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.     

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.     

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.     

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.     

Modeling of polymer melting,drop deformation,and breakup under shear flow

Polyethylene (PE) or polycarbonate (PC) drop deformation and the breakup mechanism in a PE melt under shear flow were investigated using numerical simulations. The volume of fluid (VOF) method in FIDAP was used to track the dynamic interface. Two models were built for the investigation of a PE/PE system and a PE/PC system. Experimental data of polymer properties, such as specific heat capacity, viscosity, and heat conductivity, were incorporated in the simulations. For the PE/PE system, a temperature‐dependent viscosity model was used for the matrix PE and the dispersed PE. For the PE/PC system, generalized viscosity models were used for PE and PC with time‐dependent moving boundaries. An erosion mechanism similar to that observed in previous experiments was found for deformation and breakup of both PE and PC in the PE melt under simple shear flow. Local flow information, such as temperature, shear rate, viscosity, and shear stress, was obtained from the simulation results. The shear stress at the interface was much higher than the shear stress either in the dispersed phase or in the matrix phase, which could explain the erosion breakup mechanism. Polym. Eng. Sci. 44:1258–1266, 2004. © 2004 Society of Plastics Engineers.     

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.     

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.     

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.     

Sheet formation during drop deformation and breakup in polyethylene/polycarbonate systems sheared between parallel plates

A polycarbonate drop was sheared inside a polyethylene matrix in a transparent rotating parallel plate device at 220 °C and low shear rates. A flat sheet was formed during the initial shearing of the drop. The drop then developed into either a thin thread or a sheet with a thin cylindrical tip. Sheet formation was found to occur at a critical strain or time. A stress ratio (S_r) between the matrix breakup stress, made up of the matrix normal stress and viscous stress, and the drop restoring stress, made up of the drop normal stress and the interfacial stress, is used to characterize the sheet formation during the drop deformation and breakup process. It was found that the viscosity ratio (η_r), stress ratio (S_r) and Deborah number (De) of the system could be used to predict the drop deformation and breakup.     

The effect of surfactants on deformation of falling non‐Newtonian drops in a Newtonian liquid

Deformation of settling non‐Newtonian ellipsoidal drops in a Newtonian liquid was experimentally observed. Corn oil was used as the Newtonian phase and solutions of polyacrylamide in aqueous glycerine as the non‐Newtonian phase. The shear‐thinning behaviour of the drops fluid was controlled by the amount of polymer dissolved, while the effect of interfacial tension was examined using different concentrations of sodium dodecyl sulphate (SDS). In the range of 1 < E < 2.9, 0.2 < Eo, < 23, and 0 < Ma < 17.2, drop eccentricity increased linearly with a modified Eötvös number taking into account the effect of surfactants. For the range of experimental conditions tested, drop deformation was mainly controlled by viscous and interfacial tension forces, while shear‐thinning and inertia effects were negligible.     

水力喷射空气旋流器中射流雾化过程模拟及其机理

水力喷射空气旋流器(WSA)是一种新型高效的气液传质反应设备。采用雷诺应力模型和VOF两相流模型较好地模拟了WSA的气相压降特性、液相回流比和射流雾化过程,并讨论分析了雾化过程的机理。模拟和实验研究表明,WSA的气相压降随着进口气速的增加先后出现低压降区、压降突跳区、压降过渡区和高压降区4个特征区域,并给出了不同压降区域之间转折点气速的计算方法。射流在这4个压降区域里,分别表现为稳态射流、变形与袋式破碎、袋式破碎与剪切雾化和剪切雾化与离心分离等流态。射流在压降过渡区与高压降区的转折点左右实现充分雾化并达到最大相间传质面积。研究结果为建立基于WSA压降特性的射流雾化与流场调控方法提供了理论依据。     

Viscoelastic breakup in a high velocity airstream

Viscoelastic fluids were injected into a high velocity airstream (200 m/s) to investigate how the addition of small polymer quantities to fluids significantly increase the resultant disseminated drop size. For each liquid tested several hundred resultant drops were sampled and measured using an automated image analyzer. The resultant mass median diameter (MMD) for a viscoelastic fluid was an order of magnitude larger than a comparable viscous Newtonian fluid. A relaxation time measured from a die swell experiment correlates the dissemination results suggesting, an elongational rather than shear breakup mechanism.     

Uniaxial compression and combined compression‐and‐shear response of amorphous polycarbonate at high loading rates

We present results of a study conducted to better understand the yield and flow response of amorphous poly(bisphenol A carbonate), PC‐Lexan® (PC), under uniaxial compression and combined compression‐and‐shear impact loading. A split Hopkinson pressure bar (SHPB) is utilized to obtain nearly adiabatic uniaxial compression response of the PC in the strain‐rate range of 1000–2000 s^?1. Since temperature is expected to play an important role in governing the dynamic response of PC, nearly isothermal SHPB tests are also conducted and compared with the adiabatic response. In order to investigate the coupling of shear behavior and dilatation in PC at high loading rates, combined compression‐and‐shear plate impact experiments are conducted at strain‐rates in the range of 10⁵–10⁶ s^?1. In addition, novel plate impact experiments are conducted to better understand the evolution of the shearing resistance of PC in response to sudden alterations (drop) in hydrostatic pressure under extremely high shearing rates. POLYM. ENG. SCI., 2012. © 2011 Society of Plastics Engineers     

Transient shear rheology and rheo‐optical microstructural characterization of a thermotropic liquid crystalline polymer

The shear rheology and the corresponding microstructure evolution during transient flow of a thermotropic liquid crystalline polymer (LCP; Vectran V400P) are reported; the polymer does not display a crystalline melting phenomenon. The steady shear viscosity displays three regions that are typical of LCPs. However, the transient shear stress displays a local stress maximum at a strain of ≈ 2, a local minimum at a strain of ≈ 20, and then a stress overshoot at a strain of ≈ 100 before attaining a steady state value. The transient first normal stress difference exhibits a distinct overshoot at ≈ 100 strain units. The steady‐state first normal stress difference is always positive in the tested shear rate range 0.1–10 s^–1. In situ rheo‐optical characterization revealed that the melt shows a threaded texture at rest. Upon start up of shear flow, this threaded texture becomes deformed, and the domains initially appear to stretch and align in the shearing direction. Next, the domains break up, and a significant drop in the optical intensity is observed. These microstructural features are used to explain the presence of the first maximum and the minimum observed in the transient shear stress. Polym. Eng. Sci. 45:187–197, 2005. © 2005 Society of Plastics Engineers.     

Shear and extensional properties of short glass fiber reinforced polypropylene

Shear and extensional properties of a commercial short glass fiber reinforced polypropylene were carefully investigated using commercial rheometers and a novel on‐line rheometer. This on‐line slit rheometer, installed on an injection molding press, has been designed to measure the steady shear viscosity, the first normal stress difference, and the apparent extensional viscosity of polymer melts and composites for high strain rates up to 10⁵ s⁻¹ in shear and 200 s⁻¹ in extension. Our results show that the steady‐state viscosity measurements using the on‐line rheometer are in excellent agreement with those obtained using commercial rheometers. The steady‐state and the complex viscosities of the composites were found to be fairly close to that of the matrix, but the Cox‐Merz rule was not verified for the composites at high rates. The elasticity of the composites was found to be equal to that of the polypropylene matrix. The apparent extensional viscosity was obtained from the pressure drop in the planar converging die of the slit rheometer using the analyses proposed by Cogswell [1] and Binding [2]. The extensional viscosity of the polypropylene was found to be much larger than the shear viscosity at low strain rates with a Trouton ratio of about 40 that decreased rapidly with increasing strain rate down to the value of 4 at 200 s⁻¹. The extensional viscosity of the composites was also found to be close to that of the matrix, with values 35 and 5% larger for the 30 and 10 wt% reinforced polypropylenes, respectively. These results are compared with the predictions of the Goddard model [3], which are shown to overpredict our experimental results. POLYM. COMPOS. 26:247–264, 2005. © 2005 Society of Plastics Engineers.     

Effect of the dispersed phase fraction on particle size in blends with high viscosity ratio

It has been reported that for polymer blends with high viscosity ratio (>1), the size of the dispersed particles decreases with increasing volume fraction of the dispersed phase. In order to explain this effect, an equation was derived for the affine deformation of an imaginary plane of the dispersed phase in stratified two‐phase steady, simple, shear flow. The model predicts that for viscosity ratio >1, the deformation rate increases with volume fraction of the dispersed phase, and the shear stress also increases, leading to an increase of the breakup time. Therefore, the total deformation of the dispersed phase, before breakup, increases with increase of volume fraction, resulting in a decrease of the size of the dispersed phase particles. Accordingly, one can expect that in industrial mixers, the particle size of the blends should decrease as the volume fraction increases, if coalescence is suppressed. Experiments were carried out in a Haake batch mixer, using polyethylene/polyamide‐6 blends compatibilized by adding maleic anhydride grafted polyethylene. Particle size decreased up to 20 wt% polyamide‐6, at 100, 150, and 200 RPM, and increased between 20 and 30 wt%. The decrease of the particle size is mainly due to increased deformation of the dispersed phase. The increase of the particle size above 20 wt% is due to coalescence at high fractions.     

振动力场下聚合物熔体流变行为的响应与分析 Ⅰ.毛细管压力降和熔体表观粘度

在自行设计的恒速型毛细管动态流变装置上 ,对聚合物熔体进行动态挤出实验。借助已建立的振动力场下聚合物熔体流变行为的表征公式 ,分别计算振动力场下聚合物熔体在毛细管壁处的剪切应力、剪切速率和表观粘度。与稳态挤出时相比 ,引入振动力场后 ,发现毛细管压力降、表观粘度均显著降低 ,且随着振动频率和振幅的改变呈非线性变化趋势 ,作者对此进行了深入分析。     

Analysis of Liquid Jet Breakup in One‐ and Two‐Phase Flows

The phenomenon of breakup of a jet into drops has been applied mainly to separation technologies in the chemical, pharmaceutical, and metallurgical industries. The paper deals with the experimental analysis directed at the breakup of polymer solutions flowing through an orifice nozzle. The analysis of the breakup and atomization of a liquid jet by a high‐speed gas jet is presented. Additionally, non‐Newtonian effects on the breakup of the liquid jet into drops were studied using the microphotography method. In the experiments, various aqueous solutions of polyacrylamide were used. The polymer solutions studied were power‐law fluids. Analysis of the photographs of the jet breakup showed that the length of the jets depends on the liquid and gas flow rates and on the concentration of the polymer used. High‐molecular‐weight polymers added to a solvent lead to changes in the rheological properties of the liquid and the breakup length of the jet.     

Superposed flow properties of ceramic powder‐filled polymer melts

Complicated shape products from ceramic composite materials are nowadays intensively processed via flow molding technologies. Rheological properties of these materials are essential for the clarification of the deformation behavior through channels under various conditions. In this article, ceramic powder (zirconia) was mixed (10–50 vol%) with polypropylene, paraffin, and stearic acid in an elastic extruder. Parallel superposed steady and oscillatory shear flows were measured on a cone‐plate rheometer. Flow properties at high shear rates were evaluated on a capillary rheometer. The effects of powder content, shear rate/angular frequency, and temperature were clarified. The studied filled systems showed highly non‐Newtonian behavior and apparent yield stress; their viscoelastic properties were influenced remarkably under the superposed shear flow at low shear rate and angular frequency, and they showed significantly different behavior from unfilled and fiber‐filled systems. POLYM. COMPOS., 2009. © 2008 Society of Plastics Engineers     

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.