Dispersion of water into oil in a rotor–stator mixer. Part 1: Drop breakup in dilute systems

Most previous studies of liquid–liquid dispersion in complex geometry are limited to turbulent flow at low continuous phase viscosity. In this study, a viscous continuous phase was employed over a range of flow conditions including both the laminar and turbulent regimes. Equilibrium drop size was measured for water dispersed into viscous food grade mineral oils in a batch Silverson L4R rotor–stator mixer. The influence of fluid viscosities and interfacial tension (by adding an oil-soluble surfactant) were examined. In order to isolate the effect of drop breakage from coalescence, Part 1 is limited to dilute conditions (water phase fraction, ? = 0.001). In the laminar regime, drop breakup was more likely due to a simple shear breakage mechanism than one for extension. Following Grace (1982), a semi-empirical drop size correlation was developed. For turbulent flow, the validity of the sub-Kolmogorov inertial stress model for correlating equilibrium mean drop size was verified. Surfactants were found to mostly decrease drop size by lowering interfacial tension. Except for laminar systems near the critical micelle concentration, where Marangoni stresses appear to play some role, the effect of surfactants on the drop size could be correlated using the equilibrium or static interfacial tension. The influence of water phase fraction and coalescence is considered in Part 2 ( Rueger and Calabrese, 2013) of this paper.     

Dispersion of water into oil in a rotor–stator mixer. Part 2: Effect of phase fraction

In Part 1 (Rueger and Calabrese, 2013), we monitored dilute water-in-oil dispersions in a batch Silverson L4R rotor–stator mixer to establish breakage mechanisms and develop a mechanistic basis for correlation of equilibrium mean drop size. In this study (Part 2) we consider the effect of water phase fraction under similar processing conditions, thereby requiring consideration of coalescence. Most of the work on the effect of phase fraction in stirred vessels was done with a low-viscosity continuous phase in turbulent flow with inertial subrange scaling (d > η). For that case drop size increases linearly with phase fraction, ?. In this study, viscous oils comprised the continuous phase, with water as the drop phase. The equilibrium DSD was measured in both laminar and turbulent flow conditions. The diameter of the largest drops was always less than the Kolmogorov microscale (d < η). A much greater increase (than the aforementioned linear relationship) in drop size with phase fraction was observed for ? ≤ 0.05; including cases where an oil soluble surfactant was present and where metal mixing head surfaces were rendered hydrophobic by treatment with silane functional groups. It is argued that this significantly greater dependence on ? is due to the flow field being locally laminar near the drops with coalescence rate being strongly affected by the collision efficiency, which depends on the viscosity of both phases. The presence of surfactant decreased drop size. The silane treatment decreased drop size; possibly by altering water drop interactions with mill head surfaces. Additional experiments were performed at higher phase fraction, where surfactant was required to stabilize the emulsion. The equilibrium drop size was found to plateau for 0.10 < ? < 0.50. The high phase fraction behavior is attributed to the competing rates of coalescence and breakage and their dependence on ? and drop size.     

Rotor–stator devices: The role of shear and the stator

High shear rotor–stator mixers are widely used in process industries including the manufacture of many food, cosmetic, pharmaceutical, and health care products. Many of these products involve emulsification where the drop size distribution affects the processing and the product properties. Therefore, an understanding of the mechanisms that breaks the drops is key for any design process. In rotor–stator devices there are two main mechanisms that can break drops, one due to the rotor and one due to the stator. For the inviscid systems studied, this article shows that when a rotor–stator device is used in a recycle loop the effective equilibrium drop size is largely unaffected by the presence of the stator and is mainly dependant on the rotor. The article also goes on to show that the effective equilibrium drop size data can be correlated on the agitator shear rate.     

湍流分散系统中的液滴聚并

主要分析各向同性湍流中的液滴聚并过程且建立了一个模型,用以预测表面活性剂系统和纯净系统中的最小稳定液滴直径,该模型不含任何可调参数或经验参数．在此基础上,进一步研究了液滴尺寸分布和聚并效率．     

Effect of mass transfer on drop size in a Karr column

This paper presents experimental data on drop size distribution and Sauter mean drop diameter in a 7.6 cm diameter reciprocating plate extraction column with and without mass transfer, using the liquid system toluene—acetone—water.The measured drop size distribution curves show that most of the break-up of the dispersed drops was achieved by the first few plates. The agitation rate was found to be the predominant factor in determining the mean drop diameter and the total interfacial mass transfer area.During mass transfer both the drop size distribution and the mean drop diameter were found to depend on the mass transfer direction.The measurements of the mean drop diameter in the absence of mass transfer were compared with published data and new correlations presented.     

The effects of clay fines on oil in water dispersions

The effects of the addition of clay on oil drop size were investigated for dispersions of oil in water in an agitated vessel. Three types of oil were used: hexane, a medium viscosity paraffin oil and a viscous Cold Lake bitumen. Pure kaolinite clay was used for the solids. Experiments were carried out with and without clay fines over a range of agitator speeds. The addition of kaolinite was found to increase the drop size for both the hexane and the paraffin oil, approximately doubling the drop size for hexane. The addition of the kaolinite to the bitumen/water dispersions was found to have no effect on the drop size.     

Analysis of evaporating droplets using ellipsoidal cap geometry

The evaporation of small droplets of volatile liquids from solid surfaces depends on whether the initial contact angle is larger or less than 90°. In the latter case, for much of the evaporation time the contact radius remains constant and the contact angle decreases. At equilibrium, the smaller the drop, the more it is possible to neglect gravity and the more the profile is expected to conform to a spherical cap shape. Recently published work suggests that a singular flow progressively develops within the drop during evaporation. This flow might create a pressure gradient and so result in more flattening of the profile as the drop size reduces, in contradiction to expectations based on equilibrium ideas. In either case, it is important to develop methods to quantify confidence in a deduction of elliptical deviations from optically recorded droplet profiles. This paper discusses such methods and illustrates the difficulties that can arise when the drop size changes, but the absolute resolution of the system is fixed. In particular, the difference between local variables, such as contact angle, cap height, and contact diameter, which depend on the precise location of the supporting surface, and global variables such as radii of curvature and eccentricity, is emphasized. The applicability of the ideas developed is not limited to evaporation experiments, but is also relevant to experiments on contact angle variation with drop volume.     

Detection of the fractal character of compact adsorbed layers by the dropping mercury electrode

The development of compact adsorbed layers at the dropping mercury electrode is used for the detection of resulting changes in the geometry of the electrode-solution interface from Euclidean to fractal. A simple size scaling method of the Hg drop surface is applied, which focus on the time dependence of the drop area under conditions of constant adsorbate and base electrolyte concentration, constant potential and constant mercury flow rate.It is found that the slope of the log-log plots of capacitance or capacitance current against electrode surface area or electrode radius is increasing upon the formation of a compact adsorbed layer. Under equilibrium conditions the slope values of the linear log-log plots can be reasonably identified with the fractal dimension of the electrode/solution interface. However, due to the limited extent of the power-law range of the feature vs. scale relation, the size scaling method of the dropping mercury electrode can be used to probe fractal adsorbate films on a strictly qualitative level.     

SOME ASPECTS OF SPRAY FORMATION BY PNEUMATIC NOZZLES

A study of spray formation in a pneumatic nozzle With external mixing is pre- sented. The mast importent parameters are highlighted and their influence on the mean drop diameter and size distribution is examined. A theoretical approach is outlined which yields several exponential models containing all important parame- ters in dimensionless form. The most appropriate model for drop size prediction is recommended after experimental verification and comparison with several previously published models. Special attention was paid to development of s simple model which makes its practical application easier.

Unlike the mean drop diameter, the size distribution was found to be much less affected by the operating parameters. The Rosin-Rammler distribution can be used to characterize the experimental results within the range covered. The coefficient of polydispersity was found to be practically unaffected by the operating parameters.     

闭式涡轮搅拌萃取塔液滴直径的估算

本文利用均匀各向同性湍流特性分析连续相湍流脉动液滴大小的影响，得出搅拌强度和液滴平均直径之间的关系，根据所使用的三种塔几何结构所得的实验数据检验。理论分析结果与实验所得结果较好地相符。本文也讨论了分散相存留分数对平均液滴直径的影响。     

Dynamic Contact Angles of Viscous Liquids

An empirical model has been developed which can predict the dynamic contact angle of a spreading drop of viscous liquid on a plane wettable surface from the contact area for contact angles between 90° and 0° within a specified drop size. This range of drop size is restricted to those drops having a contact area at a 90° cap condition (A₉₀) between 0.10 cm² and 0.20 cm² The drop profile was found not to be that of a spherical segment and hence could not allow a simple geometric interpretation. The model strengthens the interpretation that contact angle development in this range of drop size is mainly the geometric result of spreading. The model was found to hold over a wide variety of polymer melt temperatures (155-240°C), molecular weights and molecular weight distributions, which combined would greatly influence drop profile. The time dependency of the dynamic contact angle was also evaluated by combining the present empirical model with a previous viscosity dependent model relating contact area with time. The model was successfully applied to the unrelated systems of silicone oil and glycerol at room temperature indicating its general applicability.     

Effect of die temperature on the morphology of microcellular foams

A study on the extrusion of microcellular polystyrene foams at different foaming temperatures was carried out using CO₂ as the foaming agent. The contraction flow in the extrusion die was simulated with FLUENT computational fluid dynamics code at two temperatures (150°C and 175°C) to predict pressure and temperature profiles in the die. The location of nucleation onset was determined based on the pressure profile and equilibrium solubility. The relative importance of pressure and temperature in determining the nucleation rate was compared using calculations based on classical homogeneous nucleation theory. Experimentally, the effects of die temperature (i.e., the foaming temperature) on the pressure profile in the die, cell size, cell density, and cell morphology were investigated at different screw rotation speeds (10 ～ 30 rpm). Experimental results were compared with simulations to gain insight into the foaming process. Although the foaming temperature was found to be less significant than the pressure drop or the pressure drop rate in deciding the cell size and cell density, it affects the cell morphology dramatically. Open and closed cell structures can be generated by changing the foaming temperature. Microcellular foams of PS (with cell sizes smaller than 10 μm and cell densities greater than 10 cells/cm³) are created experimentally when the die temperature is 160°C, the pressure drop through the die is greater than 16 MPa, and the pressure drop rate is higher than 10⁹ Pa/sec.     

Experimental Study of Particle Collection by Small Cyclones

A new set of experimental data on the particle collection characteristics of small cyclones is reported. The collection efficiency for particles ranging from 2 to 10 μm in diameter was measured systematically for nine cyclones at flow rates ranging from 8.8 to 18.4 L/min. Special emphasis was given to the effects of the exit tube size and of the cyclone body size on the particle collection efficiency. The size ratio of the exit tube to the cyclone body was varied from 0.24 to 0.80. The experimental results show that the stiffness of the particle collection cutoff with size does not change noticeably with a change in the cyclone body size while operation of a cyclone at a low flow rate can cause the particle collection characteristics to become less stiff. It was also found that the exit tube diameter influences the particle collection efficiency substantially, with results showing that as the exit tube size is decreased, the collection efficiency increases. A large cyclone body size increases the efficiency. However, when the cyclone body is increased excessively, the collection efficiency appears to decrease somewhat. The experimental data were compared with existing cyclone theories and Barth's (1956) theory was found to be in good agreement. Finally, the exit tube was found to affect substantially the pressure drop of cyclones. As the exit tube size increased, the pressure drop decreased. However, when the exit tube size was further increased until it approached the body size, the pressure drop increased again.     

Drop size correlation and population balance model for an agitated-pulsed solvent extraction column

Agitated-pulsed column (APC) is a newly designed extraction column with excellent mass transfer performance. In this work, Sauter mean drop diameter d₃₂ and drop size distribution was investigated under different operation conditions in a 25 mm diameter APC. The results show that with an increase in pulsation intensity and agitation speed the drop size distribution is narrowed and d₃₂ is decreased significantly. With increasing dispersed-phase velocity, d₃₂ increased and drop size distribution become narrow, while there was no noticeable change with continuous velocity. The cumulative size distribution was found to be predicted well using the Inverse Gaussian function. A new correlation was proposed to predict the experimental d₃₂ data of the APC column used in this study. Furthermore, population balance model was applied to predict the drop size distribution with refitted parameters in the breakage, coalescence kernels functions.     

Break-up of droplets in Karr reciprocating plate extraction column

The breaking rate of individual drops was investigated in a Karr type reciprocating plate extraction column. The binary systems used were: water-1,2-dichloroethane, water-toluene and water-n-butanol. The breakage probability and the conditional probability of breaking-up into a given number of daughter droplets, as well as the drop size distribution of daughter droplets, were the measured characteristics. Relations between the breakage probabilities and the breakage frequency were derived.A mathematical model of the frequency of breaking-up into > and more droplets developed was based on the assumption that collisions with turbulent eddies of the Kolmogoroff region of universal equilibrium are responsible for the process. A probabilistic model of daughter drop size distribution was also derived in the form of a β-distribution. The models were compared with experimental results and a good agreement was obtained.     

脉冲对流化床气-固流动特性的影响

运用双流体法建立了三维脉冲流化床模型,模拟了不同脉冲下流化床内的气固流动特性。通过床层压降与气体空隙率分布的比较和分析,发现：脉冲可明显地降低床层压降,减小气泡尺寸;脉冲频率越大,床层压降越大;脉冲气流中有稳定气流的床层压降比无稳定气流的床层压降更小;脉冲振幅的增强可适量增加气体空隙率,但床层压降也增大。     

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.     

High speed imaging of drop formation from low viscosity liquids and polymer melts in spinning disk atomization

An investigation of drop formation in a recently developed spinning disk atomization (SDA) technique is presented. In‐situ observations of drop formation at the disk rim, using a high speed imaging installation, are made. Atomizations covering two orders of magnitude in flow rate show that ligaments can also form at low flow rates. Sequences of pictures indicate that drops undergo a rotary motion as they detach from a ligament. In the direct drop regime, oscillating motions dominate. The effect of teeth shape at the disk rim on the resulting drops is compared. The effect on drop size and size distribution is found to decrease with increasing rotation rate and corresponding images are studied. Experiments with liquid viscosities ranging from 1 to 120 mPas reveal a fundamental difference in drop breakup, but a negligible change in drop size. Likewise, only a small effect of liquid density is detected. The surface tension's influence on the liquid spreading at the disk rim is described and the subsequent drop formation is qualitatively analyzed.     

Influence of Nanoparticles and Drop Size Distributions on the Rheology of w/o Pickering Emulsions

The rheological behavior of particle/oil suspensions and w/o Pickering emulsions consisting of water, 1‐dodecene and different fumed silica nanoparticles was investigated. The particles varied in hydrophobicity and specific surface area. The influence of particle concentration and water content on rheology was determined and the emulsion drop size distributions were examined. Emulsions with different drop sizes were created by either varying the particle concentration or the water content. It was found that the particles in the continuous oil phase and not the drop size distribution seem to be the major influencing factor on the Pickering emulsion rheology.