Effect of emulsion drop-size distribution upon coalescence in simple shear flow: a population balance study

A population balance is used to examine the effect of the shape of the initial drop-size distribution of an emulsion upon its short and long-time evolution in simple shear flow. Initial distributions that are monodisperse, multidisperse, lognormal, bimodal, multimodal, and step functions are considered. At short times, it is shown that the rate of coalescence decreases by up to 25% for step distributions and up to 75% for lognormal distributions as the width of the distribution increases. Bimodal, multidisperse and multimodal distributions show intermediate decreases in the rate of coalescence, between these two values, with increases in the distribution width. Furthermore, it is found that the initial rate of coalescence is strongly dependent upon the presence of large drops. As the number fraction of large droplets within the distribution increases, the rate of coalescence also increases. At long times, all distributions move toward an asymptotic distribution shape in which the frequency of drops decreases algebraically with drop diameter at small drop diameters, and decreases exponentially with drop diameter at large drop diameters. Though portions of each distribution showed the expected asymptotic scaling behavior at long times, each asymptotic distribution nevertheless retains 'fingerprints' of the respective initial distribution. Overall, the rate of coalescence for a system is bounded by the initial rate, which is a function of the initial distribution shape, and the asymptotic rate, which is dependent upon the long-time scaling behavior. Finally, it is shown that the resolution with which the drop-size distribution of an emulsion is experimentally measured can have a significant effect upon predicted rates of coalescence.     

Fog deposition and accumulation on smooth and textured hydrophobic surfaces

We investigated the deposition and accumulation of droplets on both smooth substrates and substrates textured with square pillars, which were tens of micrometers in size. After being coated with a hydrophobic monolayer, substrates were placed in an air flow with a sedimenting suspension of micrometer-sized water droplets (i.e., fog). We imaged the accumulation of water and measured the evolution of the mean drop size. On smooth substrates, the deposition process was qualitatively similar to condensation, but differences in length scale revealed a transient regime not reported in condensation experiments. Based on previous simulation results, we defined a time-scale characterizing the transition to steady-state behavior. On textured substrates, square pillars promoted spatial ordering of accumulated drops. Furthermore, texture regulated drop growth: first enhancing coalescence when the mean drop size was smaller than the pillar, and then inhibiting coalescence when drops were comparable to the pillar size. This inhibition led to a monodisperse drop regime, in which drop sizes varied by less than 5%. When these monodisperse drops grew sufficiently large, they coalesced and could either remain suspended on pillars (i.e., Cassie-Baxter state) or wet the substrate (i.e., Wenzel state).     

Contact line dynamics in drop coalescence and spreading

The dynamics of coalescence of two water sessile drops is investigated and compared with the spreading dynamics of a single drop in partially wetting regime. The composite drop formed due to coalescence relaxes exponentially toward equilibrium with a typical relaxation time that decreases with contact angle. The relaxation time can reach a few tenths of seconds and depends also on the drop size, initial conditions, and surface properties (contact angle, roughness). The relaxation dynamics is larger by 5 to 6 orders of magnitude than the bulk hydrodynamics predicts, due to the high dissipation in the contact line vicinity. The coalescence is initiated at a contact of the drops growing in a condensation chamber or by depositing a small drop at the top of neighboring drops with a syringe, a method also used for the studies of the spreading. The dynamics is systematically faster by an order of magnitude when comparing the syringe deposition with condensation. We explain this faster dynamics by the influence of the unavoidable drop oscillations observed with fast camera filming. Right after the syringe deposition, the drop is vigorously excited by deformation modes, favoring the contact line motion. This excitation is also observed in spreading experiments while it is absent during the condensation-induced coalescence.     

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.     

Emulsification in turbulent flow: 3. Daughter drop-size distribution

Systematic set of experiments is performed to clarify the effects of several factors on the size distribution of the daughter drops, which are formed as a result of drop breakage during emulsification in turbulent flow. The effects of oil viscosity, etaD, interfacial tension, sigma, and rate of energy dissipation in the turbulent flow, epsilon, are studied. As starting oil-water premixes we use emulsions containing monodisperse oil drops, which have been generated by membrane emulsification. By passing these premixes through a narrow-gap homogenizer, working in turbulent regime of emulsification, we monitor the changes in the drop-size distribution with the emulsification time. The experimental data are analyzed by using a new numerical procedure, which is based on the assumption (supported by the experimental data) that the probability for formation of daughter drops with diameter smaller than the maximum diameter of the stable drops, d相似文献   

Silica particle-stabilized emulsions of silicone oil and water: aspects of emulsification

A study of the emulsification of silicone oil and water in the presence of partially hydrophobic, monodisperse silica nanoparticles is described. Emulsification involves the fragmentation of bulk liquids and the resulting large drops and the coalescence of some of those drops. The influence of particle concentration, oil/water ratio, and emulsification time on the relative extents of fragmentation and coalescence during the formation of emulsions, prepared using either batch or continuous methods, has been investigated. For batch emulsions, the average drop diameter decreases with increasing particle concentration as the extent of limited coalescence is reduced. Increasing the oil volume fraction in the emulsion at fixed aqueous particle concentration results in an increase in the average drop diameter together with a dramatic lowering of the uniformity of the drop size distribution as coalescence becomes increasingly significant until catastrophic phase inversion occurs. For low oil volume fractions (phi(o)), fragmentation dominates during emulsification since the mean drop size decreases with emulsification time. For higher phi(o) close to conditions of phase inversion, coalescence becomes more prevalent and the drop size increases with time with stable multiple emulsions forming as a result.     

Microdroplet growth mechanism during water condensation on superhydrophobic surfaces

By promoting dropwise condensation of water, nanostructured superhydrophobic coatings have the potential to dramatically increase the heat transfer rate during this phase change process. As a consequence, these coatings may be a facile method of enhancing the efficiency of power generation and water desalination systems. However, the microdroplet growth mechanism on surfaces which evince superhydrophobic characteristics during condensation is not well understood. In this work, the sub-10 μm dynamics of droplet formation on nanostructured superhydrophobic surfaces are studied experimentally and theoretically. A quantitative model for droplet growth in the constant base (CB) area mode is developed. The model is validated using optimized environmental scanning electron microscopy (ESEM) imaging of microdroplet growth on a superhydrophobic surface consisting of immobilized alumina nanoparticles modified with a hydrophobic promoter. The optimized ESEM imaging procedure increases the image acquisition rate by a factor of 10-50 as compared to previous research. With the improved imaging temporal resolution, it is demonstrated that nucleating nanodroplets coalesce to create a wetted flat spot with a diameter of a few micrometers from which the microdroplet emerges in purely CB mode. After the droplet reaches a contact angle of 130-150°, its base diameter increases in a discrete steplike fashion. The droplet height does not change appreciably during this steplike base diameter increase, leading to a small decrease of the contact angle. Subsequently, the drop grows in CB mode until it again reaches the maximum contact angle and increases its base diameter in a steplike fashion. This microscopic stick-and-slip motion can occur up to four times prior to the droplet coalescence with neighboring drops. Lastly, the constant contact angle (CCA) and the CB growth models are used to show that modeling formation of a droplet with a 150° contact angle in the CCA mode rather than in the CB mode severely underpredicts both the drop formation time and the average heat transfer rate through the drop.     

Coalescence of particle-laden drops with a planar oil-water interface

The coalescence mechanism of a particle-laden drop resting at an oil-water interface has been studied. Two mechanisms for drop coalescence are observed; (i) complete coalescence, in which the drop experiences total coalescence in one event, and (ii) partial coalescence, where a drop is observed to separate during coalescence, producing a smaller secondary drop that rebounds and comes to rest at the planar oil-water interface. For particle-laden drops of approximately 4mm in diameter, we show the critical condition for partial to complete coalescence to be dependent on the particle concentration, and the interparticle interaction energy. Colloidal silica spheres dispersed in 10(-4) M KNO(3) electrolyte solution are highly charged and remain dispersed in the drop. By increasing the solids concentration, we measure the transition from partial to complete coalescence at 20 wt.%. However, this critical condition can be reduced by increasing the interparticle interaction energy. In 1 M KNO(3) electrolyte solution, the particle surface charge is sufficiently screened such that particle clusters readily form in the water drop. With particle clustering, transition from partial to complete coalescence is measured at 8 wt.% solids.     

Superhydrophobicity of biological and technical surfaces under moisture condensation: stability in relation to surface structure

The stability of superhydrophobic properties of eight plants and four technical surfaces in respect to water condensation has been compared. Contact and sliding angles were measured after application of water drops of ambient temperature (20 degrees C) onto cooled surfaces. Water evaporating from the drops condensed, due to the temperature difference between the drops and the surface, on the cooled samples, forming "satellite droplets" in the vicinity of the drops. Surface cooling to 15, 10, and 5 degrees C showed a gradual decrease of superhydrophobicity. The decrease was dependent on the specific surface architecture of the sample. The least decrease was found on hierarchically structured surfaces with a combination of a coarse microstructure and submicrometer-sized structures, similar to that of the Lotus leaf. Control experiments with glycerol droplets, which show no evaporation, and thus no condensation, were carried out to verify that the effects with water were caused by condensation from the drop (secondary condensation). Furthermore, the superhydrophobic properties after condensation on cooled surfaces from a humid environment for 10 min were examined. After this period, the surfaces were covered with spherical water droplets, but most samples retained their superhydrophobicity. Again, the best stability of the water-repellent properties was found on hierarchically structured surfaces similar to that of the Lotus leaf.     

Spreading of Surfactant Solutions over Hydrophobic Substrates

The spreading of surfactant solutions over hydrophobic surfaces is considered from both theoretical and experimental points of view. Water droplets do not wet a virgin solid hydrophobic substrate. It is shown that the transfer of surfactant molecules from the water droplet onto the hydrophobic surface changes the wetting characteristics in front of the drop on the three-phase contact line. The surfactant molecules increase the solid-vapor interfacial tension and hydrophilize the initially hydrophobic solid substrate just in front of the spreading drop. This process causes water drops to spread over time. The time of evolution of the spreading of a water droplet is predicted and compared with experimental observations. The assumption that surfactant transfer from the drop surface onto the solid hydrophobic substrate controls the rate of spreading is confirmed by our experimental observations. Copyright 2000 Academic Press.     

Evaporation rates of water from concentrated oil-in-water emulsions

We have investigated the rate of water evaporation from concentrated oil-in-water (o/w) emulsions containing an involatile oil. Evaporation of the water continuous phase causes compression of the emulsion with progressive distortion of the oil drops and thinning of the water films separating them. Theoretically, the vapor pressure of water is sensitive to the interdroplet interactions, which are a function of the film thickness. Three main possible situations are considered. First, under conditions when the evaporation rate is controlled by mass transfer across the stagnant vapor phase, model calculations show that evaporation can, in principle, be slowed by repulsive interdroplet interactions. However, significant retardation requires very strong repulsive forces acting over large separations for typical emulsion drop sizes. Second, water evaporation may be limited by diffusion in the network of water films within the emulsion. In this situation, water loss by evaporation from the emulsion surface leads to a gradient in the water concentration (and in the water film thickness). Third, compression of the drops may lead to coalescence of the emulsion drops and the formation of a macroscopic oil film at the emulsion surface, which serves to prevent further water evaporation. Water mass-loss curves have been measured for silicone o/w emulsions stabilized by the anionic surfactant SDS as a function of the water content, the thickness of the stagnant vapor-phase layer, and the concentration of electrolyte in the aqueous phase, and the results are discussed in terms of the three possible scenarios just described. In systems with added salt, water evaporation virtually ceases before all the water present is lost, probably as a result of oil-drop coalescence resulting in the formation of a water-impermeable oil film at the emulsion surface.     

Effects of Applied Electric Fields on Drop—Interface and Drop—Drop Coalescence*

In this work, coalescence of a single organic or aqueous drop with its homophase at a horizontal liquid interface was investigated under applied electric fields. The coalescence time was found to decrease for aqueous drops as the applied voltage was increased, regardless of the polarity of the voltage. For organic drops, the coalescence time increased with increasing applied voltage of positive polarity and decreased with increasing applied voltage of negative polarity. Under an electric field, the coalescence time of aqueous drops decreases due to polarization of both the drop and the flat interface. The dependency of organic drop-interface coalescence on the polarity of the electric field may be a result of the negatively charged organic surface in the aqueous phase. Due to the formation of a double layer, organic drops are subjected to an electrostatic force under an electric field, which, depending on the field polarity, can be attractive or repulsive. Pair-drop coalescence of aqueous drops in the organic phase was also studied. Aqueous drop-drop coalescence is facilitated by polarization and drop deformation under applied electric fields. Without applied electric fields, drop deformation increases the drainage time of the liquid film between two approaching drops. Therefore, a decrease in the interfacial tension, which causes drop deformation, accelerates drop-drop coalescence under an electric field and inhibits drop coalescence in the absence of an electric field.     

Contact line dynamics in the late-stage coalescence of diethylene glycol drops

We investigated the contact line dynamics of a composite drop formed as a result of the coalescence during the condensation of two diethylene glycol (DEG) drops at -4 degrees C on a silicon surface. The composite drop relaxes exponentially toward equilibrium with a typical relaxation time, tc, which depends on the equilibrium radius, R, of the composite drop. The value of tc is found to be in the range of 10-100 s for R approximately 1-4 microm. The relaxation dynamics is found to be larger by 6 orders of magnitude than that predicted by bulk hydrodynamics because of high dissipation in the contact line vicinity. Similar to low viscous liquids (water), this high dissipation can be attributed to an Arrhenius factor resulting from the phase change in the contact line vicinity and to the influence of surface defects that pin the contact line.     

特殊浸润性表面的液滴凝结

以铝片为基底, 经电化学腐蚀和沸水处理制备了多级微纳米结构; 通过气相沉积和涂油分别制备了超疏水表面、 疏水超润滑(slippery)表面和亲水slippery表面; 探究了表面不同的特殊浸润性(超亲水、 超疏水、 疏水slippery和亲水slippery)对液滴凝结的影响. 结果表明, 超亲水表面的液滴凝结属于膜状冷凝, 超疏水表面和slippery表面的液滴凝结均属于滴状冷凝. 超疏水表面液滴合并时, 合并的液滴会不定向弹离表面. 疏水slippery表面和亲水slippery表面由于表面浸润性的不同导致液滴成核密度和液滴合并的差异, 亲水slippery表面凝结液滴的最大体积远大于疏水slippery表面凝结液滴的最大体积. 4种表面的雾气收集效率由大到小依次为亲水slippery表面>疏水slippery表面>超亲水表面>超疏水表面.     

The drop size in membrane emulsification determined from the balance of capillary and hydrodynamic forces

Here, we investigate experimentally and theoretically the factors that determine the size of the emulsion droplets produced by membrane emulsification in "batch regime" (without applied crossflow). Hydrophilic glass membranes of pore diameters between 1 and 10 mum have been used to obtain oil-in-water emulsions. The working surfactant concentrations are high enough to prevent drop coalescence. Under such conditions, the size of the formed drops does not depend on the surfactant type and concentration, on the interfacial tension, or on the increase of viscosity of the inner (oil) phase. The drops are monodisperse when the working transmembrane pressure is slightly above the critical pressure for drop breakup. At higher pressures, the size distribution becomes bimodal: a superposition of a "normal" peak of monodisperse drops and an "anomalous" peak of polydisperse drops is observed. The theoretical model assumes that, at the moment of breakup, the hydrodynamic ejection force acting on the drop is equal to the critical capillary force that corresponds to the stability-instability transition in the drop shape. The derived equations are applied to predict the mean size of the obtained drops in regimes of constant flow rate and constant transmembrane pressure. Agreement between theory and experiment is established for the latter regime, which corresponds to our experimental conditions. The transition from unimodal to bimodal drop size distribution upon increase of the transmembrane pressure can be interpreted in terms of the transition from "dripping" to "jetting" mechanisms of drop detachment.     

Studies on the Binary Coalescence Model

The jumping coalescence phenomenon between two separate water drops under microgravitation was observed for the first time. Two suspended water drops separated by quite a distance (0.558 mm) coalesce in a certain time (158 s) without any extra forces. The coalescence driving force within the water drops should be responsible for the jumping coalescence phenomenon. Copyright 2001 Academic Press.     

Heat transfer coefficient and pressure drop during refrigerant R-134a condensation in a plate heat exchanger

The condensation heat transfer coefficient and the two-phase pressure drop of refrigerant R-134a in a vertical plate heat exchanger were investigated experimentally. The area of the plate was divided into several segments along the vertical axis. For each of the segments, local values of the heat transfer coefficient and frictional pressure drop were calculated and presented as a function of the mean vapor quality in the segment. Owing to the thermocouples installed along the plate surface, it was possible to determine the temperature distribution and vapor quality profile inside the plate. The influences of the mass flux and the heat flux on the heat transfer coefficient and the pressure drop were also taken into account and a comparison with previously published experimental data and literature correlations was carried out. Presented at the 34th International Conference of the Slovak Society of Chemical Engineering, Tatranské Matliare, 21–25 May 2007.     

Coalescence during emulsification. 3. Effect of gelatin on rupture and coalescence

An oil-soluble fluorescent probe, undecyl pyrene (UDP), is used to measure the amount of coalescence that occurs during the emulsification of tri-2-ethylhexyl phosphate using a high-pressure homogenizer. From these measurements, the roles of anionic surfactant (SDS) and gelatin in stabilizing drops against coalescence and promoting drop rupture during emulsification are deduced. It is found that gelatin aids in reducing coalescence, whereas SDS aids in rupture of drops. The effect of variables such as gelatin MW, surfactant type, and pH on coalescence and final drop size is investigated.     

Growth and motion of heterogeneous water droplets in laminar diffusion chambers: 2. High nanoparticle concentrations

The heterogeneous condensation of water vapor on nanoparticles and the growth of formed droplets are numerically studied under conditions of laminar diffusion chamber (LDC) of a new type with a hot porous wall. The main attention is focused on the growth of heterogeneous droplets in the gas flow at high number densities of nanoparticles exceeding 10⁸ droplet/m³. Under these conditions, there is an interrelation between the growth of droplets and processes of heat and mass transfer in LDC due to vapor depletion and the release of latent heat of phase transition on growing droplets. The efficiency of the coverage of nanoparticles with water film is studied under LDC nonuniform conditions. It is shown that, at initial number densities of nanoparticles (N _d > 10¹¹ droplet/m³), heterogeneous droplets do not grow to optically detected sizes.     

Bitumen-clay interactions in aqueous media studied by zeta potential distribution measurement

A new method of measuring the amount of coalescence that occurs between drops during the emulsification process is proposed. The method uses a hydrophobic fluorescent probe, which is introduced into a fraction of the oil phase that is to be homogenized. The ratio of the intensity of the excimer peak to the intensity of the monomer peak in the fluorescent emission spectrum is sensitive to the concentration of the probe in the oil phase. Random coalescence events between oil drops lead to redistribution of the probe and its effective dilution in the oil phase. Coalescence results in a decrease in the intensity ratio in the fluorescence spectrum obtained from the ensemble of drops. Monte Carlo simulation is used to relate the change in intensity ratio to the coalescence rate. It is experimentally verified that the signal change is only due to coalescence and is not affected by the drop size of the distribution.