Experimental and theoretical investigation of CO2 and air bubble rising velocity through kerosene and distilled water in bubble column

This paper concerns with developing of parameters which influence terminal velocities of air and CO₂ bubbles in distilled water and kerosene pools. The objective of this study is to validate and correct the formulas that were developed by previous investigators for prediction of terminal velocities. The investigation revealed that the terminal velocity of a single rigid spherical bubble in Newtonian fluids can be developed by balancing of mechanical forces acting on the bubble. However, for large bubbles, because of deforming of the bubble which is a result of interfacial tension, the effect of surface tension should be considered in the terminal velocity prediction formula. By using PSO algorithm and plotting experimental data of terminal velocity against the size of gas bubbles, the suitable equation for each of systems was chosen. Results showed that Jamialahmadi model is more practical for terminal velocity prediction. Jamialahmadi model requires a modification to be utilized for air-kerosene, CO₂-kerosene, air- distilled water and CO₂-distilled water systems. The developed PSO algorithm model is accurate for prediction of experimental data with an average R² value of 0.9722.     

Inhibition of bubble coalescence: effects of salt concentration and speed of approach

Bubble coalescence experiments have been performed using a sliding bubble apparatus, in which mm-sized bubbles in an aqueous electrolyte solution without added surfactant rose toward an air meniscus at different speeds obtained by varying the inclination of a closed glass cylinder containing the liquid. The coalescence times of single bubbles contacting the meniscus were monitored using a high speed camera. Results clearly show that stability against coalescence of colliding air bubbles is influenced by both the salt concentration and the approach speed of the bubbles. Contrary to the widespread belief that bubbles in pure water are unstable, we demonstrate that bubbles formed in highly purified water and colliding with the meniscus at very slow approach speeds can survive for minutes or even hours. At higher speeds, bubbles in water only survive for a few seconds, and at still higher speeds they coalesce instantly. Addition of a simple electrolyte (KCl) removes the low-speed stability and shifts the transition between transient stability and instant coalescence to higher approach speeds. At high electrolyte concentration no bubbles were observed to coalesce instantly. These observations are consistent with recent results of Yaminsky et al. (Langmuir 26 (2010) 8061) and the transitions between different regions of behavior are in semi-quantitative agreement with Yaminsky's model.     

Asymmetric deformation of bubble shape: cause or effect of vortex-shedding?

Two perpendicular projections of rising bubbles were observed in counter-current downstream diverging flow. Evidently, the bubbles did not enter the boundary layer at the channel wall and a plug liquid flow assumption was acceptable in our experimental equipment. This confirmed that the experiment was appropriate for simulation of bubble rises in a quiescent liquid column. Recent data obtained by a high-speed camera permitted recording over a period of 60 s. Image analysis by a tailor-made program provided a time-series of quantities related to the position, size, and shape of bubbles. In addition to determination of the aspect ratio of the equivalent oblate ellipsoid, deviation from this shape was investigated in respect of the difference between the bubble’s centre of mass and the geometrical centre of bubble projection. Autocorrelation of the data indicated that the bubble inclination oscillated harmonically with a frequency of 5–10 Hz; cross correlation showed that the horizontal shift of the centre of mass, as well as the horizontal velocity, increased with increasing bubble inclination, and the vertical shift of the centre of mass increased with an increases in the absolute value of the bubble inclination. There is no significant phase shift in the oscillation of these quantities. The bulky bottom side of the bubbles is in accordance with the model of bubble oscillation induced by instability of the equilibrium of gravity and surface tension forces. The oscillation frequency dependence on surface forces (Eötvös number) is evident, while viscosity does not play a significant role in low-viscosity liquids. Therefore, vortex-shedding is more likely to be an effect of the oscillation and not its cause.     

Movement of fine particles on an air bubble surface studied using high-speed video microscopy

A CCD high-speed video microscopy system operating at 1000 frames per second was used to obtain direct quantitative measurements of the trajectories of fine glass spheres on the surface of air bubbles. The glass spheres were rendered hydrophobic by a methylation process. Rupture of the intervening water film between a hydrophobic particle and an air bubble with the consequent formation of a three-phase contact was observed. The bubble-particle sliding attachment interaction is not satisfactorily described by the available theories. Surface forces had little effect on the particle sliding with a water film, which ruptured probably due to the submicrometer-sized gas bubbles existing at the hydrophobic particle-water interface.     

Interactions between two bubbles on a hot or cold wall

A temperature gradient normal to a planar wall produces two-dimensional motion and aggregation or separation of bubbles on the hot or cold wall, respectively. The origin of the motion is fluid convection driven by the thermal Marangoni stress on the surface of the bubbles. Previous theories for the dynamics of two or more bubbles have been based on an analysis of flow about a single bubble and the resulting convection that entrains its neighbors. Here we extend the theory by solving the quasi-steady equations for the temperature and velocity fields for two bubbles. The result is a quantitative model for the relative velocity between two bubbles as a function of both the distance between them and the gap between each bubble and the surface. Interactions between the bubbles strongly increase the approach velocity, which is counter-intuitive because the hydrodynamic resistance increases as the bubbles approach each other. An asymptotic analysis indicates the thermocapillary force bringing them together or pushing them apart is singular in the separation when the bubbles are close to each other. The two-bubble theory agrees reasonably well with the experimentally measured velocities of pairs of bubbles on hot or cold surfaces, though it slightly overestimates the velocities.     

Bubble colloidal AFM probes formed from ultrasonically generated bubbles

Here we introduce a simple and effective experimental approach to measuring the interaction forces between two small bubbles (approximately 80-140 microm) in aqueous solution during controlled collisions on the scale of micrometers to nanometers. The colloidal probe technique using atomic force microscopy (AFM) was extended to measure interaction forces between a cantilever-attached bubble and surface-attached bubbles of various sizes. By using an ultrasonic source, we generated numerous small bubbles on a mildly hydrophobic surface of a glass slide. A single bubble picked up with a strongly hydrophobized V-shaped cantilever was used as the colloidal probe. Sample force measurements were used to evaluate the pure water bubble cleanliness and the general consistency of the measurements.     

Thermocapillary Flow and Aggregation of Bubbles on a Solid Wall

Theory suggests that thermocapillary flow about neighboring bubbles in liquids on hot walls pulls the bubbles together. A temperature gradient perpendicular to the wall establishes a surface tension gradient at the bubble-liquid interface, which in turn sustains a shear stress gradient that pumps adjacent fluid away from the wall. Neighboring bubbles are mutually entrained in this flow and also respond thermophoretically to lateral temperature gradients in the temperature near field. The theory predicts that the aggregation velocity scales with the temperature gradient, the radius of the bubbles, the derivative of the surface tension with respect to temperature, and the reciprocal of the liquid's viscosity. Bubble aggregation experiments under controlled conditions were performed to test the theory. Scaling the experimental bubble trajectories according to the theory substantially collapses all of the data onto a master curve when the interbubble separation is greater than 3 radii, which suggests that the theory is correct. Calculated velocities agree with the experimental results when hindrance of bubble motion due to the wall is included. Values for the parameter that describes the hindrance effect are obtained from fitting the data to the theory, from independent measurements, and from direct hydrodynamic calculation. The results of the three determinations agree within 15% of the possible range of the value of the parameter. Copyright 2000 Academic Press.     

Sliding behavior of liquid droplets on tilted Langmuir-Blodgett surfaces

The sliding behavior of liquid droplets on inclined Langmuir-Blodgett surfaces was investigated. The critical sliding angle defined as the tilt angle of the surface at which the drop slides down as well as the advancing and receding contact angles was measured for five different liquids on five surfaces. In addition, the contact line geometry was analyzed at critical sliding angle. The experimental relationship between the surface tension forces resulting from contact angle hysteresis and the weight of the drop was compared to theoretical predictions. Even though the shape of the drop bases was found as skewed ellipses, a model assuming parallel-sided elongated drops is shown to describe reasonably the experimental values. This result probably indicates the main influence of the capillary forces at the rear and front edges of the drop with respect to that exerted on the lateral sides.     

Measurement and modeling on hydrodynamic forces and deformation of an air bubble approaching a solid sphere in liquids

The interaction between bubbles and solid surfaces is central to a broad range of industrial and biological processes. Various experimental techniques have been developed to measure the interactions of bubbles approaching solids in a liquid. A main challenge is to accurately and reliably control the relative motion over a wide range of hydrodynamic conditions and at the same time to determine the interaction forces, bubble–solid separation and bubble deformation. Existing experimental methods are able to focus only on one of the aspects of this problem, mostly for bubbles and particles with characteristic dimensions either below 100 μm or above 1 cm. As a result, either the interfacial deformations are measured directly with the forces being inferred from a model, or the forces are measured directly with the deformations to be deduced from the theory. The recently developed integrated thin film drainage apparatus (ITFDA) filled the gap of intermediate bubble/particle size ranges that are commonly encountered in mineral and oil recovery applications. Equipped with side-view digital cameras along with a bimorph cantilever as force sensor and speaker diaphragm as the driver for bubble to approach a solid sphere, the ITFDA has the capacity to measure simultaneously and independently the forces and interfacial deformations as a bubble approaches a solid sphere in a liquid. Coupled with the thin liquid film drainage modeling, the ITFDA measurement allows the critical role of surface tension, fluid viscosity and bubble approach speed in determining bubble deformation (profile) and hydrodynamic forces to be elucidated. Here we compare the available methods of studying bubble–solid interactions and demonstrate unique features and advantages of the ITFDA for measuring both forces and bubble deformations in systems of Reynolds numbers as high as 10. The consistency and accuracy of such measurement are tested against the well established Stokes–Reynolds–Young–Laplace model. The potential to use the design principles of the ITFDA for fundamental and developmental research is demonstrated.     

Modeling the kinetics of bubble nucleation in champagne and carbonated beverages

In champagne and carbonated beverages, bubble nucleation was mostly found to take place from tiny Taylor-like bubbles trapped inside immersed cellulose fibers stuck on the glass wall. The present paper complements a previous paper about the thorough examination of the bubble nucleation process in a flute poured with champagne (Liger-Belair et al. J. Phys. Chem. B 2005, 109, 14573). In this previous paper, a model was built that accurately reproduces the dynamics of these tiny Taylor-like bubbles that grow inside the fiber's lumen by diffusion of CO(2)-dissolved molecules. In the present paper, by use of the model recently developed, the frequency of bubble formation from cellulose fibers is accessed and linked with various liquid and fiber parameters, namely, the concentration c(L) of CO(2)-dissolved molecules, the liquid temperature theta, its viscosity eta, the ambient pressure P, the course of the gas pocket growing trapped inside the fiber's lumen before releasing a bubble, and the radius r of the fiber's lumen. The relative influence of the latter parameters on the bubbling frequency is discussed and supported with recent experimental observations and data.     

Improvement of the spinning electrophorometer for zeta potential measurements

In this study, bubbles are held by centripetal force at the center of a rotating cylinder filled with an aqueous solution. Their velocities along the axe of rotation, after application of an electrophoretic force, are used for the calculation of the so-called electrokinetic potential. But this process necessitates the elimination of the electro-osmosis which occurs on the interior sides of the glass cylinder by superposing a concurrent force on the bubble. Efficiency of DEAE-Dextran reticulated with 1,4 Butanediol Diglycidyl Ether can be tested by the observation of a cloud of latex microspheres injected in the interior of the tube and allowed to move in respect with the application of an electric field. The experimental control of these velocity profiles proves the adequacy of the polymer for many cases such as surfactant solutions, presence of electrolytes, utilization with moderate pH.The dynamic interpretation of the electrophoretic motion of bubbles is possible by considering that small ones behave like rigid spheres moving in a rotating fluid. In the second part of this paper and in a previous publication, we have experimentally proved that the use of the theoretical expressions of the forces involved for rigid spheres is justified for small bubbles. So, the electrokinetic potential can be expressed versus the velocity, leading to possible interpretations of the adsorption on gas-water interfaces.     

Electrostatic attraction between a hydrophilic solid and a bubble

The contact between fine hydrophilic α-Al(2)O(3) particles and nitrogen bubbles was studied as a function of solution composition in single bubble capture experiments, where the bubble collection efficiency was measured. The surface charges of both bubble and particle were controlled by varying the electrolyte concentration and pH of the solution. In all experiments the bubbles were negatively charged while the α-Al(2)O(3) particles were either negatively (above pH of the isoelectric point, pH(IEP)) or positively (below pH(IEP)) charged. The collection efficiency was found to be strongly influenced by the surface charge of the particles. The maximum collection efficiency occurred when the bubble and particle were oppositely charged (at low pH values) and at low salt concentration, i.e. when a long range attractive electrostatic interaction is present. In the case where both bubble and particle were of the same charge, the collection efficiency was near to zero within experimental error and was not influenced by either salt concentration or pH. This is the first experimental proof of the concept of 'contactless flotation', first proposed by Derjaguin and Dukhin in 1960, with far reaching implications from minerals processing to biology.     

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.     

Influence of very small bubbles on particle/bubble heterocoagulation

Very small bubbles which partially coat the surface of particles influence whether or not heterocoagulation between a particle and a bubble occurs. The electrostatic and van der Waals forces of interaction between particles and bubbles were calculated as a function of electrolyte concentration, particle size, and the size and distributions of these very small bubbles present on the particle surface. The height of the surface force barrier was compared with the hydrodynamic pressing force under conditions of flotation. The presence of these very small bubbles has a profound effect on the interaction between particles and bubbles and, in particular, strongly decreases the critical particle radius for heterocoagulation.     

Theory of non-equilibrium force measurements involving deformable drops and bubbles

Over the past decade, direct force measurements using the Atomic Force Microscope (AFM) have been extended to study non-equilibrium interactions. Perhaps the more scientifically interesting and technically challenging of such studies involved deformable drops and bubbles in relative motion. The scientific interest stems from the rich complexity that arises from the combination of separation dependent surface forces such as Van der Waals, electrical double layer and steric interactions with velocity dependent forces from hydrodynamic interactions. Moreover the effects of these forces also depend on the deformations of the surfaces of the drops and bubbles that alter local conditions on the nanometer scale, with deformations that can extend over micrometers. Because of incompressibility, effects of such deformations are strongly influenced by small changes of the sizes of the drops and bubbles that may be in the millimeter range. Our focus is on interactions between emulsion drops and bubbles at around 100 μm size range. At the typical velocities in dynamic force measurements with the AFM which span the range of Brownian velocities of such emulsions, the ratio of hydrodynamic force to surface tension force, as characterized by the capillary number, is ~ 10^{− 6} or smaller, which poses challenges to modeling using direct numerical simulations. However, the qualitative and quantitative features of the dynamic forces between interacting drops and bubbles are sensitive to the detailed space and time-dependent deformations. It is this dynamic coupling between forces and deformations that requires a detailed quantitative theoretical framework to help interpret experimental measurements. Theories that do not treat forces and deformations in a consistent way simply will not have much predictive power. The technical challenges of undertaking force measurements are substantial. These range from generating drop and bubble of the appropriate size range to controlling the physicochemical environment to finding the optimal and quantifiable way to place and secure the drops and bubbles in the AFM to make reproducible measurements. It is perhaps no surprise that it is only recently that direct measurements of non-equilibrium forces between two drops or two bubbles colliding in a controlled manner have been possible. This review covers the development of a consistent theory to describe non-equilibrium force measurements involving deformable drops and bubbles. Predictions of this model are also tested on dynamic film drainage experiments involving deformable drops and bubbles that use very different techniques to the AFM to demonstrate that it is capable of providing accurate quantitative predictions of both dynamic forces and dynamic deformations. In the low capillary number regime of interest, we observe that the dynamic behavior of all experimental results reviewed here are consistent with the tangentially immobile hydrodynamic boundary condition at liquid–liquid or liquid–gas interfaces. The most likely explanation for this observation is the presence of trace amounts of surface-active species that are responsible for arresting interfacial flow.     

Size-selective sliding of sessile drops on a slightly inclined plane using low-frequency AC electrowetting

When placed on an inclined solid plane, drops often stick to the solid surface due to pinning forces caused by contact angle hysteresis. When the drop size or the plane's incline angle is small, the drop is difficult to slide due to a decrease in gravitational force. Here we demonstrate that small drops (0.4-9 μL) on a slightly inclined plane (~12°, Teflon and parylene-C surface) can be mobilized through patterned electrodes by applying low-frequency ac electrowetting under 400 Hz (110-180 V(rms)), which has a mechanism different from that of the high-frequency ac method that induces sliding by reducing contact angle hysteresis. We attribute the sliding motion of our method to a combination of contact angle hysteresis and interfacial oscillation driven by ac electrowetting instead of the minimization of contact angle hysteresis at a high frequency. We investigated the effects of ac frequency on the sliding motion and terminal sliding of drops; the terminal sliding velocity is greatest at resonance frequency. Varying the electrowetting number (0.21-0.56) at a fixed frequency (40 Hz) for 5 μL drops, we found an empirical relationship between the electrowetting number and the terminal sliding velocity. Using the relationship between the drop size and ac frequency, we can selectively slide drops of a specific size or merge two drops along an inclined plane. This simple method will help with constructing microfluidic platforms with sorting, merging, transporting, and mixing of drops without a programmable control of electrical signals. Also, this method has a potential in heat transfer applications because heat removal capacity can be enhanced significantly through drop oscillation.     

The thermocapillary migrations of two bubbles in microgravity environment

The thermocapillary motion of two bubbles along their line of centers in a uniform temperature gradient is investigated theoretically. The bubbles are moving in the direction of the temperature gradient. And the interaction between the leading bubble and the trailing one becomes significant as the separation distance between them is decreased greatly so that the bubble interaction is considered in this case. The appropriate equations of momentum and energy are solved using the method of reflections. In order to proceed analytically, sets of transformations between two coordinates are obtained. By using these transformations and the reflection process, accurate migration velocities of these two bubbles in the microgravity environment are derived for the limit of small Marangoni and Reynolds numbers. These results are employed to describe the thermocapillary motion of two bubbles and to estimate the effects of bubble size and the thermal gradient on the interaction between two bubbles. All of our results for the migration of the two bubbles demonstrate that the approach of the second bubble to the first one intensifies the mutual interaction between these two bubbles and yields some interesting thermocapillary motions.     

Flow field in a downward diverging channel and its application

The flow in a downward divergent channel turns out to be an interesting experimental setup for the observation of upward floating bubbles that appear to be levitating in view of the observer. A more detailed analysis of this flow and its characteristic parameters is necessary for better understanding of this phenomenon. The boundary layer theory was used to derive the velocity field for the experimental setup. The actual flow of a liquid in the presence of a bubble was studied experimentally by measuring the position of the bubble; the data were then statistically processed by an image analysis. Observation of the bubble positions distribution showed that it is reasonable to assume a flat velocity profile of the liquid in the channel and that the bubbles do not tend to move into the boundary layer. In our experiments, volume of the air bubbles floating in water was 200 mm and of that of bubbles floating in aqueous glycerin was 300 mm³. Thus, the experiment used in this work is suitable for reliable determination of instantaneous and average bubble rising velocities as well as of those of horizontal and vertical oscillations.     

Long-lived submicrometric bubbles in very diluted alkali halide water solutions

Solutions of LiCl and of NaCl in ultrapure water were studied through Rayleigh/Brillouin scattering as a function of the concentration (molarity, M) of dissolved salt from 0.2 M to extremely low concentration (2 × 10(-17) M). The Landau-Placzek ratio, R/B, of the Rayleigh scattering intensity over the total Brillouin was measured thanks to the dynamically controlled stability of the used Fabry-Perot interferometer. It was observed that the R/B ratio follows two stages as a function of increasing dilution rate: after a strong decrease between 0.2 M and 2 × 10(-5) M, it increases to reach a maximum between 10(-9) M and 10(-16) M. The first stage corresponds to the decrease of the Rayleigh scattering by the ion concentration fluctuations with the decrease of salt concentration. The second stage, at lower concentrations, is consistent with the increase of the Rayleigh scattering by long-lived sub-microscopic bubbles with the decrease of ion concentration. The origin of these sub-microscopic bubbles is the shaking of the solutions, which was carried out after each centesimal dilution. The very long lifetime of the sub-microscopic bubbles and the effects of aging originate in the electric charge of bubbles. The increase of R/B with the decrease of the low salt concentration corresponds to the increase of the sub-microscopic bubble size with the decrease of concentration, which is imposed by the bubble stability due to the covering of the surface bubble by negative ions.     

纳米通道内表面浸润性对气泡的作用

运用分子动力学模拟方法研究了在质量力驱动下不同浸润性壁面纳米通道中气泡的分布及其运动状况, 提出了一种统计纳米通道中气泡运动速度的方法. 结果显示, 在亲水性壁面的纳米通道中, 气泡位于通道中间, 气泡的运动速度接近但小于通道中心流速, 在势能强度较大时, 壁面吸附的分子较多, 气泡也较大, 反之则气泡较小; 对超疏水性壁面, 气泡则位于固壁附近, 两个壁面形成对称的一对气泡, 气泡的运动速度接近但大于边缘速度. 流体总的流动速度随着流体粒子与壁面粒子作用的减弱而增大, 滑移速度则逐渐从负转变为正.