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.     

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。     

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。     

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.     

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.     

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     

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.     

The role of elasticity in the formation of electrospun fibers

The role of fluid elasticity in the formation of fibers from polymer solution by electrospinning is investigated. Model solutions with different degrees of elasticity were prepared by blending small amounts of high molecular weight polyethylene oxide (PEO) with concentrated aqueous solutions of low molecular weight polyethylene glycol (PEG). The elastic properties of these solutions, such as extensional viscosity and the longest relaxation time, were measured using the capillary breakup extensional rheometer (CaBER). The formation of beads-on-string and uniform fiber morphologies during electrospinning was observed for a series of solutions having the same polymer concentration, surface tension, zero shear viscosity, and conductivity but different degrees of elasticity. A high degree of elasticity is observed to arrest the breakup of the jet into droplets by the Rayleigh instability and in some cases to suppress the instability altogether. We examine the susceptibility of the jet to the Rayleigh instability in two ways. First, a Deborah number, defined as the ratio of the fluid relaxation time to the instability growth time, is shown to correlate with the arrest of droplet breakup, giving rise to electrospinning rather than electrospraying. Second, a critical value of elastic stress in the jet, expressed as a function of jet radius and capillary number, is shown to indicate complete suppression of the Rayleigh instability and the transition from ‘beads-on-string’ to uniform fiber morphology.     

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.     

三维孔喉结构微通道内液滴的破裂行为研究

利用高速摄像仪研究了三维孔喉结构微通道内液滴的破裂行为。采用不同黏度的甘油-水溶液作为分散相,含4%（质量）表面活性剂（Span 20）的矿物油作为连续相。液滴通过孔喉结构后,观察到了三种流型：球形破裂、非球形破裂和不破裂。除极低连续相毛细数的情形外,分散相黏度和两相流量的增加不利于液滴破裂,液滴的破裂位置均接近于喉道出口。研究了液滴的球形破裂,结果表明,球形破裂中子液滴平均尺寸随分散相黏度和连续相流量的增加而降低,且与两相总毛细数呈幂律关系,模型预测值与实验结果吻合良好。     

电场作用下液滴分裂动力学行为的格子Boltzmann模拟

采用格子Boltzmann方法（LBM）伪势模型,耦合流场和电场控制方程,研究了电场作用下油水共存体系中水滴分裂的动力学行为及特性,借助形变率衡量液滴的形变大小,展现了液滴从形变至分裂的动态演变过程,分析了外加电场大小和液滴内外介电常数比对液滴分裂行为的影响。结果表明：外加电场能促使液滴发生振荡形变,且存在临界电毛细数和临界介电常数比决定液滴是否发生分裂：高于临界值,液滴形变率振荡幅度随时间不断增长,最终发生分裂;低于临界值,则液滴形变率振荡幅度不断衰减,并最终趋于一稳定值。在此基础上,综合考虑电场强度与介电常数比的影响,提出了基于现有电毛细数的修正电毛细数唯一地表征电场作用下液滴分裂与否。     

Mean Droplet Size and Local Velocity in Horizontal Isothermal Free Jets of Air and Water,respectively, Viscous Liquid in Quiescent Ambient Air

Measurements using two‐dimensional Phase Doppler Anemometry as well as high speed cinematography in free jets at several nozzle exit pressures and mass flow rates, show that the Sauter mean droplet diameter decreases with increasing air and liquid‐phase mass flow ratio due to the increase of the air stream impact on the liquid phase. This leads to substantial liquid fragmentation, respectively primary droplet breakup, and hence, satellite droplet formation with small sizes. This trend is also significant in the case of a liquid viscosity higher than that of water. The increased liquid viscosity stabilizes the droplet formation and breakup by reducing the rate of surface perturbations and consequently droplet distortions, ultimately also leading, in total, to the formation of smaller droplets. The droplet velocity decreases with the nozzle downstream distance, basically due to the continual air entrainment and due to the collisions between the droplets. The droplet collisions may induce further liquid fragmentation and, hence, formation of a number of relatively smaller droplets respectively secondary breakup, or may induce agglomeration to comparatively larger liquid fragments that may rain out of the free jet.     

Coalescence dynamics of two droplets of different viscosities in T-junction microchannel with a funnel-typed expansion chamber

The coalescence behavior of two droplets with different viscosities in the funnel-typed expansion cham-ber in T-junction microchannel was investigated experimentally and compared with droplet coalescence of the same viscosity.Four types of coalescence regimes were observed:contact non-coalescence,squeeze non-coalescence,two-droplet coalescence and pinch-off coalescence.For droplet coalescence of different viscosities,the operating range of non-coalescence becomes narrowed compared to the droplet coalescence of same viscosity,and it shrinks with increasing viscosity ratio η of two droplets,indicating that the difference in the viscosity of two droplets is conducive to coalescence,especially when 1 ＜ η＜ 6.Furthermore,the influences of viscosity ratio and droplet size on the film drainage time (Tdr) and critical capillary number (Cac) were studied systematically.It was found that the film drainage time declined with the increase of average droplet size,which abided by power-law relation with the size dif-ference and viscosity ratio of the two droplets:Tdr ～ (ld)0.25±0.04 and Tdr ～ (η)-0.1±002.For droplet coales-cence of same viscosity,the relation of critical capillary number with two-phase viscosity ratio and dimensionless droplet size is Cac =0.48λ0.26l-2.64,while for droplet coalescence of different viscosities,the scaling of critical capillary number with dimensionless average droplet size,dimensionless droplet size difference and viscosity ratio of two droplets is Cac =0.11 η-0.07ls-2.23ld0.16.     

In line study of droplet deformation in polymer blends in channel flow

We present in situ measurements of a dilute polymer blend in channel flow using an optical flow cell placed at the exit of a twin screw extruder. At weak shear stress, we find mildly deformed ellipsoidal droplets whereas at moderate sher rtes we find coexistence between large aspect ratio strings and ellipsoidal droplets. In the regime of low to moderate stress, depth resolved optical microscopy reveals that the deformation is a function of local shear stress. At large shear stress, the droplet breakup is suppressed; mildly deformed droplets at high capillary number are observed, in contrast to the Taylor model. Optical light scattering provides complementary morphological information that is averaged over the channel depth and confirms the optical microscopy. We discuss these results in terms of Taylor theory and normal forces.     

Asymmetric breakup of a droplet in an axisymmetric extensional flow

The asymmetric breakups of a droplet in an axisymmetric cross-like microfluidic device are investigated by using a three-dimensional volume of fluid(VOF) multiphase numerical model. Two kinds of asymmetries(droplet location deviation from the symmetric geometry center and different flow rates at two symmetric outlets) generate asymmetric flow fields near the droplet, which results in the asymmetric breakup of the latter. Four typical breakup regimes(no breakup, one-side breakup, retraction breakup and direct breakup) have been observed.Two regime maps are plotted to describe the transition from one regime to another for the two types of different asymmetries, respectively. A power law model, which is based on the three critical factors(the capillary number,the asymmetry of flow fields and the initial volume ratio), is employed to predict the volume ratio of the two unequal daughter droplets generated in the direct breakup. The influences of capillary numbers and the asymmetries have been studied systematically in this paper. The larger the asymmetry is, the bigger the oneside breakup zone is. The larger the capillary number is, the more possible the breakup is in the direct breakup zone. When the radius of the initial droplet is 20 μm, the critical capillary numbers are 0.122, 0.128, 0.145,0.165, 0.192 and 0.226 for flow asymmetry factor AS= 0.05, 0.1, 0.2, 0.3, 0.4 and 0.5, respectively, in the flow system whose asymmetry is generated by location deviations. In the flow system whose asymmetry is generated by two different flow rates at two outlets, the critical capillary numbers are 0.121, 0.133, 0.145, 0.156 and 0.167 for AS= 1/21, 3/23, 1/5, 7/27 and 9/29, respectively.     

Liquid Jet Stability in a Laminar Flow Field

The breakup of a Newtonian liquid jet into droplets injected horizontally into another flowing immiscible Newtonian fluid was studied experimentally under creeping flow conditions. Different breakup mechanisms take place in different flow regions. No filament is generated at very low velocities of the continuous phase when the droplets peel off directly at the nozzle tip. As soon as the flow rate of the continuous phase exceeds a critical value, a filament of a characteristic length begins to grow. The filament breaks up due to instabilities in terms of developing interfacial waves. The laminar breakup length of the filament is found to correlate with the flow rates of both phases and their viscosity ratio. The impact of the capillary diameter, through which the disperse phase is injected, on the filament length was investigated and the maximum droplet size was estimated.     

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     

导叶式旋流器内油滴的聚结破碎及影响因素

利用流场测试实验和模拟计算对导叶式旋流器的内部流场和湍流性能进行研究,得到导致旋流场中油滴发生聚结破碎现象的内因为时均速度梯度引起的黏性剪切力和湍流流动引起的高剪切应力及湍动能,并分析了油滴破碎的主要发生部位。同时为宏观考察导叶式旋流器内油滴聚结与破碎相对作用强弱,验证了旋流器的分离性能作为表征量的可行性,并在此基础上,利用导叶式旋流器的分离性能实验结果对油滴聚结破碎发生的外因进行研究,结果表明导向叶片的结构参数（叶片数和叶片出口角）和旋流器的操作参数（入口流速、溢流率、分散相入口浓度和操作温度）均会影响到油滴在旋流器中的存在和运动形态。     

Effect of selective localization of carbon nanotubes in pa6 dispersed phase of PP/PA6 blends on the morphology evolution with time,part 2: Relaxation of deformed droplets after cessation of flow

The relaxation of carbon nanotube (CNT)‐filled PA6 droplets in PP matrix was studied after cessation of simple shear flows. The morphology evolutions of blends with various CNT contents in PA6 were probed by optical microcopy over time. It was shown that the retraction of deformed droplets accelerates with increasing CNT content in PA6. As evidenced by linear rheological measurements, gradual formation of elastic structures within the droplets was found responsible for such observations. The pre‐shearing flow was varied to investigate the effects of different flow histories on the kinetics of relaxation. By increasing the shear‐rate of the flow prior to relaxation, the relaxation kinetics slowed down to some extent. The slowed‐down kinetics was attributed to the partial rupture of the elastic structures within PA6. This idea was evidenced by performing the startup of steady shear flow experiments on PA6/CNT nanocomposites. The final morphology of the blends after the melt blending process was analyzed. The average droplet size was found to increase with increasing the CNT content. Also, the distribution of the droplet sizes became broader as a result of the increased viscosity and elasticity ratios. POLYM. ENG. SCI., 56:51–60, 2016. © 2015 Society of Plastics Engineers     

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.