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.     

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.     

流场下不相容聚合物共混物分散相形态的研究进展

介绍了流场下不相容聚合物共混物分散相形态及演变研究进展,并指出这是获得性能优异共混材料的关键。在流场下,不相容共混物分散相尺寸由破碎和凝聚等动力学过程决定。鉴于模型的理想化,早期研究主要针对牛顿流体,且分散相的变形、破碎和凝聚等理论均发源于此。对于聚合物共混物,其在本质上与牛顿流体有很多相似之处,然而,独特黏弹性质却是影响其相形态的重要因素。最后,对一些预测分散相尺寸的理论模型进行了总结,并重点讨论了分散相浓度、聚合物弹性、增容和填料等因素对流场下分散相形态的影响。     

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.     

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     

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.     

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。     

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 mechanism of skin-core morphology formation in extrudates of polycarbonate/liquid crystalline polymer blends

The mechanism of skin/core morphology development and LCP (liquid crystalline polymer) fibril formation in polycarbonate/LCP blends was studied. A certain minimum concentration of the LCP phase must be present for the formation of continuous LCP fibrils in the extrudates. A skin-core morphology characterizes the PC/LCP extrudates. Short LCP fibrils are formed in the capillary converging entrance section, through the elongation of LCP domains and their coalescence. Continuous fibrils were formed in the skin of extrudates emerging from cylindrical capillaries, through the coalescence of the short fibrils, provided the shear stresses are high enough and the LCP viscosity is equal or lower than that of PC. Increasing capillary length enhances the LCP lateral migration and fibrils formation. The high interfacial tension stabilizes the LCP fibrils. In the core region the short fibrils recoil or breakup, resulting in spherical or elongated droplets. Long and continuous fibrils cannot be formed in a zero length capillary, even at high flow rates.     

Development of polymer blend morphology during compounding in a twin-screw extruder. Part IV: A new computational model with coalescence

In Part II of this series of publications, the first generation model of morphology evolution during polymer blending in a twin-screw extruder was presented. The model was based on a simplified flow analysis, and an assumption that dispersion occurs via drop fibrillation followed by disintegration. In the present Part IV, several modifications of the model are discussed. (i) The flow analysis was refined by computing the pressure profiles. (ii) The flow paths and strain history of the dispersed droplets within the screw elements are computed directly, which makes it possible to determine the drop susceptibility to deformation and break. (iii) Besides the fibrillation mechanism, a drop-splitting mechanism for low supercritical capillary numbers is incorporated. (iv) The choice of breakup mechanism is based on micro-rheological criteria. (v) The coalescence effects are taken into account. (vi) The theoretical model is self-consistent, without adjustable parameters. The validity of theoretical assumptions was evaluated by comparing the model predictions with the experimental droplet diameters at different positions in the twin-screw extruder.     

Effect of marangoni stresses on the deformation and coalescence in compatibilized immiscible polymer blends

The effect of physical compatibilization on the deformation and coalescence of droplets in immiscible polymer blends is discussed. Evidence is provided for the existence of concentration gradients in block copolymers along the interface during deformation. This causes complex changes in droplet shapes during deformation and relaxation. These concentration gradients also result in Marangoni stresses, which stabilize the droplets against deformation and breakup. Coalescence experiments have been performed, varying both the compatibilizer concentration and the shear rate. Existing coalescence models have been evaluated. An empirical extension of Chesters' partially mobile interface model is presented, that treats the effects of Marangoni stresses on the coalescence process as a higher effective viscosity ratio.     

微通道内表面活性剂与界面传递现象研究进展

表面活性剂在微流体应用中具有重要作用,常伴随动态界面传递现象。综述了微通道内含表面活性剂的多相流研究进展,剖析了液滴尺寸、液体流变性、压力降与微流体中动态界面张力的关系。总结了表面活性剂作用下的界面传递现象,如气泡及液滴的生成、运动、形变、破裂和聚并动力学的研究进展。综述了微流体中表面活性剂的吸附动力学,对该领域的发展方向进行了展望。     

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.     

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     

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.     

Development of polymer blend morphology during compounding in a twin-screw extruder. Part II: Theoretical derivations

In Part II of the work, the intermeshing twin-screw extruder is briefly described and the theoretical procedures used to model its operation are summarized. Based on the microrheological considerations discussed in Part I, a predictive procedure of the morphology evolution during compounding of two immiscible polymers is proposed. In this first generation model, only the shear flow effects are considered. Furthermore, to avoid complications due to coalescence a low concentration of the dispersed phase was assumed. In the procedure, two drop breakup mechanisms are discussed. The first assumes that the drops do not break under flow while the second postulates that breakup occurs under flow. Two dispersion mechanisms are considered, the first postulating continuously increasing polydispersity of drop size and the second postulating that drop polydispersity is inversely proportional to deformation strain. The influence of the screw configuration and operating conditions on blend morphology evolution is studied. It is expected that the computed drop size distribution provides limiting values for the experimental data. Dependency of predicted morphology on operating conditions is also investigated. Increasing screw rotating speed (resulting in increasing energy consumption) and decreasing throughput (resulting in decreasing productivity) lead to prediction of finer drop size. In practice, therefore, a compromise would be required. The proposed procedure is limited to melt flow (excluding the die region) within the region of large capillary parameter values, k > 4k_crit.     

Microstructural evolutions of LDPE/PA6 blends by rheological and rheo-optical analyses: Influence of flow and compatibilizer on break-up and coalescence processes

In this paper we investigate the relationships between flow and morphology in immiscible diluted non-Newtonian (LDPE and PA6) blends. Both rheological and rheo-optical techniques have been used. The effect of a steady shear flow on the blend microstructure has been studied at various shear rates. Moreover, the effects of a compatibilizing agent on rheology and morphology have been analysed. The compatibilizer causes decrease of average drop sizes and stabilization of the blend morphology during a steady shear flow. An attempt to relate the evolution of the volume-average radius with flow has been carried out by following the approach generally pursued for Newtonian polymer blends. The rescaling of both the capillary number and the viscosity ratio by using the shear-rate-dependent viscosity of blend constituents allows to roughly estimate the shear rate wherein severe drop break-up phenomena occur for the uncompatibilized system. Conversely, quantitative discrepancies between experimental data and theoretical expectations have been found for compatibilized blend. The coarsening behaviour in the early stages of an annealing process at rest has been studied, and simple model has been proposed to describe the volume average drop radius growth rate. The coalescence suppression detected for the compatibilized blend could be due to the shielding effect related to the presence of the copolymer layers at the interface between the phases.     

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。