The boundary condition at the air–liquid interface and its effect on film drainage between colliding bubbles

The drainage of thin liquid films between colliding bubbles is strongly influenced by the boundary conditions at the air–liquid interface. Theoretically, the interface should not resist any tangential stress (fully mobile) in a clean water system, resulting in very fast film drainage and coalescence between bubbles within milliseconds. In reality, under most experimental and industrial conditions, the presence of impurities or surfactants can immobilize the interface and significantly hinder bubble coalescence by several orders of magnitude. In this opinion, we introduce the recent progress on understanding the boundary conditions at the air–water interface, and how they may affect the outcome of bubble collisions. The transition from mobile to immobile boundary conditions in the presence of contaminations is discussed. Despite the considerable recent progress, there are still experimental and theoretical challenges remaining on this topic, for example, finding the mechanism for hindered bubble coalescence by high salt concentrations.     

Coalescence map for bubbles in surfactant-free aqueous electrolyte solutions

Factors influencing bubble coalescence in surfactant-free aqueous electrolyte solutions are considered in this compilation of literature results. These factors include viscous and inertial thin film drainage, surface deformation, surface elasticity, mobility or otherwise of the air-water interface, and disjoining pressure. Several models from the literature are discussed, with particular attention paid to predictions of transitions between regions where behaviour is qualitatively different. The transitions are collated onto a single chart with salt concentration and bubble approach speed as the axes. This creates a map of the regions in which different mechanisms operate, giving an overall picture of bubble coalescence behaviour over a wide range of concentration and speed. Only mm-size bubbles in water and NaCl solutions are discussed in this initial effort at creating such a map. Data on bubble coalescence or non-coalescence are collected from the literature and plotted on the same map, generally aligning well with the predicted transitions and thus providing support for the theoretical reasoning that went into creating the coalescence map.     

Effects of interface mobility on the dynamics of colliding bubbles

At its core, the outcome of the collision between air bubbles is determined by the hydrodynamic interaction forces, which in turn are strongly dependent on the tangential mobility of the gas–liquid interfaces. A clean gas–liquid interface is tangentially mobile, whereas the presence of surfactant contaminants can immobilise the interface. Bubbles with mobile surfaces coalescence much easier because of the low hydrodynamic resistance to drainage of the thin liquid film separating the colliding bubbles. In this opinion, we highlight recent experimental and numerical simulations demonstrating that in addition to the expected faster coalescence, mobile-surface bubbles can produce a much stronger rebound from a mobile liquid interface compared to an immobile one. The stronger rebound is explained by the lower viscous dissipation during collisions involving mobile surfaces. The role of the surface mobility in controlling the stability of gas or liquid emulsion should be reassessed in the light of these new findings.     

Bubble coalescence during acoustic cavitation in aqueous electrolyte solutions

Bubble coalescence behavior in aqueous electrolyte (MgSO(4), NaCl, KCl, HCl, H(2)SO(4)) solutions exposed to an ultrasound field (213 kHz) has been examined. The extent of coalescence was found to be dependent on electrolyte type and concentration, and could be directly linked to the amount of solubilized gas (He, Ar, air) in solution for the conditions used. No evidence of specific ion effects in acoustic bubble coalescence was found. The results have been compared with several previous coalescence studies on bubbles in aqueous electrolyte and aliphatic alcohol solutions in the absence of an ultrasound field. It is concluded that the impedance of bubble coalescence by electrolytes observed in a number of studies is the result of dynamic processes involving several key steps. First, ions (or more likely, ion-pairs) are required to adsorb at the gas/solution interface, a process that takes longer than 0.5 ms and probably fractions of a second. At a sufficient interfacial loading (estimated to be less than 1-2% monolayer coverage) of the adsorbed species, the hydrodynamic boundary condition at the bubble/solution interface switches from tangentially mobile (with zero shear stress) to tangentially immobile, commensurate with that of a solid-liquid interface. This condition is the result of spatially nonuniform coverage of the surface by solute molecules and the ensuing generation of surface tension gradients. This change reduces the film drainage rate between interacting bubbles, thereby reducing the relative rate of bubble coalescence. We have identified this point of immobilization of tangential interfacial fluid flow with the "critical transition concentration" that has been widely observed for electrolytes and nonelectrolytes. We also present arguments to support the speculation that in aqueous electrolyte solutions the adsorbed surface species responsible for the immobilization of the interface is an ion-pair complex.     

Bubble-size dependence of the critical electrolyte concentration for inhibition of coalescence

The interaction of pairs of bubbles with equal diameters grown on adjacent capillaries in aqueous magnesium sulfate solutions is observed for varying electrolyte concentrations and bubble diameters. As in previous investigations, a sharp transition from coalescence to bubble detachment without coalescence is observed with increasing electrolyte concentration. The critical electrolyte concentration for this transition is found to increase with decreasing bubble diameter for bubble diameters of 1.4 to 4.2 mm.     

Selective coalescence of bubbles in simple electrolytes

Simple ions in electrolytes exhibit different degrees of affinity for the approach to the free surface of water. This results in strong ion-specific effects that are particularly dramatic in the selective inhibition of bubble coalescence. I present here the calculation of electrostatic interaction between free surfaces of electrolytes caused by the ion accumulation or depletion near a surface. When both anion and cation are attracted to the surface (like H+ and Cl- in HCl solutions), van der Waals attraction facilitates approach of the surfaces and the coalescence of air bubbles. When only an anion or cation is attracted to the surface (like Cl- in NaCl solutions), an electric double layer forms, resulting in repulsive interaction between free surfaces. I applied the method of effective potentials (evaluated from published ion density profiles obtained in simulations) to calculate the ionic contribution to the surface-surface interaction in NaCl and HCl solutions. In NaCl, but not in HCl, the double-layer interaction creates a repulsive barrier to the approach of bubbles, in agreement with the experiments. Moreover, the concentration where ionic repulsion in NaCl becomes comparable in magnitude to the short-range hydrophobic attraction corresponds to the experimentally found transition region toward the inhibition of coalescence.     

Experimental analysis of the hydrodynamics of a three-phase system in a vessel with two impellers

Results of experimental analysis concerning gas hold-up and average residence time of gas bubbles in a three-phase gas-solid-liquid system produced in a baffled, double-impeller vessel are presented. Measurements were carried out in a vessel with the internal diameter of 0.288 m. Two different double-impeller configurations were used for agitation: Rushton turbine (lower) — A 315 (upper) and Rushton turbine (lower) — HE 3 (upper). Upper impellers differed in the fluid pumping mode. Coalescing and non-coalescing systems were tested. Liquid phases were distilled water (coalescing system) and aqueous solutions of NaCl (non-coalescing systems). The ability of gas bubbles to coalesce in the liquid was described using parameter Y. Dispersed phases were air and particles of sea sand. The experiments were conducted at seven different gas flow rates and two particle loadings. Effects of the ability of gas bubbles to coalesce (liquid phase properties), operating parameters (superficial gas velocity, impeller speed, solids loadings), and of the type of the impeller configuration on the investigated parameters were determined. The results were approximated mathematically. For both impeller configurations tested, significantly higher gas hold-up values were obtained in the non-coalescing gas-solid-liquid systems compared to the coalescing one. Out of the tested impeller systems, the RT-A 315 configuration proved to have better performance ensuring good gas dispersion in the liquid in the three-phase systems.     

Investigations of the spark assisted chemical engraving

The spark assisted chemical engraving (SACE) of glass has been investigated using current/voltage measurements combined with photographs of the tool electrode under different regimes. Depending on the applied potential, different domains have been identified. At low potentials (<10 V) a cone-shaped region containing finely dispersed hydrogen gas is formed around the tool cathode. At high potentials (>25 V) there are strong current fluctuations mainly due to bubble coalescence. We speculate that in this regime, due to the ohmic heating, the temperature in the vicinity of the tool electrode reaches the boiling point of the electrolyte resulting in the generation of water vapour bubbles. These bubbles cover the active surface area of the tool electrode, leading to blanketing (i.e., isolation between tool and electrolyte). Once the bubbles dislodge from the tool surface, contact between the electrolyte and tool is re-established and the cycle will be repeated. This last region (>25 V) is the working domain of the SACE. Finally some examples of glass machining are given to demonstrate the potential application of this technology.     

A microfluidic method to study demulsification kinetics

We present the results of experiments studying droplet coalescence in a dense layer of emulsion droplets using microfluidic circuits. The microfluidic structure allows direct observation of collisions and coalescence events between oil droplets dispersed in water. The coalescence rate of a flowing hexadecane-in-water emulsion was measured as a function of the droplet velocity and droplet concentration from image sequences measured with a high-speed camera. A trajectory analysis of colliding droplet pairs allows evaluation of the film drainage profile and coalescence time t(c.) The coalescence times obtained for thousands of droplet pairs enable us to calculate coalescence time distributions for each set of experimental parameters, which are the mean droplet approach velocity (v(0)), the mean dispersed phase fraction (φ) and the mean hydraulic diameter of a droplet pair (d(p)). The expected value E(t(c)) of the coalescence time distributions scales as E(t(c)) is proportional to (v(0))(-0.105±0.043)(d(p))(0.562±0.287), but is independent of φ. We discuss the potential of the procedure for the prediction of emulsion stability in industrial applications.     

Coalescence of bubbles covered by particles

The interaction between two bubbles coated with glass particles in the presence of a cationic surfactant (cetyltrimethylammonium bromide, CTAB) was studied experimentally. The time taken for two bubbles to coalesce was determined as a function of the fractional coverage of the surface by particles. The results suggested that the coalescence time increases with the bubble surface coverage. Interestingly, it was found that although the particles did not have any physical role in film rupture at low surface coverage, they still added resistance to film drainage. For particle-loaded bubbles, the initial resistance was due to the lateral capillary interactions between particles on the interface, which hold the particles firmly together. The coalescence dynamics of bubbles was also observed to be affected by the presence of attached particles.     

Coalescence of protein-stabilized bubbles undergoing expansion at a simultaneously expanding planar air-water interface

A novel design of apparatus is described that allows observation of the coalescence stability of bubbles at a planar interface when the planar interface and the bubble surface both expand. Bubbles are introduced beneath the planar air-water interface contained within a square barrier made of perfluorocarbon rubber. The bubbles are then expanded by reducing the air pressure above the interface, while at the same time the rubber barrier is mechanically expanded, maintaining its square shape, to give the same rate and extent of expansion of the planar interface. The area can typically be increased by a factor of three over time scales as short as 0.2 s. This arrangement has been designed to mimic the behavior of aerated products when they exit from a pressurized aeration unit or product dispenser. Compared to results obtained via a previous technique, where it was only possible to expand the bubbles but not the planar interface, the bubbles are less stable. The apparatus has been used to compare the stabilizing effects of ovalbumin, beta-lactoglobulin, whey protein isolate, and sodium caseinate, in a model aqueous food system thickened with 40% invert sugar. Stability improved with increasing concentration of all the proteins and with a decrease in expansion rate, but considerable instability remained even at protein concentrations as high as 4 to 6 wt % and also at very low expansion rates, though the systems were stable in the absence of expansion. However, the stability was greatly improved by the replacement of the above proteins by the hydrocolloids gelatine or polypropylene glycol alginate. Detailed analysis revealed that the coalescence of individual bubbles in clusters of bubbles were not strongly correlated in distance or time, but larger bubbles and bubbles toward the outside of a cluster were found to be, on average, less stable than smaller bubbles and bubbles located more toward the interior of a cluster. The different degrees of stability are discussed in terms of local deformation, fracture behavior, and time-dependent composition of the adsorbed layers.     

Ion-specific influence of electrolytes on bubble coalescence in nonaqueous solvents

We report the effects of electrolytes on bubble coalescence in nonaqueous solvents methanol, formamide, propylene carbonate, and dimethylsulfoxide (DMSO). Results in these solvents are compared to the ion-specific bubble coalescence inhibition observed in aqueous electrolyte solutions, which is predicted by simple, empirical ion combining rules. Coalescence inhibition by electrolytes is observed in all solvents, at a lower concentration range (0.01 M to 0.1M) to that observed in water. Formamide shows ion-specific salt effects dependent upon ion combinations in a way analogous to the combining rules observed in water. Bubble coalescence in propylene carbonate is also consistent with ion-combining rules, but the ion assignments differ to those for water. In both methanol and DMSO all salts used are found to inhibit bubble coalescence. Our results show that electrolytes influence bubble coalescence in a rich and complex way, but with notable similarities across all solvents tested. Coalescence is influenced by the drainage of fluid between two bubbles to form a film and then the rupture of the film and one might expect that these processes will vary dramatically between solvents. The similarities in behavior we observe show that coalescence inhibition is unlikely to be related to the surface forces present but is perhaps related to the dynamic thinning and rupture of the liquid film through the hydrodynamic boundary condition.     

Effects of electrolyte concentration and pH on the coalescence stability of beta-lactoglobulin emulsions: experiment and interpretation

Experimental results are presented about the effects of ionic strength and pH on the mean drop-size after emulsification and on the coalescence stability of emulsions, stabilized by a globular protein beta-lactoglobulin (BLG). The mean drop-size is determined by optical microscopy, whereas the coalescence stability is characterized by centrifugation. In parallel experiments, the zeta-potential and protein adsorption on drop surface are determined. The experiments are performed at two different BLG concentrations, 0.02 and 0.1 wt%. The electrolyte concentration in the aqueous phase, C(EL), is varied between 1.5 mM and 1 M, and pH is varied between 4.0 and 7.0. The experiments show that the mean drop-size after emulsification depends slightly on C(EL), at fixed protein concentration and natural pH = 6.2. When pH is varied, the mean drop-size passes through a maximum at fixed protein and electrolyte concentrations. A monolayer protein adsorption is registered in the studied ranges of C(EL) and pH at low BLG concentration of 0.02 wt%. In contrast, a protein multilayer is formed at higher BLG concentration, 0.1 wt%, above a certain electrolyte concentration (C(EL) > 100 mM, natural pH). The experimental results for the emulsion coalescence stability are analyzed by considering the surface forces acting between the emulsion drops. The electrostatic, van der Waals, and steric interactions are taken into account to calculate the barriers in the disjoining pressure isotherm at the various experimental conditions studied. The comparison of the theoretically calculated and the experimentally determined coalescence barriers shows that three qualitatively different cases can be distinguished. (1) Electrostatically stabilized emulsions, with monolayer protein adsorption, whose stability can be described by the DLVO theory. (2) Sterically stabilized emulsions, in which the drop-drop repulsion is created mainly by overlapping protein adsorption multilayers. A simple theoretical model is shown to describe emulsion stability in these systems. (3) Sterically stabilized emulsions with a monolayer adsorption on drop surface.     

The effect of surface-active solutes on bubble coalescence in the presence of ultrasound

The sonication of an aqueous solution generates cavitation bubbles, which may coalesce and produce larger bubbles. This paper examines the effect of surface-active solutes on such bubble coalescence in an ultrasonic field. A novel capillary system has been designed to measure the change in the total volume resulting from the sonication of aqueous solutions with 515 kHz ultrasound pulses. This volume change reflects the total volume of larger gas bubbles generated by the coalescence of cavitation bubbles during the sonication process. The total volume of bubbles generated is reduced when surface-active solutes are present. We have proposed that this decrease in the total bubble volume results from the inhibition of bubble coalescence brought about by the surface-active solutes. The observed results revealed similarities with bubble coalescence data reported in the literature in the absence of ultrasound. It was found that for uncharged and zwitterionic surface-active solutes, the extent of bubble coalescence is affected by the surface activity of the solutes. The addition of 0.1 M NaCl to such solutes had no effect on the extent of bubble coalescence. Conversely, for charged surface-active solutes, the extent of bubble coalescence appears to be dominated by electrostatic effects. The addition of 0.1 M NaCl to charged surfactant solutions was observed to increase the total bubble volume close to that of the zwitterionic surfactant. This suggests the involvement of electrostatic interactions between cavitation bubbles in the presence of charged surfactants in the solution.     

On air entrainment in coatings

A series of experiments that clarify how air bubbles become entrained into coatings are described. The contact line dynamics at the air-liquid interface surrounding a fiber is characterized for a typical coating die operating under atmospheric and pressurized conditions. Glycerin and other viscous liquids are used to reveal that a critical fiber speed exists at which air entrainment begins. The observations confirm that the critical capillary number Ca(c) depends on the physical properties of the coating material, in the form of the Morton number. When the liquid supply is pressurized, the experiments show that adjusting the pressure can stabilize the displaced free surface interface at a prescribed location. Controlling the meniscus location in this way eliminates air entrainment. The threshold occurs when the applied pressure balances the shear exerted on the coating by the moving fiber. Using this approach it is possible to eliminate air entrainment and attain stable wetting at very large values of the capillary number, e.g., Ca congruent with 50.     

环氧树脂相反转乳化过程相态发展研究

以扫描电镜为主要手段,观察了环氧树脂相反转乳化过程中的相态演化过程.结果表明:在较高乳化剂浓度下,当水含量达到某一临界值时,原W/O体系中水滴间的相互吸引大于水滴间的排斥作用,导致相邻水滴同时快速地融合为连续相并得到水基微粒,水基微粒的尺寸较小,约为亚微米级,尺寸分布窄,微粒为单个粒子.在乳化剂浓度较低情况下,非相邻较大水滴在剪切场作用下随机地融合为连续相,发生不完全相反转,并得到W/O/W结构,水基微粒尺寸较大,约10微米数量级,尺寸分布宽且为一种复合多孔结构.此外,分析了相反转发展演变过程.     

环氧树脂相反转乳化过程相态发展研究＊

以扫描电镜为主要手段,观察了环氧树脂相反转乳化过程中的相态演化过程.结果表明 在较高乳化剂浓度下, 当水含量达到某一临界值时, 原W/O体系中水滴间的相互吸引大于水滴间的排斥作用, 导致相邻水滴同时快速地融合为连续相并得到水基微粒, 水基微粒的尺寸较小, 约为亚微米级, 尺寸分布窄,微粒为单个粒子.在乳化剂浓度较低情况下,非相邻较大水滴在剪切场作用下随机地融合为连续相,发生不完全相反转, 并得到W/O/W 结构, 水基微粒尺寸较大,约10微米数量级,尺寸分布宽且为一种复合多孔结构.此外,分析了相反转发展演变过程.     

Effect of Ionic Strength of Dispersed Phase on Ostwald Ripening in Water-in-Oil Emulsions

Water-in-oil emulsions with a low electrolyte content in the internal phase are unstable with respect to Ostwald ripening. The main components of the total pressure acting on the surface of internal phase droplets are considered. The equilibrium values of the diameters of dispersed phase droplets are calculated. The dependences of the difference in the osmotic and Laplace pressures on the droplet size and electrolyte concentration in the droplets are obtained. It is shown that, at the electrolyte concentration below the critical value, the number of droplets in emulsion decreases. If the concentration is above the critical value, water diffuses from small to large droplets, but their number remains unchanged. The change in NaCl concentration in the droplets of internal phase of polydisperse emulsion during the Ostwald ripening is calculated. The results of calculations correlate with the experimental data on the stability of emulsions with respect to coalescence and sedimentation.     

Stability and disturbance of coating films

In the studies of two-roll metering and application systems, two types of disturbances were observed. These were termed “ring type” and “irregular” disturbances. This research established that the physical reason for the appearance of the ring type instability is the competition between surface tension and centrifugal forces at the liquid-air interface. The rings are generated at the surface of the dynamic liquid meniscus, in the gap between the rolls, because of the very large centrifugal forces there. Considering conditions of a constant interfacial pressure difference (pressure jump), one can reduce the problem to one with only one free parameter, viz., the radius of the meniscus, and calculate the wavelength of the disturbances. There is no single formula which will adequately describe the dynamic meniscus. Its curvature depends on the rheological properties of the fluid and on the kinematic conditions in the process. Dimensional analysis is combined with experimental findings to yield a formula for the radius of the meniscus for fluids having a high yield stress for the case of two counter-rotating rolls.The rheological behavior of a flowing starch adhesive in the dynamical meniscus is analyzed. The theoretical and experimental studies show that systems using two counter-rotating rolls practically always produced ring-type instabilities with all types of fluids.The picture is more complex for co-rotating roll systems. When non-Newtonian adhesives are used, ring type disturbances are observed in one zone of roll speed ratios, and irregular disturbances are observed in another zone. The two zones are separated by a speed ratio zone (a “speed window”) where a more or less perfectly stable fluid layer is observed. When Newtonian oils are used, there are two such speed windows. The first one corresponds to very low metering roll speeds and a minimum of liquid transfer to the applicator roll. The second stable zone occurs at high metering roll speeds and yields a maximum of liquid transfer. The physical reason for the high transfer rate in the high speed “window” is considered and shown to be the thin air layer following the surface of the metering roll. The air pumped into the metering gap returns along the applicator roll and accelerates the film on the applicator roll in the process. Under these conditions the fluid-air interface may become unstable, leading to the “irregular” type of disturbance.