Development of polymer blend morphology during compounding in a twin-screw extruder. Part I: Droplet dispersion and coalescence—a review

The theoretical and experimental data on the breakup of droplets are reviewed. Several factors influence development of droplets: flow type and its intensity, viscosity ratio, elasticity of polymers, composition, thermodynamic interactions, time, etc. For Newtonian systems undergoing small, linear deformation, both the viscosity ratio and the capillary number control deformability of drops. On the other hand, the breakup process can be described by the dimensionless breakup time and the critical capillary number. Drops are more efficiently broken in elongational flow than in shear, especially when the viscosity ratio λ ? 3. The drop deformation and breakup seems to be more difficult in viscoelastic systems than in Newtonian ones. There is no theory able to describe the deformability of viscoelastic droplet suspended in a viscoelastic or even Newtonian medium. The effect of droplets coalescence on the final morphology ought to be considered, even at low concentration of the dispersed phase, ?_d ? 0.005. Several drop breakup and coalescence theories were briefly reviewed. However, they are of little direct use for quantitative prediction of the polymer blend morphology during compounding in a twin-screw extruder. Their value is limited to serving as general guides to the process modeling.     

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.     

Snap‐off of a liquid drop immersed in another liquid flowing through a constricted capillary

Emulsions are encountered at different stages of oil production processes, often impacting many aspects of oilfield operations. Emulsions may form as oil and water come in contact inside the reservoir rock, valves, pumps, and other equipments. Snap‐off is a possible mechanism to explain emulsion formation in two‐phase flow in porous media. Quartz capillary tubes with a constriction (pore neck) served to analyze snap‐off of long (“infinite”) oil droplets as a function of capillary number and oil‐water viscosity ratio. The flow of large oil drops through the constriction and the drop break‐up process were visualized using an optical microscope. Snap‐off occurrence was mapped as a function of flow parameters. High oil viscosity suppresses the breakup process, whereas snap‐up was always observed at low dispersed‐phase viscosity. At moderate viscosity oil/water ratio, snap‐off was observed only at low capillary number. Mechanistic explanations based on competing forces in the liquid phases were proposed. © 2009 American Institute of Chemical Engineers AIChE J, 2009     

Void transport in resin transfer molding

The transport of single drops through a hexagonal cylinder array is used to study the void movement and deformation in a resin transfer molding process. A transparent flow cell is used to visualize the transport of voids through a porous media model. Experiments are conducted with nearly inviscid water drops and viscous glycerol drops with drop sizes ranging from 0.4 to 80 μl, and with both a Newtonian fluid and Boger fluid with average resin velocities ranging from 0.011 to 0.140 cm/s. Two critical capillary numbers, which determine the breakup (Ca_b) and mobilization (Ca*) of drops, are measured to better understand the flow dynamics of voids. As demonstrated by the experiments, there is a critical drop size, below or above which a quite different flow behavior is observed. Such a transition is analyzed with consideration of the geometry characters in the flow field. Results expand the former studies in this area to a significantly larger range of drop sizes and capillary numbers. Particle Tracking Velocimetry is also used to quantify the local velocity, shear stress, extensional stress and energy dissipation in the flow field. Polym. Compos. 25:417–432, 2004. © 2004 Society of Plastics Engineers.     

Drop Deformation and Breakup Mechanisms in Viscoelastic Model Fluid Systems and Polymer Blends

This paper reviews the dispersion mechanisms in viscoelastic systems under relatively high shear rate conditions. In particular, two non‐Newtonian deformation and breakup mechanisms were revealed by flow visualization in a transparent Couette shearing setup. The first one is the dispersed droplet elongation perpendicular to the flow direction. This was observed only for viscoelastic drops and had been associated to normal force buildup in the droplet. The second deformation/breakup mechanism was observed in very high viscosity ratio polymer systems. It consists in erosion at the drop surface. Clouds of very small ribbons and sheets were developed around the drop then stretched and finally broken into very small droplets, rapidly distributed in the matrix.     

Effect of compatibilization on the deformation and breakup of drops in step-wise increasing shear flow

Drop deformation and breakup were investigated in the presence of a block copolymer in step-wise simple shear flow using a home-made Couette cell connected to an Anton Paar MCR500 rheometer. Polyisobutylene (PIB) was used as the matrix, while five different molecular weights of polydimethylsiloxane (PDMS) were selected to provide drops with a relatively wide range of viscosity ratio. A block copolymer made of PDMS-PIB was used for interfacial modification of the drop-matrix system. The copolymer concentration was 2 wt% based on the drop phase. The experiments consisted in analyzing the drop shape and measuring the variation of the length to diameter ratio, L/D, both in steady state and in transient regimes till breakup. This allowed revising of the classical Grace curve that reports the variation of the critical capillary number for breakup as a function of viscosity ratio and providing also a new one for blends compatibilized with an interfacial active agent with a given molecular weight.     

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.     

In situ visualization of drop deformation,erosion, and breakup in high viscosity ratio polymeric systems under high shearing stress conditions

In this paper, deformation and breakup under simple shear of single molten polymer drops in a polymer matrix were investigated. Flow visualization was carried out in a Couette‐Flow apparatus under relatively high shear rates and temperatures up to 230°C. Drop/Matrix combinations were composed of polystyrene drops of 0.5–0.6 mm in diameter in polyethylene matrix, and ethylene–propylene copolymer drops of approximately the same size in polypropylene matrix. The deformation and breakup processes were studied under steady state and time‐dependent shearing conditions. Either for steady state or time‐dependant shearing conditions, drop elasticity generated at relatively high shear rates helped the drops to align perpendicular to the flow direction, i.e., parallel to vorticity axis. Also, the most striking non‐Newtonian effects for the high viscosity ratio systems were the surface erosion and the drop splitting mechanisms. The particles eroded off the main droplet surface were very fine, in the range of 10–50 μm, and led to a significant reduction in main drop size before its final breakup. © 2006 Wiley Periodicals, Inc. J Appl Polym Sci 100: 2582–2591, 2006     

Erosion and breakup of polymer drops under simple shear in high viscosity ratio systems

The deformation and breakup of a single polycarbonate (PC) drop in a polyethylene (PE) matrix were studied at high temperatures under simple shear flow using a specially designed transparent Couette device. Two main breakup modes were observed: (a) erosion from the surface of the drop in the form of thin ribbons and streams of droplets and (b) drop elogation and drop breakup along the axis perpendicular to the velocity direction. This is the first time drop breakup mechanism (a), “erosion,” has been visualized in polymer systems. The breakup occurs even when the viscosity ratio (η_r) is greater than 3.5. although it has been reported that breakup is impossible at these high viscosity ratios in Newtonian systems. The breakup of a polymer drop in a polymer matrix cannot be described by Capillary number and viscosity ratio only; it is also controlled by shear rate, temperature, elasticity and other polymer blending parameters. A pseudo first order decay model was used to describe the erosion phenomenon and it fits the experimental data well.     

ONE-DIMENSIONAL SIMULATION OF THE BREAKUP OF CAPILLARY JETS OF CONDUCTING LIQUIDS. APPLICATION TO E.H.D. SPRAYING

Nonlinear breakup of charged liquid jets is numerically analyzed in this work in the limit of a very small electrical Strouhal number T_e/T_b≪1 (i.e. negligible charge relaxation effects, applicable to highly conducting liquids), where T_e is the electric relaxation time of charges, and T_b is the breakup time in a Lagrangian framework following the liquid jet at its average axial velocity. The influence of the electrical Bond’s number and viscosity on (i) the capillary Rayleigh’s most probable breakup length, (ii) the breakup time, (iii) the volume of the satellite, and (iv) the charge of both main drop and satellite, are analyzed. The model is related to the microjet break-up phenomena in the electrospraying of liquids in steady cone-jet mode, and its range of applicability to those particular problems discussed. Previous experimental results [Mutoh et al., 1979, Convergence and disintegration of liquid jets induced by an electrostatic field. J. Appl. Phys. 50, 3174–3179; Clopeau and Prunet-Foch, 1989, Electrostatic spraying of liquids in cone-jet mode. J. Electrostatics 22, 135–159.] support our numerical finding that the influence of the electrical Bond’s number on Rayleigh’s length is small within the usual parametrical limits of stability of a steady Taylor cone-jet at atmospheric pressure.     

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.     

Experimental study on drop breakup time and breakup rate with drop swarms in a stirred tank

The direct experimental data for breakup parameters of drop breakup time, multiple breakage, and breakup rate are urgently required to understand drop breakup phenomena. In this regard, drop breakup experiments were carried out in a stirred tank using a high-speed online camera. The influences of the rotating speed, interfacial tension, and drop viscosity on the above breakup parameters were then quantitatively investigated. An mechanism correlation for the breakup time is proposed and is further verified by comparing with the results of Solsvik and Jakobsen (Chem Eng Sci, 2015;131:219-234). The percentage of multiple breakage comparing to binary breakup was statistically counted. The results indicated that the dimensionless drop diameter η = d/d_max can be adopted to characterize the proportion of binary breakup. Finally, the breakup rate was experimentally measured and the breakup probability was calculated using the inverse method.     

Numerical investigation of upstream pressure fluctuation during growth and breakup of pendant drops

Growth and breakup of pendant drops from the tip of a capillary is of great importance due to its wide applications and the richness of the underlying physics. During the growth and breakup of a pendant drop, the size variation will produce pressure fluctuation in the upstream, which is studied numerically with the level set method to predict the interface. The numerical results are validated against experimental images showing the growth and breakup of pendant drops obtained from a high speed camera. The effects of the surface tension and the outer diameter of the capillary on the amplitude and the period of the pressure fluctuation are examined. Compared to other methods of surface tension measurement, this method shows potential advantages of its good accuracy, simplicity, and low cost.     

Evaluation of polymer rheology from drop spreading experiments

In this paper, spreading experiments on “heavy” polymer drops are performed. “Heavy” refers to large polymer drops, i.e., the radius of the drop, R, is much larger than the capillary length, κ^-1, so that the spreading is dictated by gravity. The zero-shear viscosity can be found from measurements of the time-dependent drop radius or vice versa. Viscosity values found from spreading experiments compare well with the viscosity values found from dynamic rheological experiments.     

Drop Breakup in an SMX Static Mixer in Laminar Flow

The mechanism of drop breakup inside SMX static mixers in the laminar flow regime was studied using experimental observations and computational fluid dynamics (CFD). The deformation and breakup of a single drop was simulated using the volume of fluid (VOF) model. It was observed that drops break up after collision with the leading edges and cross‐points of the bars in the SMX static mixer. It was found that drop collision with the bar cross‐points of the SMX static mixer elements is most effective for drop breakup. Elongation and folding result in drop breakup at the cross‐points.     

Characterization of liquid‐liquid dispersions with variable viscosity by coupled computational fluid dynamics and population balances

Sustaining stable liquid‐liquid dispersion with the desired drop size still relies on experimental correlations, which do not reflect our understanding of the underlying physics and have a limited prediction capability. The complex behavior of liquid‐liquid dispersions inside a stirred tank, which is equipped with a Rushton turbine, was characterized by a combination of computational fluid dynamics and population balance equations (PBE). PBE took into account both the drop coalescence and breakup. With the increasing drop viscosity, the resistance to drop breakage also increases, which was introduced by the local criteria for drop breakup in the form of the local critical Webber number (We_c). The dependency of We_c on the drop viscosity was derived from the experimental data available in the literature. Predictions of Sauter mean diameter agree well with the experimentally measured values allowing prediction of mean drop size as a function of variable viscosity, interfacial tension, and stirring speed. © 2015 American Institute of Chemical Engineers AIChE J, 61: 2403–2414, 2015     

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.     

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.     

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     

Influence of elasticity on dispersed‐phase droplet size in immiscible polymer blends in simple shearing flow

The influence of elasticity of the blend constituent components on the size and size distribution of dispersed‐phase droplets is investigated for blends of polystyrene and high density polyethylene in a simple shearing flow. The elasticities of the blend components are characterized by their first normal stress differences. The role played by the ratio of drop to matrix elasticity at fixed viscosity ratio was examined by using high molecular weight polymer melts, high density polyethylene and polystyrene, at temperatures at which the viscosity ratios roughly equaled each of three different values: 0.5, 1, and 2. The experiments were conducted by using a cone‐and‐plate rheometer, and the steady‐state number and volume‐mean averages of droplet diameters were determined by optical microscopy. After steady‐state shearing, the viscoelastic drops were larger than the Newtonian drops at the same shearing stress. From the steady‐state dispersed‐phase droplet diameters, the steady‐state capillary number, Ca, defined as the ratio of the viscous shearing stress over the interfacial tension stress, was calculated as a function of the ratio of the first normal stress differences in the droplet and matrix phases. For the blend systems with viscosity ratio 0.5, 1 and 2, the values of steady‐state capillary number were found to increase with the first normal stress difference ratio and followed a power law with scaling exponents between 1.7 and 1.9.