An induction time model for the attachment of an air bubble to a hydrophobic sphere in aqueous solutions

A phenomenological model is developed to describe the induction time of an air bubble in contact with a hydrophobic sphere, based on an analytical solution of Reynolds approximation under the specific boundary conditions. A modified version of induction time apparatus is used to measure the induction time of an air bubble with a methylated silica bead, an untreated silica bead in dodecylamine solutions and a bitumen droplet in alkaline solutions. It was found that the induction time between an air bubble and a silica bead (or a bitumen droplet) increased with increasing bubble size. The bubble size dependence is stronger for the large silica beads (or bitumen droplets) tested. The induction time, obtained from two different methylated silica beads diameters, is used to estimate the average net driving force (F̄_o) for the intervening liquid film drainage and rupture and the critical film thickness (h_c) in the established model. Through curve fitting, the values for F̄_o and h_c are found to be 3.5×10⁻⁸ N and 150 nm, respectively, for a methylated silica–bubble system. The predicted values of critical film thickness and the net driving force for the systems used in this study are in excellent agreement with those reported in the literature, confirming the present theoretical analysis and model development. The suitability of using the liquid drainage time to represent the induction time, or the attachment time, is experimentally justified.     

Selective separation of very fine particles at a planar air–water interface

Selective fine particle separation is a key unit operation in the mineral and related industries. In flotation, the capture of fine particles by bubbles is inefficient due to their low mass and momentum, which result in low particle–bubble collision efficiency. We demonstrate that it is possible to selectively separate a mixture of very fine hydrophobic graphite and hydrophilic quartz particles by direct contact with an air–water interface without a particle–bubble collision step involved. We demonstrate that it is possible to scale-up the process from a simple batch to a continuous process. Good selective separation of graphite from quartz gangue could be obtained under continuous conditions.     

New method and equations for determining attachment tenacity and particle size limit in flotation

A new method and simple, yet accurate, equations for determining the tenacity of particle attachment and the particle size limit in flotation were developed by applying the force analysis of the gravity–capillarity coupling phenomena controlling the bubble–particle stability and detachment. Approximate solutions to the Young–Laplace equation were used to develop simple equations for the tenacity of attachment of particles with diameter up to 20 mm. Simple equations for the maximum size of floatable particles were derived as explicit functions of the particle contact angle, the surface tension, the particle density and the mean centrifugal acceleration of turbulent eddies. For the typical particle size and contact angle encountered in flotation, the analysis showed that the bubble size has little effect on the tenacity of particle attachment. The prediction for the largest size of floatable particles is compared with the experimental data and signifies influence of turbulence on the particle detachment.     

Some features of the streamer belt in the solar corona and at the Earth’s orbit

The rays of enhanced brightness making up the structure of the coronal-streamer belt can be traced to the lowest atmospheric layers in the Sun, with the angular size remaining nearly constant, d ≈ 2.5° ± 0.5°. This suggests that the physical mechanism generating the slow solar wind in the rays of the streamer belt differs from the mechanism giving rise to the fast solar wind from coronal holes. At distances of R < (4–5) R _⊙, the rays of the streamer belt are not radial in the plane of the sky and show deviations toward the corresponding pole. They then become essentially radial at R > (4–5) R _⊙. A transverse cross section of streamers in the corona and its continuation into the heliosphere—a plasma sheet—can be represented as two radially oriented, closely spaced rays (d ≈ 2.0°–2.5°) with enhanced density and an angular size of d. We also show that the ray structure of the streamer belt is involved in the development of coronal mass ejections (CMEs). The motion of a small-scale CME occurs within a magnetic flux tube (ray of enhanced brightness) and leads to an explosive increase in its angular size (rapid expansion of the tube). It seems likely that large-scale CMEs are the result of the simultaneous expansion of several magnetic tubes. We suggest that a small-scale CME corresponds to a “plasmoid” (clump of plasma of limited size with its own magnetic field) ejected into the base of a magnetic tube, which subsequently moves away from the Sun along the tube.     

Sorption of inorganic 14C on to calcite,montmorillonite and soil

Although ¹⁴C occurs naturally, it is also a waste product of the nuclear industry, and can be important because of its long half-life, high mobility as an anion, and ready incorporation into biota. Some aqueous inorganic species are anionic with migration minimally retarded by most geological and soil materials. Substantial retardation is expected when calcite is present, but there are few data to quantify this effect. The present study measured partition coefficient values, R_d (concentration on solids divided by concentration in liquids), of 8–85 l kg⁻¹ for a series of calcite materials and for a carbonated soil. In contrast, R_d was zero for montmorillonite. The series of calcite materials varied in particle size. In order to investigate the effects of particle size, dissolution and degassing of ¹⁴C and ¹²C were monitored as pH was slowly decreased. The change in pH with addition of acid was strongly affected by particle size, as expected, but there was no systematic effect of particle size on the relative dissolution rates of ¹⁴C vs ¹²C, or on R_d. Apparently, surface area was not a limiting factor in the interaction of ¹⁴C with these materials. The ¹⁴C in soil behaved most like the very fine calcite, indicating that the specific surface of the soil carbonate was similar to that of the very fine calcite.     

Onset of natural terrain landslides modelled by linear stability analysis of creeping slopes with a two-state variable friction law

This paper further examines the possibility of modelling landslide as a consequence of the unstable slip in a steadily creeping slope when it is subject to perturbations, such as those induced by rainfall and earthquakes. In particular, the one-state variable friction law used in the landslide analysis by Chau is extended to a two-state variable friction law. According to this state variable friction law, the shear strength (τ) along the slip surface depends on the creeping velocity (V) as well as the two state variables (θ₁ and θ₂), which evolve with the ongoing slip. For translational slides, a system of three coupled non-linear first-order ordinary differential equations is formulated, and a linear stability analysis is applied to study the stability in the neighbourhood of the equilibrium solution of the system. By employing the stability classification of Reyn for three-dimensional space, it is found that equilibrium state (or critical point) of a slope may change from a ‘stable spiral’ to a ‘saddle spiral with unstable plane focus’ through a transitional state called ‘converging vortex spiral’ (i.e. bifurcation occurs), as the non-linear parameters of the slip surface evolve with its environmental changes (such as those induced by rainfall or human activities). If the one-state variable friction law is used in landslide modelling, velocity strengthening (i.e. dτ_ss/dV > 0, where τ_ss is the steady-state shear stress) in the laboratory always implies the stability of a creeping slope containing the same slip surface under gravitational pull. This conclusion, however, does not apply if a two-state variable friction law is employed to model the sliding along the slip surface. In particular, neither the region of stable creeping slopes in the non-linear parameter space can be inferred by that of velocity strengthening, nor the unstable region by that of velocity weakening. Copyright © 1999 John Wiley & Sons, Ltd.     

Computation of surface energies in an electrostatic point charge model: I. Theory

The attachment energies, the slice energies and the specific surface energies can be calculated in an electrostatic point charge model using the formula derived by Madelung for the potential introduced by an infinite row of equally spaced point charges. Power series are given for the Hankel function iH ₍₀₎ ⁽¹⁾ (iy) and Ψ(x)=d ln x!/dx. The logarithmic expression in the Madelung formula converges rapidly when applying a power series, which combines equally charged cations and anions. Besides the specific surface energy (γ ^hkl), the slice energy (E _s ^hkl ) and the attachment energy (E _a ^hkl ) can be considered as special categories of surface energies as they depend on surface configurations as well. The specific surface energy γ is the energy per unit area of surface needed to split the crystal parallel to a face (hkl). The attachment energy (E _a) is the energy released per mole, when a new slice of thickness d _hkl crystallizes on an already existing crystal face (hkl). The growth rate of the crystal face (hkl) is a function of its attachment energy. The slice energy (E _s) is the energy released per mole, when a new slice d _hkl is formed from the vapour neglecting the influence of edge energies. The lattice energy (E _c) which is the energy released per mole of a crystal crystallizing from the vapour, is given by the following relation: E _c=E _a+E _s.     

Effect of Model Scale and Particle Size Distribution on PFC3D Simulation Results

This paper investigates the effect of model scale and particle size distribution on the simulated macroscopic mechanical properties, unconfined compressive strength (UCS), Young’s modulus and Poisson’s ratio, using the three-dimensional particle flow code (PFC3D). Four different maximum to minimum particle size (d _max/d _min) ratios, all having a continuous uniform size distribution, were considered and seven model (specimen) diameter to median particle size ratios (L/d) were studied for each d _max/d _min ratio. The results indicate that the coefficients of variation (COVs) of the simulated macroscopic mechanical properties using PFC3D decrease significantly as L/d increases. The results also indicate that the simulated mechanical properties using PFC3D show much lower COVs than those in PFC2D at all model scales. The average simulated UCS and Young’s modulus using the default PFC3D procedure keep increasing with larger L/d, although the rate of increase decreases with larger L/d. This is mainly caused by the decrease of model porosity with larger L/d associated with the default PFC3D method and the better balanced contact force chains at larger L/d. After the effect of model porosity is eliminated, the results on the net model scale effect indicate that the average simulated UCS still increases with larger L/d but the rate is much smaller, the average simulated Young’s modulus decreases with larger L/d instead, and the average simulated Poisson’s ratio versus L/d relationship remains about the same. Particle size distribution also affects the simulated macroscopic mechanical properties, larger d _max/d _min leading to greater average simulated UCS and Young’s modulus and smaller average simulated Poisson’s ratio, and the changing rates become smaller at larger d _max/d _min. This study shows that it is important to properly consider the effect of model scale and particle size distribution in PFC3D simulations.     

Partial mixing in early-type main-sequence B stars

Partial mixing of material in the radiative envelopes and convective cores of rotating main sequence stars with masses of 8 and 16 M _⊙ is considered as a function of the inital angular momentum of the stars. Losses of rotational kinetic energy to the generation of shear turbulence in the radiative envelope and the subsequent mixing of material in the envelope are taken into account. With an initial equatorial rotational velocity of 100 km/s, partial mixing develops in the upper part of the layer with variable chemical composition and the lower part of the chemically homogeneous radiative envelope. When the initial equatorial rotational velocity is 150–250 km/s, the joint action of shear turbulence and semi-convection leads to partial mixing in the radiative envelope and central parts of the star. The surface abundance of helium is enhanced, with this effect increasing with the angular momentum of the star. With an initial equatorial rotational velocity of 250 km/s, the ratio of the surface abundances of helium and hydrogen grows by ~30% and ~70% toward the end of the main-sequence evolution of an 8 M _⊙ and 16 M _⊙ star, respectively. The transformation of rotational kinetic energy into the energy of partial mixing increases with the angular momentum of the star, but does not exceed ~2%?3% in the cases considered.     

Meridional circulation in young massive stars with laminar rotation

We study the rotation of a chemically homogeneous star with a mass of 16M_⊙, assuming that the angular-momentum distribution in its radiative envelope is determined by hydrodynamical processes—flows and turbulent diffusion. Meridional circulation and horizontal shear turbulence are the main hydrodynamical processes forming the radial distribution of the angular momentum in young massive stars in the absence of magnetic fields. The rotation of such stars is close to steady-state. The angular velocity of rotation of the convective core can be ～5–20% higher than the surface value. Under these conditions, the characteristic time for the radial transport of angular momentum by meridional flows and shear turbulence is comparable to the nuclear time scale.     

Kinetics of bubble collision and attachment to hydrophobic solids: I. Effect of surface roughness

Influence of surface roughness of the Teflon plates on kinetics of the bubble attachment was studied. Phenomena occurring during collisions of the air bubble, rising in clean water, with Teflon plates, differing only in their surface roughness, were recorded and analysed using a high-speed camera. Variations of the local velocity of the bubble during the collisions and the time of the bubble attachment were determined. It was found that the Teflon surface roughness was the parameter of a crucial importance for the attachment time of the colliding bubble. Depending on degree of the surface roughness the time of the attachment varied by over order of magnitude (from 3 to over 80 ms). In the case the Teflon surfaces having roughness below 1 μm there were recorded four to five “approach–bounce” cycles prior to the bubble attachment. Moreover, after the first collision the rapid pulsations of the bubble shape (within fraction of millisecond) were recorded. For surfaces of roughness ca. 50 μm and larger the attachment always occurred during the first collision—there was no bouncing observed and the time of the attachment was below 3 ms. It was documented that presence of a micro-bubble at the surface facilitated attachment of the colliding bubble.     

Modeling the behaviour of alluvial and blasted quarried rockfill materials

Two types of modeled rockfill materials were collected from Renuka dam site, Himachal Pradesh, India and Salma dam site, Afghanistan. The rockfill material collected from Renuka dam site is rounded to sub-rounded in shape and the rockfill material collected from Salma dam site is angular to sub-angular in shape. The prototype gradation rockfill material consists maximum particle size larger than 1,000 mm. Therefore, for carrying out laboratory testing and modeling the bahaviour, the prototype rockfill material is scaled down to the maximum particle size (d_max) of 25, 50 and 80 mm for both projects material using parallel gradation technique. Triaxial compression and Index properties tests were conducted on both project rockfill materials and are presented. From the triaxial behaviour, it is observed that the stress–strain behaviour is non-linear, inelastic and stress dependent for both the materials. The material compresses during the initial shearing and shows dilation effect with further shearing. It is observed that the ?-value for alluvial rockfill material increases with increase in d_max and reverse trend is observed for blasted quarried rockfill material which shows the importance of the type of material. The stress–strain-volume change behaviour of both projects modeled rockfill material was predicted by using hierarchical single surface (HISS) model based on elasto plasticity and compared with the laboratory test results. From the comparison, it is observed that both results match closely. It is, therefore, suggested that the behaviour of both types of rockfill materials can be characterized successfully using HISS model.     

Flow slides run-out prediction using a sliding-consolidation model

The estimation of maximum travel distance of flow slides is an important topic to assess the consequence of natural disasters caused by landslides. During debris transportation, dissipation rules of pore-water pressure determine movement properties of flow slides. Based on 1-D Terzaghi consolidation theory, expressions of excess pore-water pressure with three cases of initial conditions are deduced and are programmed using Mathematica^® language. Furthermore, the factors affecting the distribution of pore-water pressure are studied using nondimensional method interactively, such as z/h, u _b /u _a , and T _v , which are fairly significant to investigate soil consolidation during the movement of flow slides. On the basis of the sliding-consolidation model first provided as reported by Hutchinson (Can. Geotech. J. 23(2):115-126, 1986), equations of pore-water pressure, velocity, and travel distance of flow slides are obtained and the physical quantities are coded as mathematical functions using Mathematica^® language characterized by its user-friendly interfaces to study run-out properties of flow slides very easily. The program can be used to compute velocity of flow slide, time, and pore-water pressure at a certain position, and thus judge automatically when and where flow slide will stop on slopes with different slope angles, solving the computing difficulties encountered during the Hutchinson's model application, especially in the last decades when computing technique with computers did not develop so rapidly as at present. At last, back analysis for properties of the 1966 flow slide at Aberfan, South Wales is done to test the model and the program, whose results are compared with those as reported by Hutchinson (Can. Geotech. J. 23(2):115-126, 1986). The results show that the program developed by the authors makes the application of Hutchinson's model more correct and easier.     

Electrochemical studies of sulphides,I. The electrocatalytic activity of galena,pyrite and cobalt sulphide for oxygen reduction in relation to xanthate adsorption and flotation

The electrocatalytic activity of galena, pyrite and Co₃S₄ for oxygen reduction has been studied by potentiostatic methods. Open circuit potentials of the sulphide electrodes have also been measured as a function of pH in nitrogen, air and oxygen atmospheres and also in the presence of H₂O₂ and ethyl xanthate. The adsorption of xanthate on sulphides was followed by observing bubble attachment to the electrodes.The catalytic activity for oxygen (or H₂O₂) reduction (the cathodic currents), the electrode potentials and the xanthate adsorption as shown by bubble attachment within certain pH limits, all varied as $\text{Co}{}_3\text{S}{}_4\text{> pyrite (≈ PbS in H}{}_2\text{O}{}_2\text{) ? PbS}$ indicating considerable dependence of the redox processes in flotation on the d - electron character of the sulphides.In the absence of oxygen, xanthate is probably bonded to the water structure of the surface through hydrogen-bonding, thus keeping the surface hydrophilic. Such adsorption reduces the electrode potential and inhibits oxygen reduction.     

On leakage and seepage of CO2 from geologic storage sites into surface water

Geologic carbon sequestration is the capture of anthropogenic carbon dioxide (CO₂) and its storage in deep geologic formations. The processes of CO₂ seepage into surface water after migration through water-saturated sediments are reviewed. Natural CO₂ and CH₄ fluxes are pervasive in surface-water environments and are good analogues to potential leakage and seepage of CO₂. Buoyancy-driven bubble rise in surface water reaches a maximum velocity of approximately 30 cm s⁻¹. CO₂ rise in saturated porous media tends to occur as channel flow rather than bubble flow. A comparison of ebullition versus dispersive gas transport for CO₂ and CH₄ shows that bubble flow will dominate over dispersion in surface water. Gaseous CO₂ solubility in variable-salinity waters decreases as pressure decreases leading to greater likelihood of ebullition and bubble flow in surface water as CO₂ migrates upward.     

Relationships Between Abrasion Index and Shape Properties of Progressively Abraded Dolerite Railway Ballasts

Sub-angular-shaped aggregates are used as rail foundation ballasts and must remain sub-angular during their service life time to maintain particle–particle interlocking, in order to ensure the stability of the rail line and prevent accidents by derailment. Here, the screening of dolerite quarry aggregates for use as railway foundation ballasts was investigated by employing simple digital image and chart methods. The average particle size (d ₅₀), flakiness index (FI), Los Angeles abrasion index (LAAI), sphericity (SPH) and roundness (RND) were determined for two batches of dolerite ballasts from the Rooikraal quarry in Johannesburg and Ngagane quarry in Newcastle. Thirty samples from each of the two batches of ballast were analysed. The ballasts were progressively abraded using a Los Angeles abrasion device and were analysed after each cycle of abrasion. A decrease in d ₅₀ and an increase in FI with increased number of abrasion cycles were observed for both batches of dolerite ballast. The difference in the chart and digital image values of RND and SPH were marginal before abrasion; however, these differences increased with each abrasion cycle. The LAAI, d ₅₀, mean RND and mean SPH correlated significantly and were found to have high regression coefficients. Thus, statistical models are proposed for the non-destructive routine screening of in-place ballasts in order to track marginal changes in aggregate shapes, facilitate ballast replacement programmes and avoid rail line instability.     

Surface wave studies for shear wave velocity and bedrock depth estimation over basalts

Shear wave velocity (V _S) estimation is of paramount importance in earthquake hazard assessment and other geotechnical/geo engineering studies. In our study, the shear wave velocity was estimated from ground roll using multichannel analysis of surface wave (MASW) technique making use of dispersive characteristics of Rayleigh type surface waves followed by imaging the shallow subsurface basaltic layers in an earthquake-prone region near Jabalpur, India. The reliability of MASW depends on the accurate determination of phase velocities for horizontally traveling fundamental mode Rayleigh waves. Inversion of data from surface waves resulted in a shear wave velocity (V _S) in the range of 200–1,200 m/s covering the top soil to weathering and up to bedrock corresponding to a depth of 10–30 m. The P-wave velocity (V _P) obtained from refraction seismic studies at these locations found to be comparable with V _S at an assumed specific Poisson’s ratio. A pair of selected set of V _S profiles over basalt which did not result in a hazardous situation in an earthquake of moderate magnitude are presented here as a case study; in other words, the shear wave velocity range of more than 200 m/s indicate that the area is highly unlikely prone to liquefaction during a moderate or strong earthquake. The estimated depth to basalt is found to be 10–12 m in both the cases which is also supported by refraction studies.     

Shear wave velocity imaging of landslide debris deposited on an erodible bed and possible movement mechanism for a loess landslide in Jingyang,Xi’an,China

The South Jingyang Plateau, with a total area of 70 km², is located in Shaanxi Province, China. Since 1976, more than 50 landslides of different types have occurred repeatedly on the edge slopes of the plateau due to the start of diversion irrigation on the plateau, resulting in great loss of lives and property. To better understand the initiation and movement mechanisms of these loess landslides, we surveyed them and carried out a detailed investigation of a large landslide in the Xihetan area. Our field survey results revealed that although most of these landslides had a long runout with high mobility, most of the landslide materials originating from the edge slopes may have been in an unsaturated state when the landslide occurred. This suggests that the materials at the toe of the edge slope as well as on the travel path along the river terrace might have played a key role in landslide movement. To examine how the materials on the travel path were involved in the landsliding, we used a multichannel surface wave technique and surveyed shear wave velocity (V _s ) profiles of the landslide deposits. We also examined the internal geometry of the deposits that outcropped on the right-side slope of the landslide foot. The longitudinal profile of V _s along the direction of movement showed that terrace deposits near the toe of the edge slope may have been sheared upward, indicating that at the toe, the surface of rupture might be located inside the terrace deposits. The V _s contours showed an A-shaped fold within the landslide deposits in the middle part of the travel path and became greater in the most distal toe part. The V _s profile across the deposits showed a U-shaped belt, in which the soil layers have smaller V _s . This belt may be the boundary between the sliding landslide debris and terrace deposits. The observed internal geometry of the landslide deposits indicates that a sliding surface developed within the sandy layer underlying the gravel layer. Therefore, we inferred that after failure, the displaced landslide materials overrode and sheared the terrace deposits along its main sliding direction, resulting in the formation of thrust folds within the terrace deposits, and greater V _s on the distal toe part of the landslide.     

An integrated law of the wall for hydrodynamically transitional flow over plane beds

The velocity profile for unidirectional currents is usually determined by two forms of the law of the wall, which are valid for smooth and rough boundaries, respectively. The law of the wall for smooth boundaries outside the viscous sublayer and buffer layer applies where the boundary Reynolds number (Re_*) is less than 5. The velocity in this case depends only on the dimensionless distance (y_d) from the bottom. For rough boundaries where Re_* is more than 65, the law of the wall is independent of the boundary Reynolds number, but the bottom roughness (k) has to be taken into account. The mean or median particle grain size (D) is commonly substituted for bottom roughness. At present, there is no generally accepted law of the wall for the transitional flow regime between hydrodynamically smooth and rough conditions. In this paper, an integrated law of the wall is proposed for the transitional regime, yielding velocity profiles that correspond well to observed velocity profiles under these conditions. The result is applied to a set of flume data, using an improved procedure to determine the bedload transport rate.