Studies of drop break-up in liquid-liquid systems in a rotating disc contactor. Part II: Effects of mass transfer and scale-up

The number fraction of drops of a given size which break up at rotor level in a rotating disc contactor has been observed during mass transfer in either direction to or from solvent or aqueous drops. Critical rotor speeds for a given drop size undergoing mass transfer can be used to find an effective interfacial tension. Using this interfacial tension value, the break-up fractions are correlated within experimental uncertainties in the same manner as for no mass transfer. Drop break-up fractions depend on column size and relevant empirical correlations of the data are presented. The results may be used to estimate the effect of mass transfer on drop size distributions in an RDC.     

Drop break-up in intermittent turbulence: Maximum stable and transient sizes of drops

A multifractal method describing the fine-scale structure of turbulence, including its intermittency, is applied to derive the drop breakage functions for drops whose diameter falls within the inertial subrange of turbulence, including effects of the viscosity of the dispersed phase. The model predicts well the transient drop size distributions of dispersions undergoing breakage at long stirring times. Concepts of quasi-stable and asymptotically stable drop sizes are presented and discussed in relation to the exponent on the Weber number. The functions for drop break-up in the viscous subrange are proposed and discussed.     

Drop break-up in turbulent pipe flow downstream of a restriction

This work addresses the drop fragmentation process induced by a cross-sectional restriction in a pipe. An experimental device of an upward co-current oil-in-water dispersed flow (viscosity ratio λ≈0.5) in a vertical column equipped with a concentric orifice has been designed. Drop break-up downstream of the restriction has been studied using a high-speed trajectography. The first objective of this work deals with a global analysis of the fragmentation process for a dilute dispersion. In this context, the operating parameters of the study are the orifice restriction ratio β, the flow Reynolds number, Re and the interfacial tension, σ. The break-up domain has been first mapped on a β(Re) graph and drop size distributions have been measured for different flow Reynolds numbers. It was observed that the mean drop diameter downstream of the restriction linearly increases as a function of the inverse of the square root of the pressure drop. This behaviour is in agreement with the observations previously made by Percy and Sleicher [A.I.Ch.E. Journal, 1983, 29(1), 161-164]. In addition, experiments based on the observation of single drop break-up downstream of the orifice have allowed the identification of different break-up mechanisms, and the determination of statistical quantities such as the break-up probability, the mean number of fragments and the daughter drop distribution. The drop break-up probability was found to be a monotonous increasing function of the Weber number based on the maximal pressure drop through the orifice. The mean number of fragments is also an increasing function of the Weber number and the reduced mean daughter drop diameter decreases as the Weber number increases. The daughter drop distributions are multimodal at low and moderate Weber numbers as a result of asymmetrical fragmentation processes. The statistical analysis of single drop break-up experiments was implemented in a simple global population balance model in order to predict the evolution of the size distribution across the restriction at different Reynolds numbers, in the limit of dilute dispersions.     

Break-up of a drop in a stirred tank

The drop break-up mechanism was studied in a stirred tank containing two immiscible liquids. The daughter drops formed by break-up of a single drop of known size were recorded photographically. From the experiments at constant agitator speed the following results were obtained. There is a critical drop size under which drops do not break up under given conditions. The break-up frequency increases approximately linearly with increase in drop volume. The number of daughter drops, v, is a random variable with a mean v > 2 which increases with the volume of the mother drop. The relative volume of a daughter drop has a β-distribution.     

Drop breakup and entrainment in the updraft

This study aims to investigate the characteristics of gas–liquid countercurrent contact processes. In spray towers or other applications, several drops containing pollutants are entrained by the updraft flue gas, which can easily cause environmental pollution. Traditionally, this drop entrainment phenomenon is alleviated by increasing the diameter of the drops. However, the breakup of a large drop would also cause drop entrainment to become serious, a process referred to as secondary atomization. Herein, we propose the boundary of three drop modes in the updraft: drop falling mode, reverse entrainment mode, and breakup entrainment mode. The critical Weber number (We) is the key dimensionless number marking the beginning of the drop breakup. The ratio of the drag force to gravity and We are proposed as criteria for the drop entrainment.     

转盘离心粒化中丝状成粒特性

针对转盘离心粒化工艺,以水为工质开展可视化实验。采用高速摄影仪对液膜波动、液丝断裂等粒化过程进行了捕捉,并利用MATLAB自编程序对获得的图像进行了处理。分析了离心粒化过程中液丝形成过程以及液丝断裂形成液滴的过程。研究了运行工况对液丝、液滴形成机制的影响。讨论了液丝形成对液滴形成的影响并获得了Weber数、Reynolds数对粒化效果的影响程度。结果表明,表面不稳定波是形成液丝的主要因素,且液丝在Rayleigh不稳定性的作用下断裂形成液滴。升高转速或者减小流量有利于获得均匀的小液滴。Weber数对液丝、液滴形成具有显著影响;Reynolds数仅对液丝数目有显著影响。     

LIQUID DISPERSION MECHANISMS IN AGITATED TANKS PART III. LOW VISCOSITY DISCRETE PHASE INTO HIGH VISCOSITY CONTINUOUS PHASE

The dispersion or a low viscosity liquid into a high viscosity liquid was investigated in an agitated tank using a pitched blade turbine. The trailing vortex system was found to be responsible for the formation of ligaments and sheets of the low viscosity liquid. Dispersion, though, was found to occur due to: 1) the break-up of ligaments and 2) small drop production from large drops in a recirculation flow; both dispersion mechanisms were a classical Rayleigh type break-up. The drop size produced in the recirculation flow from large drops was on the order of those observed in the turbulent fragmentation mechanism. The flow, though, was entirely laminar.     

LIQUID DISPERSION MECHANISMS IN AGITATED TANKS PART III. LOW VISCOSITY DISCRETE PHASE INTO HIGH VISCOSITY CONTINUOUS PHASE

The dispersion or a low viscosity liquid into a high viscosity liquid was investigated in an agitated tank using a pitched blade turbine. The trailing vortex system was found to be responsible for the formation of ligaments and sheets of the low viscosity liquid. Dispersion, though, was found to occur due to: 1) the break-up of ligaments and 2) small drop production from large drops in a recirculation flow; both dispersion mechanisms were a classical Rayleigh type break-up. The drop size produced in the recirculation flow from large drops was on the order of those observed in the turbulent fragmentation mechanism. The flow, though, was entirely laminar.     

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.     

液-液水力旋流器中的液滴破碎

在总结前人研究成果的基础上,分析了液-液水力旋流嚣中液滴破碎产生的原因,指出流场的湍流特性是产生液滴破碎的主要原因。对水力旋流器中的湍流度、雷诺切应力及颗粒的湍动能进行了分析,给出了水力旋流器中液滴破碎可能性较大的几个部位,并对旋流器边壁液滴破碎的可能性进行了讨论。分析了水力旋流器中液滴破碎的机理,阐明了液滴破碎判据——临界Weber数的表达式,并对理想球形液滴的破碎进行了分析。     

A model for drop and bubble breakup frequency based on turbulence spectra

In this article, a new Eulerian model for breakup frequency of drops induced by inertial stress in homogeneous isotropic turbulence is developed for moderately viscous fluids, accounting for the finite response time of drops to deform. The dynamics of drop shape in a turbulent flow is described by a linear damped oscillator forced by the instantaneous turbulent fluctuations at the drop scale. The criterion for breakup is based on a maximum value of drop deformation, in contrast with the usual critical Weber criterion. The breakup frequency is then modeled as a function of the power spectrum of Weber number (or velocity square), based on the theory of oscillators forced by a random signal, which can be related to classical statistical quantities, such as dissipation rate and velocity variance. Moreover, the effect of viscosities of both phases is included in the breakup frequency model without resorting to any additional parameter. © 2018 American Institute of Chemical Engineers AIChE J, 65: 347–359, 2019     

Dynamic modelling of the deformation of a drop in a four-roll mill

The deformation of a drop flowing along the centre streamline of a four-roll mill (4RM) has been investigated. The velocities and elongation rates along the centre streamline in the 4RM were measured using particle tracking velocimetry. The deformation and position of the deforming drops were photographed with a video camera. A dynamic, one-dimensional, analytical simulation model describing the drop deformation has been developed. The model is based on Taylor's [1964. International Congress on Applied Mechanics, vol. 11, 790-796] static conical drop shape model, but has been extended to include elliptic drops undergoing rapid deformation. The model was incorporated into a numerical scheme using Matlab and the drop deformation in the 4RM was simulated. The simulations were compared with the results of the experiments with the help of a dynamic Weber number incorporating the exact effect of the continuous phase stress on the deformation of the drop. With a dynamic Weber number of 0.42 the agreement between the experiments and the simulations along the whole deformation process was excellent for all three drop diameters studied. With this model the deformation of drops of all sizes in different elongation fields can be calculated, for example sub-micron-sized drops in a high-pressure homogeniser.     

On the effect of phase fraction on drop size distribution of liquid–liquid dispersions in agitated vessels

The theory of Kolmogorov–Hinze is the base for many studies that have been done on mean drop size and drop size distribution of liquid–liquid dispersions in agitated vessels. Although this theory has been used extensively in the literature, but it does not always give a satisfactory result in the studies and therefore needs to be modified. This paper addresses the effect of phase fraction on drop size distribution in agitated vessels and on the proportionality coefficient and Weber number exponent in the relation d₃₂/D ∝ We^m. The experimental data that were taken from Pacek et al. (1998) and Desnoyer et al. (2003) have been applied to this relation to investigate the effect of phase ratio. It is shown that even at low phase fractions, the Kolmogorov–Hinze theory necessarily does not give the best result with the −0.6 exponent for the Weber number. Furthermore, for the non-coalescing system, a range of exponent for the Weber number typically from −0.6 to −0.43 can be considered where the system may be approximated as a pseudo-coalescing system at Φ = 0.4 in which the obtained results are in good agreement with the results of Pacek et al. (1998).     

液滴碰撞亲-疏水性组合壁面的数值分析

采用VOF方法对液滴碰撞亲-疏水性组合壁面过程进行数值模拟。通过量纲1化,在Reynolds数不变的情况下,研究Weber数和亲水性区域直径对液滴碰撞动态特性的影响,绘制了液滴碰撞结果分区图。结果表明：随着Weber数从1增加至100,液滴呈现出附着、短液滴一次破碎和长液滴多次破碎3种状态;液滴破碎过程受到表面张力、壁面黏附力及Rayleigh不稳定性的影响,亲水性区域直径增加时,液滴破碎所对应的临界Weber数随之增大;此外,Weber数较大时,液滴最大铺展因子不受亲水性区域直径的影响,Weber数较小时,最大铺展因子随亲水性区域直径的增大而增大。     

An experimental study of Mesler entrainment on a surfactant‐covered interface: The effect of drop shape and Weber number

Mesler entrainment is the formation of large numbers of small bubbles which occurs when a drop strikes a liquid reservoir at a relatively low velocity. Existing studies of Mesler entrainment have focused almost exclusively on water as the working fluid in a nominally clean state, where even very small levels of contamination can cause significant changes in surface tension that affect the repeatability of the results. Herein water combined with the soluble surfactant Triton X‐100 is used as the working fluid in an attempt to stabilize the state of the water surface. Despite this approach, nominally identical drops did not always result in the same bubble formation event. Accordingly, Mesler entrainment was quantified by its frequency of occurrence for drops having the same nominal diameter and impact velocity. This frequency of occurrence was found to be well correlated to both the Weber number and the shape of the drop on impact. © 2011 American Institute of Chemical Engineers AIChE J, 2012     

Effective interfacial area in agitated liquid-liquid continuous reactors

A chemical method has been used to quantify the effective interfacial area in a baffled continuous stirred liquid-liquid reactor. Two and four straight paddle impellers were used in the experimental runs, at 34°C, with hold-up fractions of dispersed organic phase between 0.061 and 0.166 and stirring speed ranging from 360 to . Influence of the residence time on the formation of the interfacial area generated in this system was not registered; however, differences were reported between continuous and batch mode operations.The interfacial area was correlated to hold-up fraction and Weber number by a new empirical model proposed in this work. This model allows to use only one equation to calculate the interfacial area in this continuous stirred reactor in the wide range of operating conditions tested (490<We<9600), which include different flow regimes. This is a relevant contribution as previous studies in this field only contemplate turbulent flow. In the transitional regime the mean drop size diameter decreases abruptly with Weber number, but this pattern changes in the higher range of Weber where the dispersed drops become smaller very smoothly. This pattern does not depend on the agitator used or hold-up fraction. The mean drop size diameter is smaller for the four paddle impeller and increases with hold-up fraction. The model developed may be applicable to dispersions in aromatic nitration reactors, improving its operation and design.     

水包油型乳化液油滴的管内节流破碎行为与机理

实验研究了水包油型乳化液油滴在管内节流元件处的破碎行为,分析了破碎机理. 结果表明,液滴破碎主要发生在节流元件内壁及下游附近,其概率是施于液滴上湍流应力与液滴表面能之比的递增函数,是流体韦伯数及节流元件两侧最大压差的递增函数;在湍流状态(Re>4000)下,液滴充分振荡且受到较大的水流惯性力和速度梯度剪切力,更易破碎;由苏丹红IV染色的正庚烷体系界面张力由非染色时的47 mN/m降到23.6 mN/m,黏性力对液滴破碎的影响程度下降,受流速、压差等影响的惯性力起决定性作用,液滴破碎程度更大;流速决定流体对分散相油滴的湍流剪切破碎力,流速增大则油滴粒径破裂程度加大,而流速取决于流量和节流比;注入染色正庚烷油相体积增大(0.5~5 mL),削弱了节流元件的液滴破碎作用,两相流体系倾向于形成更大直径的液滴,中位径一般为20~35 mm.     

NUSSELT NUMBER FOR DIRECT CONTACT EVAPORATION OF A MOVING ELLIPSOIDAL DROP IN AN IMMISCIBLE LIQUID

Since Sideman et al.^[1] derived an analytical solution of the Nusselt number for a spherical drop in the direct contact evaporation in an immiscible liquid, many researchers have performed theoretical research on this field under different assumptions [2]-[6]. However drops moving in another immiscible liquid do not take a spherical form, but oblate form, which may be well approximated as an ellipsoid. This paper establishes the mathematical model of heat transfer for a moving ellipsoidal drop in an immiscible liquid, and presents results from numerical calculation. The relationship of the Nusselt number with the Weber number and the Peclet number is given, which is suitable for a relatively large range of We and Pe. The theoretical results for the Nusselt number show good agreement with experimental data. Some important conclusions are obtained.