Energy Budget in Atomization

An equation of mechanical energy balance in a liquid jet atomizing in an ambient gas is derived. The time rate of change of kinetic energy of the fluctuating disturbance in a given volume of the jet is shown to be equal to the sum of four types of works done per unit time on the jet and the energy dissipation rate through the agent of viscosity. The four types of works involved are the work by the surface tension, the work by the pressure fluctuation in the ambient gas, the work done by the fluctuating pressure in the jet, and the work by the viscous stress. Numerical results obtained for a wide range of relevant parameters are used to show that the surface tension work is negative in jet atomization. This is contrary to the situation in the breakup of an ink jet for which the surface tension work is positive, and thus the breakup is due to capillary pinching. It is shown that the work by fluctuating gas pressure is responsible for the atomization process, since the pressure work term is the dominant positive term in the energy budget of the jet atomization.     

Breakup of non-newtonian emulsion jets

The breakup of non-Newtonian emulsion jets into drops was experimentally studied by ejecting both O/W and W/O emulsions vertically downward into stagnant air through nozzles. Breakup lengths of non-Newtonian emulsion jets were found to be almost equivalent to those of Newtonian jets. Experimental breakup data establish that the static surface tension of the oil phase can be used as the surface tension of W/O emulsion jets, whereas the dynamic surface tension of aqueous surfactant solutions is used as that of O/W emulsion jets. Diameters of drops formed from non-Newtonian emulsion jets are in good agreement with the prediction from the stability theory previously developed by the authors. When the rheological index in a power law model is appreciably smaller than unity and the Ohnesorge number is significantly large, however, drop sizes are larger than the prediction because of the profile relaxation in jets. The critical velocity of emulsion jets, either O/W or W/O emulsion, is significantly lower than that of homogeneous Newtonian jets.     

Some surface tension and contact angle problems in industry

Contact angle, surface tension and wetting properties are of fundamental importance in many industrial processes, e.g. coating of television screens and fluorescent lights. In addition, different stages of many processes may involve immersion cleansing and subsequent drying. We consider two different problems: one being very practical and involving cleansing and drying of silicon substrates in the semiconductor industry, and the other being theoretical whereby the problem of the shape of scssile and pendant drops is addressed with a possible practical application for making contact angle and surface tension measurements. In the case of cleansing of silicon substrates, we model a process whereby dirt particles are removed as a result of the surface tension forces exerted on a particle passing through a water/air interface and give a possible explanation as to why the efficiency of the process is vclocity dependent. For the case of small liquid drops, a new formulation of the governing equation yields solutions for multiple pendant and extended sessile drops.     

BUOYANCY-DRIVEN MOTION OF DROPS AND BUBBLES IN A PERIODICALLY CONSTRICTED CAPILLARY

Buoyancy-driven motion of viscous drops and air bubbles through a vertical capillary with periodic constrictions is studied. Experimental measurements of the average rise velocity of buoyant drops are reported for a range of drop sizes in a variety of two-phase systems. The instantaneous drop shapes at various axial positions within the capillary are also quantitatively characterized using digital image analysis. Periodic corrugations of the capillary wall are found to have a substantial retarding effect on the mobility of drops in comparison with previous experimental results in a straight cylindrical capillary. For systems characterized by small Bond numbers, drop deformations are found to be periodic. In large Bond number systems, however, drop breakup eventually occurs as the drop size is increased beyond a critical limit. The observed mode of breakup is a tail-pinching process similar to that observed by Oibricht and Leal (1983) for pressure-driven motion of low viscosity ratio drops through a sinusoidally constricted capillary. In contrast to their results, however, the same mode of breakup was also observed for systems with O (1) viscosity ratios,     

Surface Tension and Density of Molten A12O3

An X-radiographic technique was developed to obtain profiles of molten ceramic menisci and pendant drops sealed in molybdenum or tungsten capsules. The surface tension for Al₂O₃ was calculated from the shape of the drops or menisci. Molybdenum capsules lowered the surface tension value. The density was 3.01 g/cm⁸ at the melting point.     

Interfacial tension measurements between α-tocopherol and carbon dioxide at high pressures

The interfacial tension of the binary system α-tocopherol/carbon dioxide was measured using the pendant drop method in the pressure range between 10 and 37 MPa at nine different temperatures: 313, 333, 343, 353, 363, 373, 383, 393, and 402 K. At every interfacial tension measurement, densities of both the liquid and the supercritical gas phase were also determined as the knowledge of these values is essential for calculating interfacial tension from the shape and size of drops. The interfacial tension decrease with rising pressure at a constant temperature and increases with increasing temperature at a constant pressure. The interfacial tension was found to be mainly a function of the mutual solubility of the two system components and of the density of pure carbon dioxide.     

CFD-PBM耦合模型模拟气液鼓泡床的通用性研究

通过对不同操作压力和不同液体性质气液鼓泡床的模拟值与实验数据进行对比，从而验证CFD-PBM耦合模型的通用性。结果表明，CFD-PBM耦合模型在加入了气泡破碎修正因子后，可以很好地预测压力对鼓泡床流体力学行为的影响趋势，当压力升高时，气含率显著升高。不同液体黏度和表面张力条件下CFD-PBM耦合模型的模拟结果与实验结果均吻合较好。随液体黏度增大，气泡破碎速率减小，气泡尺寸分布变宽，曳力显著下降，气含率随之降低。随表面张力减小，气泡破碎速率增大，气泡变小，气含率升高。CFD-PBM耦合模型具有很好的通用性，原因在于考虑了压力、液体黏度和表面张力对气泡聚并、破碎和气液相间作用力的影响。     

Physico-chemical and dynamic study of oil-drop removal from bare and coated stainless-steel surfaces

We have studied the removal of sessile oil drops from stainless-steel surfaces under the action of water flow. A shear-flow cell is used to compare bare and polysiloxane-coated stainless-steel surfaces. We consider a rectangular channel where initially deposited drops are subjected to drag, gravity and pressure gradient forces. Our results indicate that a drop detachment mode is observed for the bare steel, whereas a sliding mode is observed for the coated steel. The removal of large drops, which requires low critical shear flows, is essentially dominated by the combined action of the lift and gravity forces. However, for small drops with a large critical shear flow, the capillary forces are the key factor. The detachment was also studied with surfactants added to water. It was found that the detachment mode exhibits a 'depinning effect', which results in drops sliding. Due to low pressure near the triple line, an accumulation of the surfactant induces surface tension gradients along the interface (Marangoni effect), which, in turn, facilitates depinning of the contact line. These results underline the crucial role of the capillary forces governed by the physico-chemical nature of stainless steels, a key factor for understanding the cleanability processes of these materials.     

表面张力变化对含气泡液体射流破裂的影响

使用高速相机研究了表面张力变化对含气泡液体射流破裂过程的影响。通过改变表面活性剂浓度获得了不同表面张力的液体射流。实验发现当液体射流速度保持不变时,减小液体表面张力会增加射流破裂长度。表面活性剂一方面降低了液体动态表面张力,减小了射流表面不稳定波的增长率,增大了射流破裂长度;另一方面表面活性剂在射流表面的非均匀分布会产生Marangoni应力,促使液体向射流变形区运动,从而推迟了射流破裂的发生,增大了射流破裂长度。通过理论分析得到了液体射流破裂长度表达式。发现射流内部气泡会显著缩短含表面活性剂射流的破裂长度。通过气泡扰动射流速度和吸附表面活性剂的分析,揭示了内部气泡对含表面活性剂射流破裂的影响规律。     

Drop formation in a co-flowing ambient fluid

Drop formation at a capillary tip in laminar flow is investigated experimentally. The disperse phase is injected via a needle into another co-flowing immiscible fluid. Two different drop formation mechanisms are distinguished: Either the drops are formed close to the capillary tip—dripping—or they break up from an extended liquid jet—jetting. The effect of the process and material parameters on the drop formation depends on the breakup mechanism and has to be investigated for each flow domain separately. In this study, we focus on dripping. The drop breakup is affected by the flow dynamics of both the disperse and the continuous phase. Consequently, we investigate the effect of flow rates, fluid viscosities and interfacial tension on the droplet size and observe the dynamics of satellite drop generation. Whereas the fundamentals of disperse fluid injection via a capillary into an ambient fluid have been investigated extensively, the focus of this article is on providing a comprehensive experimental data set for proving the applicability of this technique as a dispersing tool. It is shown that drop formation at a capillary tip into a co-flowing ambient liquid represents a promising technique for the production of monodisperse droplets where the droplet size is controlled externally by the flow strength of the continuous phase. The breakup dynamics changes significantly at the transition point from dripping to jetting. Consequently, the transition point between the flow domains represents an important operating point. In this article, dripping is demarcated from jetting by studying the influence of the various material and process parameters on the transition point.     

The interfacial tension between a thermotropic liquid crystalline copolyester and polyethersulfone: A comparison of methods

Three dynamic methods to determine the interfacial tension between the thermotropic liquid crystalline polymer (TLCP) Vectra A900 and polyethersulfone were evaluated: (1) thread breakup, (2) fiber retraction and (3) dynamic shear rheometry. The thread breakup and retraction methods, were suitable for measuring the interfacial tension, provided that the shear thinning flow behavior of the TLCP was taken into account. The viscosity of the TLCP during breakup or retraction was estimated from steady-shear measurements at the observed overall rate of deformation during growth of capillary instabilities or during retraction. The calculation of the interfacial tension from breakup rates of TLCP threads was improved by accounting for transient flow behavior during distortion growth using a single-element Maxwell model. Determination of the interfacial tension by oscillatory shear measurements on TLCP/PES dispersions using the emulsion model of Palierne, was not applicable for this system. Only for dispersions containing low TLCP volume fractions (e.g. 9 vol%) was there reasonable agreement between the emulsion model and measurements. At higher volume fractions agreement was poor, possibly because of different dynamic flow behavior of the TLCP in the pure form and in blends. The interfacial tension values obtained from thread breakup and fiber retraction ranged from 4 to 6 mN/m, which demonstrate that in-situ determination of the interfacial tension is possible for blends containing TLCPs, despite their complex flow behavior.     

MEASUREMENT OF SURFACE TENSION OF VISCOUS LIQUIDS *

The surface tensions of liquids of widely differing viscosities have been measured by the maximum bubble-pressure method. With liquids whose viscosities are greater than about five poises, a modification of the customary technique is employed, which consists in observing the maximum pressure at which a bubble is stable. This is the same procedure which Parmelee used. The applicability of this method for viscous liquids has been tested by measuring the surface tensions at 25° C of a series of solutions of rosin in benzyl-benzoate whose viscosities varied from about 100 to 2500 poises. The values obtained are within 1 % of those observed by the method of capillary rise. The method has been applied to the measurement of the surface tensions of molten glasses whose viscosities varied from 50 to 2500 poises. The precision obtained is about 1%. A technique for the approximate measurement of surface tension of glasses by means of sessile drops is described.     

Transformation of single drop breakup from binary to ternary and multiple in turbulent jet flows

By releasing liquid drops in turbulent jet flows,we investigated the transformation of single drop breakup from binary to ternary and multiple.Silicone oil and deionized water were the dispersed phase and con-tinuous phase,respectively.The probability of binary,ternary,and multiple breakup of oil drops in jet flows is a function of the jet Reynolds number.To address the underlying mechanisms of this transfor-mation of drop breakup,we performed two-dimensional particle image velocimetry(PIV)experiments of single-phase jet flows.With the combination of drop breakup phenomenon and two-dimensional PIV results in a single-phase flow field,these transformation conditions can be estimated:the capillary number ranges from 0.17 to 0.27,and the Weber number ranges from 55 to 111.     

The marangoni effect and enhanced oil recovery Part 2. Interfacial tension and drop instability

A computer-based method is described for the determination of the interfacial tension between pendant and sessile drops in a surrounding continuous phase. This has been used to determine the effect on interfacial tension of increasing amounts of aliphatic alcohols, from methanol up to n-octanol, equilibrated between a hydrocarbon solvent (Shellsol) and water. The results indicated large decreases in interfacial tension, with n-butanol, followed by n-propanol giving the greatest reduction. Measurements were also made of the rate of change of interfacial tension during the mass transfer of 2.5% of the alcohols between phases. Changes were observed for all alcohols from ethanol to n-pentanol, the effect being greatest for transfer into water drops and out of solvent drops. Application of the linear stability theory of Sørensen to these results failed to predict the observed instability for transfer into solvent drops.     

简单剪切流动中液滴断裂机理

The experimental results of the deformation and breakup of a single drop immersed in a Newtonian liquid and subjected to a constant shear rate which generated by counter rotating Couette apparatus were presented in this paper. From experimental observations, the breakup occurred by three mechanisms, namely, necking, end pinching, and capillary instability. Quantitative results for the deformation and breakup of drop are presented. The maximum diameter and Sauter mean diameter of daughter drops and capillary thread radius are linearly related to the inverse shear rate and independent of the initial drop size, the dimensionless wavelength which is the wavelength divided by the thread width at breakup is independent of the shear rate and initial drop size, and the deformation of threads follows a pseudo-affine deformation for Cai/Cac larger than 2.     

Interfacial tension in polymer melts. I: An improved pendant drop apparatus

An apparatus is described to measure interfacial tension for molten polymer pairs. The apparatus is based on the pendant drop method. A CCD color video camera captures the image of a pendant drop profile, which is analyzed on-line using a microcomputer. These almost continuous measurements permit the detection of possible changes in the behavior of the melt that might affect the interfacial tension through thermal degradation. A special syringe to inject the pendant drop has been designed in order to avoid problems such as the capillary effect of the tube of the syringe and the necking and detachment of the pendant drop. The accuracy of the apparatus was verified using water/n-hexane and water/n-octane. Experimental results for polypropylene/polystyrene (PP/PS) are presented. The interfacial tension between the polymer pair decreases as temperature increases and as molecular weight decreases. Interfacial tension is estimated from the drop shape when the drop is at mechanical equilibrium. For polymer systems, mechanical equilibrium normally takes from 1 to 10 h to occur. However, transient values of interfacial tension (apparent interfacial tension values obtained before mechanical equilibrium is reached) may be used to estimate the interfacial tension at equilibrium by extrapolation, thus reducing the required experimental time.     

A novel theoretical breakup kernel function for bubbles/droplets in a turbulent flow

Several models for the daughter bubble/droplet size distribution are reviewed and a detailed discussion is given to get a better understanding of the daughter size distribution. A novel theoretical breakup kernel function for bubbles/droplets in a turbulent flow, based on an eddy-bubble/droplet collision method, is developed. It takes into account the energy distribution of turbulent eddies, effect of capillary pressure and surface energy increase during bubble/droplet breakup. An increase in the mother bubble/droplet size and energy dissipation rate increases the probability of unequal breakup. The model prediction is in good agreement with experimental results and the underlying physical situation.     

Use of NMR imaging to measure interfacial properties of asphalts

An NMR imaging method that allows for direct calculation of interfacial surface tensions of asphalts is described. The method is based upon acquiring NMR images of water drops on the surface of asphalt as a function of time. By expressing the contact angle for the water drop either in terms of Young's equation, or the liquid lens equation for the initial placement of the water drop on the asphalt surface, and for a later time when the water drop has penetrated below the asphalt surface, two equations that incorporate the asphalt-air surface and asphalt-water interfacial tensions are obtained which can be solved analytically. The NMR imaging method was used to determine the surface tensions of the eight Strategic Highway Research Program (SHRP) core asphalts at 25 °C. Asphalt-water interfacial tension values ranged from 25 to 40 dynes/cm, and asphalt-air surface tension values ranged from about 38-50 dynes/cm. These results are in general agreement with other asphalt surface tension measurements that have been made using the du Noüy ring tensiometer, or the Wilhelmy Plate method. Spreading coefficients and capillary numbers derived from the surface tension calculations are also reported.     

水在非相溶油中滴流雾化的界面追踪模拟

基于欧拉法和流体体积函数建立了描述相界面运动、变形、破碎等复杂变化的界面追踪模型(VOF-CSF),该模型采用了二相界面重构技术,并考虑了界面张力和接触角的影响,将水在非相溶油中滴流雾化形成液滴过程简化为二维轴对称数值模拟,模拟了层流环境中低喷射流率下液滴形成的全过程.模拟结果表明:在滴流雾化方式下,液滴形成过程由液滴...     

The role of elasticity in the formation of electrospun fibers

The role of fluid elasticity in the formation of fibers from polymer solution by electrospinning is investigated. Model solutions with different degrees of elasticity were prepared by blending small amounts of high molecular weight polyethylene oxide (PEO) with concentrated aqueous solutions of low molecular weight polyethylene glycol (PEG). The elastic properties of these solutions, such as extensional viscosity and the longest relaxation time, were measured using the capillary breakup extensional rheometer (CaBER). The formation of beads-on-string and uniform fiber morphologies during electrospinning was observed for a series of solutions having the same polymer concentration, surface tension, zero shear viscosity, and conductivity but different degrees of elasticity. A high degree of elasticity is observed to arrest the breakup of the jet into droplets by the Rayleigh instability and in some cases to suppress the instability altogether. We examine the susceptibility of the jet to the Rayleigh instability in two ways. First, a Deborah number, defined as the ratio of the fluid relaxation time to the instability growth time, is shown to correlate with the arrest of droplet breakup, giving rise to electrospinning rather than electrospraying. Second, a critical value of elastic stress in the jet, expressed as a function of jet radius and capillary number, is shown to indicate complete suppression of the Rayleigh instability and the transition from ‘beads-on-string’ to uniform fiber morphology.