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.     

Studies of drop break-up in liquid-liquid systems in a rotating disc contactor. Part I: Conditions of no mass transfer

Observations on the break-up of single drops in a rotating disc contactor show that there is a critical rotor speed below which drops of a given size do not break. Weber and Reynolds numbers are required to correlate the data and not simply a Weber number as for turbine agitated systems. The probability of break-up of a drop at the rotor edge is expressed in terms of a Weber number with a lower limit for critical conditions. The mean number of daughter drops produced on break-up is correlated as a simple function of drop diameter based on the critical diameter and agreement is found with data from other types of agitated equipment.     

油水两相分散流液滴粒径预测模型

油水两相分散流的液滴粒径及其分布在很大程度上影响管路压降等流动参数,研究液滴粒径预测模型对揭示油水两相流的流动特性具有重要意义。通过研究湍流脉动动能与乳状液的界面能之间的平衡、管流径向速度脉动与摩擦速度之间的关系以及泵的剪切作用,建立了油水两相管流中分散相液滴粒径预测模型;在水平管道上对油水两相分散流的液滴特性进行了实验研究,采用高速摄像和显微镜拍摄获得液滴数据,探索含油率、流量和温度等因素对粒径的影响。预测模型计算结果与不同流量、温度和含油率条件下的实验数据吻合较好。根据预测模型计算了有泵和无泵情况下分散流液滴粒径,发现泵的剪切和扰动作用使得分散液滴具有更小的粒径,泵对液滴粒径及其分布起到了显著作用。     

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.     

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.     

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.     

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.     

Dynamic behaviour of drops in oil/water/oil dispersions

The dynamic behaviour of drops of oil/water/oil (O/W/O) and water/oil (W/O) in abnormal polymer/water/surfactant systems was investigated. The size of internal oil droplets continuously decreased with time until it reached a steady-state value. Whereas the size of multiple water drops showed a minimum. After the minimum, the size of multiple water drops either reached a steady-state value or continued enlarging until phase inversion occurred. The phase inversion occurred because inclusion of oil droplets into water drops resulted in a continuous increase in effective volume fraction of dispersed phase. The time evolution of the size of multiple drops was described in terms of a balance between (a) drop break-up and escape and (b) drop coalescence and inclusion. The inclusion events retarded the initial decrease in the size of multiple water drops with time and increased the drop size after the minimum. By reducing the surfactant concentration, the ability of the dispersed phase to entrain the continuous phase decreased so that no minimum was achieved for the size of multiple drops with time, similar to conventional systems with simple drops. The size distribution of the multiple water drops initially narrowed and then widened again, whereas the size distribution of internal oil droplets continuously narrowed with time until it reached a constant value. Generally, the size distribution of drops narrowed as the average size of drops decreased. The possible mechanisms for complex drop formation were discussed and drop deformation was suggested as the main cause for inclusion at a low dispersed phase ratio.     

Self-similar inverse population balance modeling for turbulently prepared batch emulsions: Sensitivity to measurement errors

We investigate the sensitivity of an inverse population balance equation (PBE) modeling technique for extracting single particle functions from transient size distribution measurements. A dynamic PBE model of a turbulently agitated batch emulsification vessel is used to generate volume size distribution data under the assumption of negligible drop coalescence. The distribution data are subjected to various types of error consistent with available measurement technologies and then introduced as input data to the inverse PBE modeling algorithm, which includes validation of the self-similar assumption. The errors considered include measurement noise, data skewed towards smaller or larger drops, skewed data due to the presence of large dust peaks, and reduced resolution caused by data binning. For each case, the computed functions for the drop breakage rate and the distribution of daughter drops are compared to the actual functions to assess the impact of input data errors on the effectiveness of the inverse PBE modeling approach. The type of measurement errors considered generally lead to underprediction of the breakage rate and, consequently, to overprediction of the number of large drops. Because the estimated and actual breakage rates tend to converge at small drop sizes, the inverse algorithm generates accurate predictions of the drop size distribution at sufficiently long batch times when small drops dominate. Implications for our future work on PBE modeling of drop size distributions in pharmaceutical emulsions prepared with high pressure homogenization are discussed.     

Effects of cross-flow velocity, capillary pressure and oil viscosity on oil-in-water drop formation from a capillary

The formation of oil drops from a single capillary with a diameter of 200 μm into a cross-flowing continuous water phase has been studied experimentally with the particle image velocimetry (PIV) technique and numerically with the computational fluid dynamics (CFD) software Fluent. The drop formation time and the volume of the detached drop were used as validation parameters and the results from the two methods corresponded well, with a difference of less than 5% for the drop formation time and 10% for the drop volume. The cross-flow velocity has a major impact on drop size, which decreases as the cross-flow increases. An increase in cross-flow, oil viscosity and capillary pressure displace the position of necking and drop detachment away from the capillary opening, which will have a decreasing effect on the final size of the drop.     

Identical Feed Drops in a Flow Vessel May not Always Be Desirable

In this paper, the effect of feed size and daughter drop size distributions on the steady‐state drop size distribution in a continuous flow vessel is discussed. For identical sizes of feed drops, a new criterion has been proposed to ensure the complete breakage of the feed drops giving rise to smooth continuous drop size distributions. This has been predicted on the basis of two competing time scales, namely, breakage and residence times.     

Modeling of the break-up of deformable particles in developed turbulent flow

Dynamic behavior of the drops and bubbles in developed turbulent flow depend on turbulent length scale (λ), Morton (Mo), Weber (We) and Reynolds (Re_a) numbers. In the present work, in order to calculate the maximum stable size of drops and bubbles, the A factor of break-up, Ay (Ay=ωa/U), that is the ratio of the break-up rate in developed turbulent flow to the mean velocity of the flow has been introduced and the effect of the pipe roughness on this factor has also been given. Comparison of all the results obtained in this study with those taken from the literature for the range of Mo?7, We?10 and Re_a?100 showed a good agreement.     

Determination of the interfacial tension of low density difference liquid-liquid systems containing surfactants by droplet deformation methods

The interfacial tension, σ, between two low density difference liquids containing a surfactant was determined using drop deformation method with a computer-controlled parallel bands apparatus. This device applies a linear homogeneous shear flow field to a fluid matrix in which a droplet of another immiscible and buoyancy-free fluid is immersed. The flow induces topological changes on the initially spherical drop, which deforms into an ellipsoid and orients respect to the flow direction. The time evolution of the sheared droplets was recorded with two CCD cameras (placed along the x and z directions) for extended times, allowing the steady state of the drops to be achieved accurately, and further digitally analyzed. Appropriate theories corresponding to each flow-induced mechanism of the droplet under shear (steady-state deformation and orientation) were employed for determining the interfacial tension, under the basis of reaching equilibrium states of deformation of the sheared drop. The calculated σ values via the drop deformation theories were checked for a wide range of viscosity ratios of binary systems conformed by silicon oils as droplets and a water solution of polyvinylpyrrolidone as continuous phase (both Newtonian), being found that σ is independent on λ. These values were compared with measurements carried out in a conventional tensiometer, using the drop volume method. The comparison showed a very good agreement between both techniques.     

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.     

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.     

MAXIMIZING SELECTIVITY OF LIQUID-LIQUID REACTION SYSTEMS. CONTROL OF THE DISPERSION PROCESS

Currently available information on droplet coalescence and break-up rates in turbulent flows in mixing vessels can be used to control drop sizes in dispersed phase equipment. The effect of drop size distributions on the selectivity and productivity in multi-reaction systems is examined in this paper.

The reaction system features the primary desired product (C) as resulting from reaction (in the bulk phase) between a reactant (A) in the drop phase and a second reactant (B) in the bulk phase. An adverse reaction is also envisaged which consumes (C) by further reaction with (B) to form a waste product. While small drops promote conversion because of large interfacial area, larger drops promote selectivity because of the facility of the product to re-enter the drop phase avoiding further reaction (to form waste) in the bulk phase. The effect of the bivariate distribution of drop size and reactant (A) concentration in the feed to a continuous stirred tank reactor on the selectivity and productivity of (C) is investigated within the framework of film theory while neglecting drop dynamics such as coalescence and break-up.

The results show the selectivity can be substantially improved by controlling drop size and distribution of the reactants among the differently sized droplets. Contrary to conventional wisdom which emphasizes creation of interfacial area by promoting very small droplets, it emerges that optimal distributions of drop size and reactant concentration which maximize productivity of the desired product exist. The practical implications are discussed.     

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.     

Effect of impeller geometry on drop break-up in a stirred liquid—liquid contactor

Drop size measurements were made in the break-up zone at the tip of three 6 bladed disc turbines of different geometries in a 0·30 m dia. vessl. Three systems kerosene, methyl iso-butyl ketone (MIBK) and n-butanol at a volumetric fractional hold-up of 0·05 in water were examined. Power input and circulation time characteristics were determined and a new dimensionless group (?^{?$\text{1}\text{3}$}t_c/T^{$\text{2}\text{3}$}) is proposed to account for the effect of geometric parameters in the correlation of the drop size.