygen mass transfer rate by means of the mass transfer coefficient, for a stirred bioreactor and different fermentation broths, using a large domain of operating variables. For quantifying the effects of the considered factors (concentration and morphology of the biomass, specific power input, superficial air velocity surface aeration) on k\a, the experiments were carried out for non-respirating biomass suspensions of Propionibacterium shermanii Saccharomyces cerevisiae and Penicillium chrysogenum, mycelial aggregates (pellets) and free mycelia morphological structures.

Deposition of Particles in the Impinging-Jet Cell for the High Coverage Regime

Particle deposition in the radial impinging-jet cell for the high coverage regime was studied theoretically and experimentally. A detailed description of the flow distribution in the cell was attained by solving the governing Navier-Stokes equation numerically. The macroscopic flow pattern was decomposed into simpler local flows. It was demonstrated that for tangential distances r/R>0.5 the overall flow at the interface was dominated by the simple shear. The intensity of this flow was calculated numerically as a function of the Reynolds number and the distance from the cell center. Knowing the fluid velocity field the convective diffusion equation was formulated describing a two-dimensional transport of particles. As a result of nonlinearity of the boundary condition this equation was solved in an exact manner for low coverage only. For higher coverage, approximate methods were proposed exploiting the random sequential adsorption (RSA) approach. The validity of the theoretical predictions was verified experimentally using the direct microscope observation method and polystyrene latex particles of the size 0.87 mum. Particle coverage distribution was studied in detail as a function of the Re number governing the local shear rate. It was demonstrated that for low Re number (Re<4) uniform particle monolayers of high coverage can be attained. On the other hand, for Re>8 the particle coverage distribution became nonuniform as a result of the hydrodynamic scattering. This effect, leading to an apparent kinetic saturation of the surface at coverages of a few percents, was quantitatively interpreted in terms of the theoretical model.

Wetting film stability and flotation kinetics

Single bubble experiments performed with different size fractions of quartz particles and different, but known, contact angles revealed two modes of flotation dynamics in superclean water. (1.) A monotonic increase of collection efficiency Ecoll with increasing particle size was observed at high particle hydrophobicity and, correspondingly, a low wetting film stability (WFS). (2.) At low particle hydrophobicity and, correspondingly, high WFS, an extreme dependence of Ecoll on particle size was observed. The use of superclean water in our experiments prevented the retardation of bubble surface movement caused by surfactants or other impurities that is usual for other investigations and where particle-bubble inertial hydrodynamic interactions are suppressed. In the present study the free movement of the bubble surface enhances particle-bubble inertial interaction, creating conditions for different flotation modes, dependent on WFS. At the instant of inertial impact, a particle deforms the bubble surface, which may cause its rebound. Where the stability of the thin water film, formed between opposing surfaces of a bubble and a particle, is low, its rupture is accompanied with three phase contact line extension and contact angle formation before rebound. This prevents rebound, i.e. the first collision is accompanied by attachment. A high WFS prevents rupture during an impact. As a result, a contact angle does not arise and rebound is not prevented. However, rebound is accompanied by a second collision, the kinetic energy of which is smaller and can cause attachment at repetitive collision. These qualitative considerations are confirmed by the model quantification and comparison with measured Ecoll. For the first time the Sutherland equation (SE) for Ecoll is confirmed by experiment for smaller particle sizes and, correspondingly, very small Stokes numbers. The larger the particle size, the larger is the measured deviation from the SE. The SE is generalized, accounting for the centrifugal force, pressing hydrodynamic force and drainage in the low WFS case and, correspondingly, attachment occurs at first collision or during sliding. The derived generalized Sutherland equation (GSE) describes experimental data at low WFS. However, its application without account for possible rebound does not explain the measured extreme dependence in the case of high WFS. The theory for drainage during particle impact and the beginning of rebound enables conditions for either attachment or rebound in terms of the normal component of the impact velocity and the critical film thickness to be derived. Combining this condition with the GSE allowed the equation for Ecoll to be derived, accounting for attachment area shrinkage and attachment during a repetitive collision. This equation predicts the extreme dependence. Thus the WFS determines the modes of flotation dynamics and, in turn, probably affects the mechanisms, which control the flotation domain. At low WFS its upper boundary is controlled by the stability of the particle-bubble aggregate. At high WFS the upper boundary can be controlled by rebound because the latter reduces the attachment efficiency by a factor of 30 or more even with repetitive collision.

Particle-bubble collision models--a review

A critical review of the various models existing in the literature for the calculation of the collision efficiency between particles and single, rising gas bubbles is presented. Although all of these collision models predict that the collision efficiency increases with particle size, their dependence on the latter is different because of the various assumptions and hydrodynamic conditions used in each model. Collision efficiencies of quartz particles with single bubbles have been obtained from experimental flotation experiments under conditions where the attachment and stability efficiencies were at, or near, unity. These collision efficiencies were then used to test various collision models. Good agreement between the experimental and calculated collision efficiencies was only obtained with the Generalised Sutherland Equation. The differences in collision efficiencies obtained between the various models were mainly explained in terms of, firstly, the degree of mobility of the bubble surface and, secondly, a consideration of the inertial forces acting on the particles.

Exact and Approximate Expressions for Bubble-Particle Collision

The flotation microprocess of collision is investigated and an exact expression for the probability of collision (Pc) is developed based on the intermediate flow of Yoon and Luttrell (1). This expression for Pc only assumes that the bubble and particle are spherical and that the particle radius is less than the bubble radius (i.e., Rp < RB). In addition to removing the requirement that Rp << RB, the influence of a particle settling velocity is also included in the model development. The expression for Pc is shown to be a function of three dimensionless groups: (i) the magnitude of the dimensionless particle settling velocity, ||G ||; (ii) the bubble Reynolds number, ReB; and (iii) the ratio of particle to bubble radius, Rp/RB. The probability of collision model is compared to available experimental data and good agreement is shown. A parametric study is also completed for 0 </= ||G || </= 1, 0 </= ReB </= 500, and 0.001 </= Rp/RB < 1. In general, Pc is independent of ReB when Rp/RB less, similar 0.03, the particle settling velocity is important for small values of Rp/RB, and Rp/RB dominates as Rp/RB --> 1. Copyright 1999 Academic Press.

Colloid Particle Adsorption in the Slot Impinging Jet Cell

A detailed description of flow distribution in the slot impinging jet cell (SIJ) is presented. Numerical solutions of the governing Navier-Stokes equation showed that for Re < 30 the flow resembles closely the one occurring near a cylinder placed in a uniform flow. It was also shown that for tangential distances x/d < 0.25 the flow configuration in the vicinity of the solid can be approximated by the plane-parallel stagnation flow with the perpendicular velocity component independent of this distance. This flow field was used for deriving the mass transfer equation, which was then numerically solved to obtain the initial flux (adsorption rate) for various transport conditions. These theoretical predictions were verified experimentally using polystyrene latex particles of the size 1 and 1.48 µm. A good agreement between predicted and measured initial flux values was found for a broad range of Reynolds number and ionic strength of the particle suspension. This confirmed that the SIJ cell surface was uniformly accessible for particles at distances x/d < 0.5. At larger distances a systematic deviation from uniform deposition rates was observed, becoming important for higher coverages and Re. This effect was attributed to the hydrodynamic scattering of adsorbing particles on particles already attached to the surface. This phenomenon was quantitatively accounted for by the Brownian dynamics type simulations. Copyright 1999 Academic Press.