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.     

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     

混炼机横截面PP熔体液滴分散过程的数值模拟研究

对Fluent进行二次开发,通过用户自定义函数,将黏弹性流体的动量方程和变形张量输运方程加载到Fluent中,从而实现了对聚合物黏弹性流体流动的模拟。采用VOF界面追踪方法,对聚合物熔体中的单个液滴在混炼机横截面流场作用下发生的变形、破碎行为和二次团聚过程进行了分析研究。探讨了液滴在混炼腔复杂流场中的分散过程和微观结构的形成机理,对揭示共混改性过程中分散相织态结构发展演变过程和机理具有指导意义。结果表明,PP液滴在混炼过程中经历了变形、破碎、聚并过程;PP液滴在C形区发生了不均匀变形行为,在相互作用窗混沌流场下发生了拉伸、挤压、交叉行为;PP液滴的破碎行为包括毛细不稳破碎、末端夹断以及在螺棱背风面的松弛破碎。     

Transient and steady-state deformations and breakup of dispersed-phase droplets of immiscible polymer blends in steady shear flow

Transient and steady-state deformations and breakup of viscoelastic polystyrene droplets dispersed in viscoelastic high-density polyethylene matrices were observed in a simple steady shear flow between two transparent parallel disks. By separately varying the elasticities of the individual blend components, the matrix shear viscosity, and the viscosity ratio, their effects on the transient deformation, steady-state droplet size, and the breakup sequence were determined. After the startup of a steady shear flow, the viscoelastic droplet initially exhibits oscillations of its length in the flow direction, but eventually stretches preferentially in the vorticity direction. We find that at fixed capillary number, the oscillation amplitude decreases with increasing droplet elasticity, while the oscillation period depends primarily on, and increases with, the viscosity ratio. At steady-state, the droplet length along the vorticity direction increases with increasing capillary number, viscosity ratio, and droplet elasticity. Remarkably, at a viscosity ratio of unity, the droplets remain in a nearly undeformed state as the capillary number is varied between 2 and 8, apparently because under these conditions a tendency for the droplets to widen in the vorticity direction counteracts their tendency to stretch in the flow direction. When a critical capillary number, Ca_c, is exceeded, the droplet finally stretches in the vorticity direction and forms a string which becomes thinner and finally breaks up, provided that the droplet elasticity is sufficiently high. For a fixed matrix shear stress and droplet elasticity, the steady-state deformation along the vorticity direction and the critical capillary number for breakup both increase with increasing viscosity ratio.     

A numerical procedure for calculating droplet deformation in dispersing flows and experimental verification

A three-step numerical procedure for studying droplet deformation in mixed, dispersing-type, flow fields is described. Finite element and numerical particle tracking techniques are used to obtain the history of shear and elongation rates along a particle trajectory in the flow field, and from this history, boundary integral techniques are used to determine the deformation a drop would experience along this path. This approach is then used to investigate the effect of a small change in geometry on the breakup behavior of drops in the annular gap flow between two eccentric cylinders. This flow geometry serves as an idealization of a rotor-stator dispersing device used for highly viscous fluid systems. It is found that an increase in eccentricity produces an increase in dispersing capability. Experiments in an eccentric cylinder geometry were performed to verify the simulation procedure. Under the experimental conditions considered, it is found that the simulations perform well, correctly predicting whether or not drop breakup occurs and the qualitative drop evolution behavior. The simulation procedure outlined in this paper can serve as an effective tool to determine drop breakup in dispersing geometries and hence to optimize dispersing procedures.     

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.     

均匀电场中液滴变形特性的耗散粒子动力学模拟

基于耗散粒子动力学方法,建立了电场作用下近似的液滴粒子力学模型,对两相不相溶液体中液滴在电场作用下的变形特性进行了模拟。模拟结果与他人的实验结果比较表明,模拟结果对液滴形状随时间的演化预测基本符合实际,仅在液滴变形较大时有一定偏差。模拟结果还表明,当外加场强较小时,液滴变形度随时间呈现振荡状态,变形度不会随时间继续增大。增大外加场强,液滴变形幅度增大,振荡频率变慢。当外加场强增大到一定程度时,液滴变形度不再振荡,而是随时间急剧增大,以至液滴最终破碎。场强越大,液滴破碎所需的时间也越短。     

电场作用下液滴的变形及库仑分裂模式

基于高速成像技术,本文对电场作用下甲醇液滴的显微形貌特征进行了可视化研究,精确捕捉了两相流体系中不同生长阶段的荷电液滴基于时间分辨特性的变形及库仑分裂演变行为,得到不同工况下荷电液滴的变形分裂过程及行为演化细节。基于液滴所受库仑力和介电泳力与周围流域的耦合作用,揭示了电场作用下不同生长阶段的液滴库仑分裂形成机理。结果表明,电场强度和液滴粒径是决定液滴变形及库仑分裂模式的主要因素,荷电液滴的变形及库仑分裂模式可以分为推压变形、顶部破碎、顶部-边端破碎、伞状破碎。结合量纲为1参数对液滴的变形及破碎特征进行了定量分析,随着电场强度的增大及液滴粒径的减小,液滴变形及顶部破碎的程度更加剧烈,液滴临界伞状破碎长度减小。     

Comparative efficiency of shear,elongation and turbulent droplet breakup mechanisms: Review and application

The study of phase dispersion of two immiscible fluids in different flows requires identifying the relevant breakup mechanisms. We propose here a detailed investigation of droplet breakup in a multifunctional exchanger-reactor of the vortex generator type in which transfer intensification is due to longitudinal vortical structures. We compare the efficiency of the mean gradients and turbulent mechanisms in droplet breakup in this industrial reactor. This efficiency is essentially characterized by the resulting distribution of droplet diameters. Then, the roles of the mean flow and the turbulent field, intensity, energy spectrum, and turbulence scales are examined in relation to the liquid/liquid dispersion in order to explore the governing mechanisms of drop breakup. In the complex flow considered here – nonhomogeneous and anisotropic turbulence at moderate Reynolds numbers (<15,000) – with weak turbulence intensity (about 10%), it can be demonstrated that turbulent breakup mechanisms largely dominate mean flow effects; elongation and shear effects are shown to have minor effects on the breakup mechanisms. Moreover, the global characteristic scales of the flow are not the relevant parameters in predicting the final size of the emulsion, but instead the Kolmogorov microscale, implying that the residence time in the reactor is not a limiting factor. Hence, the local dissipation rate governs the performance of the actual multifunctional reactor. This study provides some insight in the design and scaling-up of multiphase reactors.     

Study on droplet deformation of an immiscible fluid system by selective radiation heat using infrared laser

The droplet deformation's mechanism in a simple shear flow is well understood, but most studies only considered a uniform temperature field of immiscible droplet systems. This research investigates the possible droplet deformation and visualizes its evolution under selective radiation heating, which is a novel method to modify droplet dispersion via thermo-physical mechanism. Polybutenes and PDMS silicone oils were employed as the dispersed droplet phase and matrix phase, respectively. Results showed that the mean value of the droplet's modified deformation parameter was limited to 0.12 and 0.08 at an isothermal ambient room temperature having a viscosity ratio of 4.32 and 17.69, respectively. The droplet under selective radiation was visualized. Experimental investigation showed that the selective radiation method enhanced the droplet deformation, as confirmed by the obtained droplet image during laser irradiation process, even allowing droplet breakup. At a moderate level of viscosity ratio (4.32), selective radiation can be applied effectively, whereas at a higher level of viscosity ratio (17.69), droplet elongation-breakup and droplet retraction were observed.     

Effect of viscoelasticity on drop dynamics in 5:1:5 contraction/expansion microchannel flow

Recently, we reported how viscoelasticity affects drop dynamics in a microchannel flow using the finite element-front tracking method (FE-FTM). In this work, we investigate drop dynamics for a wider range of parameters: viscosity ratio between droplet and medium (χ), capillary number (Ca), droplet size, and fluid elasticity. The Oldroyd-B model is adopted as the constitutive equation for the viscoelastic fluid. We observe that the drop deformation in a microfluidic channel is dependent on Ca, which is more pronounced for smaller χ values. The present work shows that viscoelasticity plays an important role in drop dynamics with increasing χ values for Newtonian droplet in viscoelastic medium, which can be attributed to high normal stress developed in narrow film thickness between droplet and channel for higher χ values. We also study circulation problem inside droplets, which is important in practice, such as in droplet reactor application. The present work shows that circulation intensity is enhanced with decreasing χ values. We find that the relevance of viscoelastic effects on internal circulation is dependent on χ values, and the circulation intensity is distinctively decreased with increasing elasticity for high χ values for Newtonian droplet in viscoelastic medium. We expect that the present work be helpful not only in controlling droplets but also to improve our physical insight on drop dynamics in microchannel flows.     

Experimental study of two types of stripping breakup of the drop in the flow behind the shock wave

Results of an experimental study of two regimes of stripping breakup of low-viscosity liquid drops in the flow behind the shock wave in the range of Weber numbers from 200 to 8000 are reported. A phenomenological pattern of drop breakup is constructed on the basis of data on drop deformation and on the flow around the drop. A physical criterion of the change in stripping mechanisms of drop breakup is formulated.     

十字聚焦型微通道内弹状液滴在黏弹性流体中的生成与尺寸预测

利用高速摄像仪对十字聚焦微通道内液滴在黏弹性流体中的生成过程进行了实验研究。微通道截面为600μm×600 μm 的正方形结构,采用硅油作为分散相,含0.3%表面活性剂十二烷基硫酸钠(SDS)的聚环氧乙烷(PEO)水溶液(质量分数分别为0.1%,0.3%,0.6%)为连续相。实验观察到了弹状流、滴状流和喷射流3 种流型。对弹状流型下液滴生成过程的颈部动力学进行了研究,考察了两相流率、连续相毛细数及弹性数对液滴尺寸的影响。结果表明:弹状液滴尺寸随连续相流率、毛细数及弹性数的增加而减小,随分散相流率的增加而增加,连续相弹性对液滴尺寸的影响相对较小。以油水两相流率比和连续相的毛细数及Reynolds 数为变量建立了弹状液滴尺寸的预测关联式,预测值与实验值吻合良好。     

Single drop breakup in turbulent flow

The breakup process of a single drop in homogeneous isotropic turbulence was studied using direct numerical simulations. A diffuse interface free energy lattice Boltzmann method was applied. The detailed visualization of the breakup process confirmed breakup mechanisms previously outlined such as initial, independent, and cascade breakups. High‐resolution simulations allowed to visualize another drop breakup mechanism, burst breakup, which occurs when the mother drop has a large volume, and the flow is highly turbulent. The simulations indicate that the type of the breakup mechanism is a strong function of mother drop size and energy input. Large mother drops in highly turbulent flow fields are more likely to burst, producing a large number of drops of the size close to the Kolmogorov length scale. Small drops in moderate turbulence tend to break only once (initial breakup). The interfacial energy of a drop was tracked as a function of time during drop deformation and breakage. The maximum energy level of the deformed mother drop was compared to commonly used estimates of critical energy necessary to break a drop. Our results show that these reference levels of critical energy are usually underestimated. Moreover, in some cases even if the critical energy level was exceeded, the drop did not break because the time of the interaction between the drop and the eddies was not enough to finish the breakup. The numerical insight presented here can be used as a guideline for the selection of assumptions and simplifications behind breakup kernels.     

Development of fibrillar morphology in immiscible PP/PS blends under shear flow

The formation dynamics of fibrillar morphology in dilute immiscible polypropylene (PP)/polystyrene blends under simple shear flow is investigated using optical‐shear technique. Two strategies in generating fibrillar droplets under shear flow, namely temperature quench and shear jump, are studied. It is found that the shear‐induced deformation of PP droplets is closely related to the total shear strain and changes of rheological properties of components during the temperature quench or shear‐jump process. The shape evolution of fibrillar droplets under shear flow displays large deviation to the prediction of affine deformation theory based on Newtonian fluids and that of three deformation models, which consider the viscoelastic properties of components. The possible effect of droplet coalescence, breakup, and interfacial slip on the deviation between the experimental data and the prediction values for droplet deformation are discussed. © 2011 Wiley Periodicals, Inc. J Appl Polym Sci, 2011     

T型微流控芯片中微液滴破裂的数值模拟

利用VOF模型对T型结构微流控芯片中微液滴的三维破裂过程进行了数值模拟,获得了液滴发生破裂和不会破裂两种流型。一定轴向长度的微液滴对应着一个临界毛细数,当主流流体的毛细数大于此临界毛细数时,微液滴发生破裂并分别流向T型结构两侧;否则不会发生破裂,微液滴流向任意一侧。通过多个工况的计算,拟合了临界毛细数与微液滴相对轴向长度的关系,探讨了黏度比对微液滴破裂的影响。发现黏度比越小,微液滴越易发生破裂。     

Theory of competition between breakup and coalescence of droplets in flowing polymer blends

The Smoluchowski equation for the breakup and coalescence of dispersed droplets has been solved for flowing polymer blends. A scaling form for the distribution of droplet sized derived and published for a system of clusters with fragmentation and coagualation was used in our dervation. Equations are developed here for the average droplet size and for the characteristic time of transition to steady state flow of blends with a high content of the dispersed phase. Expressions reasonably describing the average size of droplets for all concentrations were obtained by a theory modification. Measured dependences of droplet size on the blend composition can be matched only if simultaneous collisions of three and more droplets are considered. The results of the theory indicate that the mechanism of droplet breakup (formation of pieces with the same or different volumes) has only a small effect on their average size in concentrated systems. The dependence of droplet size on the shear rate in flow is determined by properties of the blend components, and is generally nonmonotonic.     

匀强电场作用下分散相液滴的变形和破裂

基于Cahn-Hilliard方程的相场方法,建立了在匀强电场作用下液滴的变形和破裂行为模型。从微观角度研究分散相液滴变形过程中电荷密度、电场强度和电场力的分布规律以及流场和电场分布,探讨了微观液滴变形机理;采用数值模拟方法研究了电场强度、液滴直径和界面张力对液滴变形的影响,结果表明电场强度越强,液滴直径越大,界面张力越小,液滴变形量越大;分析了液滴的两种主要破裂方式,其破裂主要取决于连续相和分散相物性条件,为电破乳技术提供了理论基础。     

Self‐similar breakup of viscoelastic thread for droplet formation in flow‐focusing devices

The self‐similarity of the breakup of viscoelastic dispersed thread for droplet formation in flow‐focusing devices is investigated experimentally. A high‐speed camera is used to capture the evolution and angles of the cone‐shaped liquid‐liquid interface. The self‐similar profiles for the liquid‐liquid interface are obtained by normalizing the interface with the minimum width of the dispersed thread. The breakup of the dispersed thread transfers from a self‐similar power law scaling stage with an exponent of 0.36 to a self‐similar exponential scaling stage. The asymptotic cone angles prior to final breakup are consistent with the value of 125.5° and 151°, respectively. The viscoelasticity inhibits the development of finite‐time singularity for the breakup of the liquid‐liquid interface at microscale, similar to the capillary breakup at macroscale. The results demonstrate that the breakup of the viscoelastic dispersed thread for droplet formation exhibits self‐similarity at microscale. © 2017 American Institute of Chemical Engineers AIChE J, 2017