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.     

Morphology development during blending of immiscible polymers in screw extruders

The present work reports evolution of morphology from initial (presence of striation) to final (droplet formation) stages in a single‐screw extruder. Morphology development during the blending process controls the final size of the dispersed phase, which in turn significantly affects the properties of the blends. The experiments were carried out using a 70/30 wt% polypropylene/ethylene vinyl acetate (PP/EVA) blend; samples were collected along the length of the screw, by screw pullout experiment, to analyze the size and size distribution of the dispersed phase present both as striated layers and subsequently as droplets. Average size of the dispersed phase and standard deviation were taken into account to monitor the morphology evolution along the length of the screw. Pre‐breakup morphology development was studied by analyzing the sample collected from the feed zone of the extruder in terms of upper and lower layers along the cross section of screw channel. Examination of micrographs revealed the existence of pattern of ordered striations along the length of the melting zone containing striations from average size of 1000 μm down to 50 μm decreasing rapidly along the length of the screw. The breakup process was captured at the start of compression zone where step‐up in the shear as well as elongational flow was applied due to decrease in the channel depth along the compression zone. The observed droplet size formed by the breakup of filaments is found to be in accordance with theory. The final droplet size is found to be governed by the emulsification process occurring as a result of stretching, breakup and coalescence in the metering section of the screw and is in the order of 2 μm.     

Dispersion of water into oil in a rotor–stator mixer. Part 1: Drop breakup in dilute systems

Most previous studies of liquid–liquid dispersion in complex geometry are limited to turbulent flow at low continuous phase viscosity. In this study, a viscous continuous phase was employed over a range of flow conditions including both the laminar and turbulent regimes. Equilibrium drop size was measured for water dispersed into viscous food grade mineral oils in a batch Silverson L4R rotor–stator mixer. The influence of fluid viscosities and interfacial tension (by adding an oil-soluble surfactant) were examined. In order to isolate the effect of drop breakage from coalescence, Part 1 is limited to dilute conditions (water phase fraction, ? = 0.001). In the laminar regime, drop breakup was more likely due to a simple shear breakage mechanism than one for extension. Following Grace (1982), a semi-empirical drop size correlation was developed. For turbulent flow, the validity of the sub-Kolmogorov inertial stress model for correlating equilibrium mean drop size was verified. Surfactants were found to mostly decrease drop size by lowering interfacial tension. Except for laminar systems near the critical micelle concentration, where Marangoni stresses appear to play some role, the effect of surfactants on the drop size could be correlated using the equilibrium or static interfacial tension. The influence of water phase fraction and coalescence is considered in Part 2 ( Rueger and Calabrese, 2013) of this paper.     

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.     

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.     

Description of interaction processes in agitated liquid-liquid dispersions

Phenomenological models are proposed to describe drop breakup and coalescence in a turbulently agitated liquid-liquid dispersion. Based on these models, breakage and coalescence rate functions are developed and used to solve the general population balance equation describing drop interactions in a continuous flow vessel. Parameters of the models are evaluated by comparison with experimental data on drop size distributions and mixing frequencies obtained in a continuous flow vessel over a range of operating conditions. The favorable agreement between experimental observation and the model are encouraging that the model is suitable for predicting dispersion properties such as drop size distributions, interfacial areas and mixing frequencies.     

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.     

Estimation of the morphology development of immiscible liquid–liquid systems during single screw extrusion

A mathematical model to predict the evolution of the morphology of immiscible liquid–liquid systems in single screw extruders has been developed. The model computes the dimensions of the dispersed phase in the polymeric matrix, taking into account the stretching, break‐up, and coalescence phenomena. The corresponding routine was inserted in a process modeling software, describing the flow in a single screw extruder from hopper do die. The drop dimensions were computed along the melting and melt conveying zones. This enabled the study of the morphological evolution of a two‐phase liquid system in a single screw extruder, taking into consideration the effects of the material properties, operating conditions, and screw geometry. The limited experimental data obtained was generally in line with the theoretical predictions. POLYM. ENG. SCI., 2010. © 2010 Society of Plastics Engineers     

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。     

A theoretical approach to solid filler dispersion in a twin‐screw extruder

Compounding of highly filled minerals in a polymeric matrix has never been an easy task. The objective of this work was to build a theoretical model to predict the evolution of dispersion of an inorganic filler in a polymer matrix along a twin‐screw extruder as a function of the screw geometry and processing conditions. We developed a general kinetic model of agglomeration/breakup of the fillers, based on chemical‐like equations. It allowed us to describe the evolution of a population of agglomerates, taking into account the deformation field. When implemented in a flow model of a twin‐screw extrusion process, the model can be used to pinpoint the main effects of twin‐screw operating conditions on dispersion.     

CFD simulations of single-phase flow in pulsed disc and doughnut columns: Axial dispersion and pressure drop

CFD simulations of pulsed disc and doughnut columns are performed to understand the effects of operating and geometric parameters on axial dispersion and pressure drop in single-phase flow. CFD simulations have been carried out using a two-step approach. In the first step, the flow field is obtained by solving the continuity and the momentum equations along with the equations of the standard k–ε model of turbulence. In the second step, the species transport equation is additionally solved to obtain the residence time distribution and hence the Peclet number and axial dispersion coefficient. The computational approach is validated by comparing its predictions with the experimental data reported in the literature and then used for detailed parametric analysis.     

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.     

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.     

Comparative study of dry pressure drop and flow behaviour of gas flow through sieve plate packing

Sieve plate packing is a newly developed packing that has been used in several industries due to its simple structure and operating flexibility, and no liquid flooding. In this work, first, systematic experiments were conducted to measure the pressure drop of gas flow through six sieve plate packings. The results indicated that the geometric characteristics of the packing have complicated effects on the pressure drops. Based on this, CFD simulations on the gas flow field were conducted using the realizable k-ε model, and flow behaviours such as the pressure drop, pressure nephogram, and velocity distributions within different packings were obtained. The simulation results clearly showed interesting flow patterns, including the contraction and expansion of the gas stream through the sieve hole, the flow separation on the sharp edge of the hole, and the vortexes formed when gas impacts the downstream plate. By comparing the flow patterns and the pressure drop under different packings operating at different conditions, the effects of the geometric characteristics of the packing on the pressure drop could be clearly distinguished from the flow behaviours, so that the variations in pressure drop with various packing structures were clearly indicated. Finally, based on the experimental data and the simulated results, correlations for the prediction of the pressure drops were proposed. This work will provide a useful basis for understanding the flow behaviour of gas and liquid two-phase flow in sieve plate packing.     

Spray and mixing characteristics of liquid jet in a tubular gas–liquid atomization mixer

For the design and optimization of a tubular gas–liquid atomization mixer,the atomization and mixing characteristics of liquid jet breakup in the limited tube space is a key problem.In this study,the primary breakup process of liquid jet column was analyzed by high-speed camera,then the droplet size and velocity distribution of atomized droplets were measured by Phase-Doppler anemometry (PDA).The hydrodynamic characteristics of gas flow in tubular gas–liquid atomization mixer were analyzed by computational fluid dynamics (CFD) numerical simulation.The results indicate that the liquid flow rate has little effect on the atomization droplet size and atomization pressure drop,and the gas flow rate is the main influence parameter.Under all experimental gas flow conditions,the liquid jet column undergoes a primary breakup process,forming larger liquid blocks and droplets.When the gas flow rate (Q_g) is less than 127 m~3·h~(-1),the secondary breakup of large liquid blocks and droplets does not occur in venturi throat region.The Sauter mean diameter (SMD) of droplets measured at the outlet is more than 140μm,and the distribution is uneven.When Q_g127 m~3·h~(-1),the large liquid blocks and droplets have secondary breakup process at the throat region.The SMD of droplets measured at the outlet is less than 140μm,and the distribution is uniform.When 127Q_g162 m~3·h~(-1),the secondary breakup mode of droplets is bag breakup or pouch breakup.When 181Q_g216 m~3·h~(-1),the secondary breakup mode of droplets is shear breakup or catastrophic breakup.In order to ensure efficient atomization and mixing,the throat gas velocity of the tubular atomization mixer should be designed to be about 51 m·s~(-1)under the lowest operating flow rate.The pressure drop of the tubular atomization mixer increases linearly with the square of gas velocity,and the resistance coefficient is about 2.55 in single-phase flow condition and 2.73 in gas–liquid atomization condition.     

Influence of atomizer exit area ratio on the breakup morphology of coaxial air and round water jets

The goal of this article is to study the effect of atomizer exit area ratio on atomizer performance. The experiments are performed on the round liquid jet breakup of seven coaxial air‐blast atomizers with water–air systems. The breakup morphology of liquid jet is observed first. The membrane‐type breakup can be divided into two subregimes called bag‐type breakup and membrane‐fiber breakup, and a correlation of characteristic length on bag‐type breakup regime is obtained. Then, we analyze the influence of atomizer exit area ratio on the breakup morphology of water‐air jets. To obtain reasonable atomization morphology criterions, the atomizer exit area ratio is used to modify the Weber number and momentum flux ratio per unit volume. This method is found to be able to explain different experimental results in the literature, which is also close to the results of round liquid jet in cross air flow and secondary atomization. © 2014 American Institute of Chemical Engineers AIChE J, 60: 2335–2345, 2014     

An experimental investigation on the breakup of surfactant-laden non-Newtonian jets

The combined effect of polymers and soluble surfactants on the dynamics of jet breakup, and especially on satellite drop formation, was experimentally investigated. Xanthan gum and Carbopol^® 934 NF were dissolved in water with Sodium Dodecyl Sulfate as the surfactant. Controlled disturbances were imposed at the laminar jet interface using a piezoelectric vibrating nozzle with breakup dynamics recorded using a high-speed camera. Drop and ligament diameters were measured from the digital images. The focus of the work was investigating how bulk and interfacial properties of the prepared fluids influenced ligament and drop evolution. It was found that if the proper concentration of surfactant (close to the critical micelle concentration, CMC) was selected, and if the flow time scales were large enough, Marangoni interfacial stresses may lead to an increase in satellite drop size as previously reported for breakup simulations of shear-thinning jets covered with insoluble surfactant. It was also experimentally confirmed that the introduction of surfactant contributes to a delay in jet breakup.     

Continued self-similar breakup of drops in viscous continuous phase in agitated vessels

Drop breakup in viscous liquids in agitated vessels occurs in elongational flow around impeller blade edges. The drop size distributions measured over extended periods for impellers of different sizes show that breakup process continues up to 15–20 h, before a steady state is reached. The size distributions evolve in a self-similar way till the steady state is reached. The scaled size distributions vary with impeller size and impeller speed, in contrast with the near universal scaling known for drop breakup in turbulent flows. The steady state size of the largest drop follows inverse scaling with impeller tip velocity. The breadth of the scaled size distributions also shows a monotonic relationship with impeller tip velocity only.