Dynamic simulation of agitated liquid—liquid dispersions—II. Experimental determination of breakage and coalescence rates in a stirred tank

Using the theoretical procedure outlined in the first part of this work, breakage and coalescence rates were determined experimentally in a stirred tank. After reaching steady-state conditions, the intensity of agitation was suddenly changed and the variation in drop size distribution with time was monitored. The coalescence and breakage constants were evaluated by optimising the fit of the experimental results with the theoretical solution of the model equations. No a priori assumptions concerning the dependence of the interaction rates on drop size, system properties and operating conditions were made. Precise techniques for measuring the drop size distribution in turbulent dispersions were developed and tested. Empirical equations for dependence of breakage and coalescence constants on drop volume, holdup and system properties were derived.     

Steady state multiplicity depending on coalescence in liquid—liquid continuous stirred reactors with reaction in the dispersed phase

The influence of drop coalescence and breakup on the existence of multiple steady states is studied for a two-phase stirred isothermal reactor where the chemical reaction in the d?ispersed phase obeys the rate expression ? r = kC/(1 + KC)². The random coalescence model developed by Curl was simulated using a modified Spielman and Levenspiel Monte Carlo technique.For certain range of the coalescence rate, Damköhler number, and dimensionless feed concentration, multiple steady states have been investigated.A special case has also been considered wherein the existence of multiple steady states for finite values of the coalescence rate is contrasted to the unique steady state solution for an infinite coalescence rate.     

The effect of pH on experimental and simulation results of transient drop size distributions in stirred liquid-liquid dispersions

A novel parameter study with experimental and numerical investigations of transient drop size distributions was carried out in order to study published model approaches for dispersed systems on the basis of the population balance equation. In terms of breakage and coalescence behaviour the dependency of the drop size distributions on power input, phase fraction, and especially pH was studied with the system toluene-water. With higher pH, coalescence is hindered considerably. As a consequence, the transient evolution of drop size distributions after starting the stirrer is changing and the time for reaching the stationary distribution increases. For the simulation applying the breakage and coalescence models a very efficient solver for the population balance equation (PBE), the program PARSIVAL^® is used. The simulation results of transient drop size distributions are in good agreement with the experimental data for various power inputs. The influence of the dispersed phase fraction is not characterized correctly.A proportionality between the Sauter mean diameter and the Weber number d₃₂∼We^-0.5 was measured for pH 13 and different phase fractions. The commonly reported exponent -0.6 for systems with low coalescence seems to be not applicable with higher pH and increased dispersed phase fraction.     

Drop mixing in suspension polymerisation

In suspension polymerisation, monomer is suspended as liquid droplets in a continuous water phase by means of strong agitation and the presence of a suspending agent. As the suspension polymerisation proceeds, the viscosity of a monomer-polymer droplet increases with conversion. Hence, the physical behaviour of the droplet changes during the process. When new dispersible material is added to the existing suspension drops, the new material and existing drops can remain segregated for significant amounts of time. The aim of this project was to study the behaviour of drop mixing when new material is added to the existing suspension polymerisation. This study concentrated on the effect of the dispersed phase viscosity on drop mixing. The results show that viscosity affects drop size and that may then affect the rate of coalescence between drops. A critical drop size exists which determines the coalescence efficiency effect. Above the critical drop size, mixing rate increases as the drop viscosity decreases. While below the critical drop size, drop size of the dispersion determines the coalescence rate; as the drop size increases, coalescence rate also increases. The investigation of the effect of suspending agent shows that Tween 20 is more efficient in stabilising and protecting the drops, based on a weight basis, than PVA as the coalescence rate is lower with Tween 20.     

The effect of coalescence on drop size distribution in an agitated liquid-liquid dispersion

A procedure involving high speed cine photography and novel optical probes has been used to study droplet interaction phenomena in liquid-liquid dispersions. Coalescence and breakup events were observed and the rate of coalescence was measured at various positions in a stirred tank for dispersions of methylisobutylketone in water. For the conditions studied, drop breakup occurred near the impeller and droplet coalescence predominated at other locations, as expected. However, the extent of this behavior was unexpected. Beyond distances from the impeller region of order of only $\text{1}\text{6}$ the impeller diameter, breakup was virtually nonexistent. Outside the impeller region, extensive coalescence measurements showed (1) collisions between droplets are extremely inefficient for this chemically equilibrated system—at most 10% of collisions result in a coalescence, (2) only binary coalescence occurs even at the highest dispersed phase concentration investigated, (3) coalescence rate shows little preference on drop size, and (4) the coalescence rate is directly proportional to turbulence level; that is, the highest coalescence rates occur closest to the impeller. On the basis of these measurements, drop balance methods and a circulation path model were used to relate the drop size distribution at various locations in the region where coalescence predominates. In this case good agreement was obtained between measured and predicted drop size distributions.     

Effect of geometrical arrangement and interdrop forces on coalescence time

According to the Reynolds' equation the time taken for a thin film to reach a critical thickness at which rupture occurs is a function of the film area and applied force. It follows that the coalescence time of a liquid drop is greatly affected by its geometrical configuration. If the drop is unconstrained the coalescence time increases when a vertical force is applied to the drop, but if the drop is constrained by the presence of surrounding drops its coalescence time decreases as the applied force increases. This explains why the rate of coalescence at the disengaging interface of a close-packed dispersion increases with the dispersion height. The coalescence time for a planar film is usually less than for the spherical film formed between a drop and its homophase which explains why near-horizontal surfaces inserted into close-packed dispersion increase the rate of coalescence. The coalescence time of a drop in a close-packed dispersion decreases as it approaches the disengaging interface. This means that the volume rate of coalescence at the interface may equal the disperse phase throughout without the necessity for interdrop coalescence. When the applied pressure is much greater than the van der Waals pressure, as in a close-packed dispersion, the critical film thickness is itself a function of the film area and applied force, but this has little effect on the above conclusions. When the applied pressure is much less than the van der Waals pressure, as in a loose-packed dispersion, the critical film thickness is only a function of the film area and the affect of the applied force on the coalescence time is then increased.     

Electric Field-Enhanced Coalescence of Liquid Drops

Abstract

A fundamental understanding of drop coalescence and growth is of importance to separations and materials processing. Under external driving forces, drops dispersed in an immiscible fluid collide and coalesce with each other due to their relative motion. As a result of drop coalescence, the average drop size in the dispersion increases over time, improving the separation process. Collision and coalescence of spherical, conducting drops bearing no net charge in dilute, homogeneous dispersions are considered theoretically under conditions where drop motion results from gravity settling and electric field-induced attraction. A trajectory analysis is used to follow the relative motion of two drops and predict pairwise collision rates. A population dynamics equation is then solved to predict the time evolution of the size distribution and the average size of drops. The results show that the rate of drop collision and growth can be increased significantly by applying an electric field, in accord with fundamental experiments and patents on electrocoalescence.     

Bimodal drop size distributions during the early stages of shear induced coalescence

Drop sizes and drop size distributions were determined by means of an optical shear cell in combination with an optical microscope for the systems polyisobutylene/poly(dimethylsiloxane) [I] and poly(dimethyl-co-methylphenylsiloxane)/poly(dimethylsiloxane) [II] at low concentrations of the suspended phases and at different constant shear rates ranging from 10 to 0.5 s⁻¹. After pre-shearing the two-phase mixtures [I: 50 s⁻¹; II: 100 s⁻¹] for the purpose of producing small drop radii, the shear rate was abruptly reduced to the preselected value and coalescence was studied as a function of time. In all cases one approaches dead end drop radii, i.e. breakup is absent. The drop size distributions are for sufficiently long shearing always unimodal, but within the early stages of coalescence they are in some cases bimodal; the shape of the different peaks is invariably Gaussian. The results are discussed by means of Elmendorp diagrams and interpreted in terms of collision frequencies and collision efficiencies.     

The effect of temperature on coalescence of liquid drops at liquid/liquid interfaces

Drop/interface coalescence times measured at 293–343K are reported for three oil/water systems (benzene, paraffin oil and 1,1,2,2-tetrabromoethane) with different interface ages. The anomalous coalescence behavior of water droplets is explained by considering the static electrical double-layer residing at the interface which influences the film thinning and the film rupture processes. Analyses using simplified coalescence models reveal that the incorporation of temperature dependence on the physical properties such as density difference between phases, viscosity of the continuous medium and interfacial tension, does not produce satisfactory agreement with the measured coalescence times. The effect of mutual saturation in contrast to unsaturated systems on coalescence times is illustrated. The reproducibility of the drop/interface coalescence times is examined and explanations are offered, relating the method and the conditions of the experimentation. Finally the importance of both the coalescence time and the film thickness to drop stability analysis is demonstrated.     

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.     

DYNAMIC BEHAVIOUR OF LIQUID DISPERSION IN A VIBRATING PLATE TANK

In this paper a new model of the drop breakage in a vibrating plate tank has been developed by a me-chanism based on the shearing stress in the neighborhood of the holes in the plates as a breakage force,andthe coalescence of drops may be dealt with by the process of gas molecule collision.Based on the theoreticalanalyses,simulation of drop breakage and coalescence which are random processes has been carried out byMonte-Carlo simulation technique.The parameters of breakage and coalescence rate have been obtained.     

A Model of dispersion hydrodynamics in a vibrating plate extractor

A stagewise polydisperse model of the Karr vibrating plate extractor hydrodynamics is presented. It describes the drop size distribution and the dispersed phase hold-up as functions of drop transport, breakage and coalescence. ¹ The predicted stationary hold-up profiles and drop size distributions are proved to be in good agreement with the experimental data.     

Analysis of droplet expulsion in stagnant single water-in-oil-in-water double emulsion globules

Double emulsions created by phase inversion can be used for fast liquid–liquid separation; therefore, the coalescence behaviors of these types of multiple emulsions need to be predictable for different physical properties and drop size ratios. The aim of this study is to determine the influence of the effective overall drop diameter and the internal droplet size on the coalescence time and the coalescence behavior. Experimental investigations on the physical stability of single stagnant water-in-oil-in-water (W₁/O/W₂) double emulsion globules are performed. For this investigation, a formation device to inject one water droplet into an oil drop inside a water bulk phase is developed. The coalescence process of the sole internal water droplet floating on the O/W₂ interface with the water bulk phase, often termed droplet expulsion or external coalescence, is recorded with a high speed camera. Based on image analysis, the diameters of the effective overall drop D, containing the oil and entrapped water volume, and the internal water droplet d are determined. Additionally, the coalescence time τ, including the time from the first contact of the internal droplet and the drop-bulk interface to the film rupture is measured. A large increase in coalescence time with increasing water droplet diameters is found. For the investigated paraffin oil–water system and initial drop sizes, partial coalescence occurs. In this case, the diameter ratio of daughter-to-mother droplet ψ is determined.     

液滴凝并端效应对单液滴传质测定的影响及消除

For the mass transfer to single drops during the stage of steady buoyancy-driven motion, experimental measurement is complicated with the terminal effect of additional mass transfer during drop formation and coalescence at the drop collector. Analysis reveals that consistent operating conditions and experimental procedure are of critical significance for minimizing the terminal effect of drop coalescence on the accuracy of mass transfer The novel design of a totally-closed extraction column is proposed for this purpose, which guarantees that the volumetric rate of drop phase injection is exactly equal to that of withdrawal of drops. Tests in two extraction systems demonstrate that the experimental repeatability is improved greatly and the terminal effect of mass transfer during drop coalescence is brought well under control.     

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．     

Systematic Analysis of Single Droplet Coalescence

Coalescence behavior in liquid‐liquid dispersions is controlled by various parameters. Thus, data from different research groups can differ significantly. Dynamic coalescence processes were analyzed systematically with the EFCE standard test system toluene/water in two different research laboratories. After comparability was proven with standardized batch settling tests and drop rise velocity measurements, the influence of drop size ratio and varying NaCl and NaOH concentrations on coalescence probability was investigated. Since the ions led to a coalescence inhibition, no clear impact of drop size ratio could be observed. The analysis of drop contact showed longer contact times for increasing equivalent drop diameter. This promotes coalescence and corresponds to film drainage model.     

Description of interaction processes in agitated liquid-liquid dispersions

Phenomenological models are proposed to describe drop breakup and coalescence in a turbulently agitated liquid-liquid dispersion. Based on these models, breakage and coalescence rate functions are developed and used to solve the general population balance equation describing drop interactions in a continuous flow vessel. Parameters of the models are evaluated by comparison with experimental data on drop size distributions and mixing frequencies obtained in a continuous flow vessel over a range of operating conditions. The favorable agreement between experimental observation and the model are encouraging that the model is suitable for predicting dispersion properties such as drop size distributions, interfacial areas and mixing frequencies.     

振动筛板槽中液滴分散动力学的研究(Ⅰ)实验研究及理论分析

本文通过实验观察发现,液滴的破碎只有在液滴与振动筛板孔口发生碰撞时才发生.基于这个实验现象,建立了振动筛板槽内液滴破碎的新模型.把筛板孔口附近的剪应力作为破碎力,破碎速率可表示为:G(d)=C_12Af/H(?)~n_4(d/d_h)~n_5[1-(d_(cr)/d)~(2n_1+1)]~0.5n(d)液滴的凝聚可以按气体分子碰撞过程来处理.凝聚速率可以用下式表示:ω(d_1,d_2)=C_Ⅱ(d_1+d_2)~(7/3)∈~（1/3)[β_d∈~(2/3)d_1+d_2/σ(d_1+d_2）~（1/3）]~n_6n(d_1)n(d_2)     

Droplet break-up by in-line Silverson rotor–stator mixer

Silverson high shear in-line rotor–stator mixers are widely applied in industry for the manufacture of emulsion-based products but the current understanding of droplet breakage and coalescence in these devices is limited. The aim of this paper is to increase the understanding of droplet break-up mechanisms and to identify appropriate literature correlations for in-line rotor–stator mixers. Silicone oils with viscosities ranging from 9.4 to 969 mPa s were emulsified with surfactant in an in-line Silverson at rotor speeds up to 11,000 rpm and flow rates up to 5 tonnes/h. The effect of rotor speed, flow rate, dispersed phase fraction up to 50 wt%, inlet drop size and viscosity ratio on droplet size was investigated. It was found that rotor speed and dispersed phase viscosity have a significant effect on the droplet size, while flow rate, inlet droplet size, viscosity ratio and dispersed phase volume have a lesser effect. The results indicate that low viscosity droplets are broken by turbulent inertial stresses, while droplets smaller than the Kolmogorov length scale are broken by a combination of inertial and viscous stresses. It also appears that the weak dependence of drop size on flow rate enables the energy efficiency of an in-line high shear Silverson to be significantly improved by operating at as high a flow rate as possible.