A study of residence time distribution in co‐rotating twin‐screw extruders. Part II: Experimental validation

In the first part of this paper, a new approach to model the residence time distribution (RTD) in a co‐rotating twin‐screw extruder was proposed. It consists of coupling a continuum mechanics approach with a chemical engineering one, yielding an RTD curve without any fitting parameter. However, the choice of ideal reactors that depict the behavior of each particular profile is not evident. In this second part, we present an experimental study based on two types of extruder (Leistritz 30–34 and Clextral BC45), different screw profiles and two measurement techniques (off‐line and in‐line). Global, partial and local RTD curves were obtained, both experimentally and by means of a deconvolution technique. This series of experiments permitted the definition of the best association between ideal reactors and screw elements. Using this association, a comparison has been made between experimental results and theoretical calculations. A good agreement was generally obtained in terms of the RTD shape, delay time, mean residence time and variance.     

A study of residence time distribution in co‐rotating twin‐screw extruders. Part I: Theoretical modeling

A theoretical model to determine the residence time distribution (RTD) in a co‐rotating twin‐screw extruder is proposed. The method consists of coupling a continuum mechanics approach with a chemical engineering one and allows us to obtain the RTD without any adjustable parameter. The process parameters are obtained using Ludovic® twin‐screw modeling software, and ideal reactors are chosen to depict the screw profile. The influence of screw speed, feed rate and viscosity on RTD are described on a fictive screw profile. The predictions of the model are in qualitative agreement with literature data. The key point of this procedure is obviously the correct association between an ideal reactor and a screw element.     

Assessing local residence time distributions in screw extruders through a new in‐line measurement instrument

This work aimed at developing a new instrument to measure in real time the residence time distribution (RTD) in screw extruders. The instrument followed the same principle as the one reported in the literature but possessed several important advantages. For example, the detection system had two probes that allowed to simultaneously measure RTDs at any two different locations of an extruder, thus providing the possibility of calculating the local RTD between them by a deconvolution method based on a statistical theory for the RTD. Its performance was evaluated on a corotating twin‐screw extruder using anthracene as tracer and polystyrene as flowing material. The effects of various process parameters such as feed rate and screw speed on the RTDs were investigated. The emphasis was placed, however, on the effect of the staggering angle of kneading discs on local RTDs both in the kneading zone itself and its neighboring upstream and downstream screw zones. This work is in support of an ongoing project on the simulation of flow in corotating twin‐screw extruders. POLYM. ENG. SCI., 46:510–519, 2006. © 2006 Society of Plastics Engineers.     

Residence time distribution of a pharmaceutical grade polymer melt in a single screw extrusion process

The residence time distribution (RTD) of a flowing polymer through a single screw extruder was studied. This extruder allows injecting supercritical carbon dioxide (scCO₂) used as physical foaming agent. The tested material is Eudragit E100, a pharmaceutical polymer. RTD was measured at various operating conditions and a model describing RTD has been developed. High screw speed or high temperature implies short residence time, but these parameters do not have the same effect on polymer flow. In the flow rate range studied, scCO₂ has no significant influence. A mathematical model consisting of a plug flow reactor in series with a continuous stirred tank reactor (CSTR) cross-flowing with a dead volume fitted well the experimental data.     

Residence time distributions in a co‐kneader: A chemical engineering approach

In this article, we have studied the residence time distributions (RTD) in a modular co‐kneader. Several papers have already addressed the co‐kneader modeling and operating mode but there is still a lack of experimental data on RTD. To investigate the RTD, we have used a colored tracer dispersed in polypropylene (PP) that was injected in the flow during the compounding of neat PP. The effect of operating parameters such as temperature, feed rate, and screw configuration was investigated, focusing on the influence of mixing and conveying elements in a zone where the polymer is molten. As can be expected, results on various screw configurations show that increasing the number of kneading elements makes the RTD longer. More interestingly, for a defined set of elements, their position does not change the experimental RTD. A chemical engineering approach was used to model the RTD, with an equation derived from a cascade of continuous stirred tank reactors. The model allows to retrieve an elementary RTD for each section of a defined type of elements and to propose a law for their combination in good agreement with experiments. POLYM. ENG. SCI., 55:1237–1245, 2015. © 2015 Society of Plastics Engineers     

Experimental study of maleation of polypropylene in various twin‐screw extruder systems

A range of continuous mixing machines were used as continuous reactors for grafting maleic anhydride onto polypropylene. The machines used were (1) a nonintermeshing modular counterrotating twin‐screw extruder, (2) an intermeshing modular corotating twin‐screw extruder, (3) intermeshing modular counterrotating twin‐screw extruder, and (4) a Kobelco Nex‐T continuous mixer. The grafting reaction of maleic anhydride onto polypropylene and degradation of polypropylene during the grafting reaction were investigated as means for comparing these different machines for reactive extrusion. The influence of processing variables such as screw speed and processing temperature on polymer characteristics also was investigated. Generally, in a comparison of the different machines, the intermeshing counterrotating twin‐screw extruder had the lowest levels of grafted maleic anhydride, whereas the Kobelco Nex‐T continuous mixer under the conditions used had the highest levels of grafted maleic anhydride. © 2003 Wiley Periodicals, Inc. J Appl Polym Sci 90: 1755–1764, 2003     

Residence time and conversion in the extrusion of chemically reactive materials

Twin‐screw extruders offer improved control of the residence time distribution (RTD) and mixing in materials such as plastics, rubber and food. Based on the flow and the heat transfer characteristics obtained for a self‐wiping, co‐rotating twinscrew extruder, the residence time and chemical reaction are studied by tracking the particles. For normally starve‐fed twin‐screw extruders, the length of the completely filled section is calculated as function of the process variables using the coupling of the flow with the die. With a model of the solid conveying section, the RTD for the whole extruder is calculated for corn meal at different screw speeds and flow rates. The calculated variation of RTD with the screw speed and the flow rate yields good agreement with observations from many experiments. The variation of the fully filled section length, chemical conversion and mixing effectiveness are also obtained under different operation conditions. Most of the results are in qualitative agreement with experimental results and may be used as guidelines for extruder design and determination of optimal operating conditions.     

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.     

Preparation of macromolecular tracers and their use for studying the residence time distribution of polymeric systems

In this study, an easy route was developed to incorporate antracene moieties in polymer chains. It consisted of copolymerizing the monomer of a polymer of interest with 3-isopropenyl-α, α'-dimethylbenzyl isocyanate (TMI) and then reacting the isocyanate-bearing polymer with 9-(methylamino-methyl)anthracene. Such an antracene-bearing polymer was then used as a tracer (macrotracer) to determine the RTD function of polymers in a twin screw extruder and compared with an antracene as a microtracer. As long as the tracers were well mixed with a polymer of interest and the resulting mixture had the same geometrical form as the polymer before they were charged to the flow stream, the differences between the microtracer and the macrotracer were not reflected in the measured RTD distribution. A variation in the feed rate (Q) or screw speed (N) changes both the RTD and the intensity of axial mixing. On the other hand, for a given but small Q/N, commonly called specific throughput, variations in Q and N change the RTD but not the intensity of axial mixing. When it is small, Q/N can be used as an operating parameter to separate the effect of the residence time from that of mixing for a small Q/N.     

Comparison of scale‐up methods for dispersive mixing in twin‐screw extruders

Twin‐screw extrusion processes are commonly refined on laboratory‐scale extruders then scaled‐up to manufacturing systems. When using twin‐screw extrusion to compound filler into a polymer, the dispersion of the filler must be considered during scale‐up. In this work, two scale‐up methods are evaluated for how accurately they scale dispersion as measured by the Residence Stress Distribution, an experimental method that quantifies stress developed in a twin‐screw extruder. The first scale‐up method evaluated is the industry‐standard scaling based on maintaining equivalent volumetric flow rate across extruder sizes. Volumetric scaling is compared to a second, novel scale‐up method, the percent drag flow rule, which maintains the same degree of fill in the strongest dispersive screw elements on all extruder sizes. Both scale‐up rules have been used to scale between three extruder sizes and have been evaluated for how accurately the larger extruders recreate the dispersive mixing of the smallest machine. Results indicate that the percent drag flow scale‐up more accurately maintains dispersive mixing behavior than the volumetric scaling. Furthermore, percent drag flow scale‐up resulted in all three extruder sizes behaving similarly to changes in operating conditions. These results indicate that percent drag flow scale‐up is a valid technique to scale real industrial processes. POLYM. ENG. SCI., 57:345–354, 2017. © 2016 Society of Plastics Engineers     

Amplitude–frequency characteristics of polymer electro‐magnetic dynamic tri‐screw extrusion

The mechanism of plastic forming and processing in electromagnetic dynamic tri‐screw extruder is very sophisticated and the investigation of amplitude–frequency characteristic acts as the foundation of equipment design and the optimization of polymer processing parameters. A mathematical and analytical model of plastic forming in such extruder was developed and the results were nondimensional‐normalized. To validate the mathematical solutions experiments based on LDPE were carried out and the experimental vibration amplitude and vibration frequency curve was obtained. Three conclusions can be drawn herein: (1) the experimental results hold a good agreement with the calculations, and thus the feasibility of the proposed model is validated; (2) the possibility of resonance closely relates to polymer melt viscosity, rotating speed, and geometry parameters of the screw; (3) resonance of the tri‐screw extruder is seldom observed under normal conditions and there exists an inverse correlationship between vibration frequency and amplitude. © 2011 Wiley Periodicals, Inc. J Appl Polym Sci 122:1778–1784, 2011     

Modeling of the plasticating process in a single‐screw extruder: A fast‐track approach

A new mathematical model has been developed to analyze the entire flow field of a single screw extruder under steady‐state conditions. Intended as a rational design tool for practising engineers in the polymer processing industry, the model contains no partial differential equations and hence does not require the use of numerical solution techniques. To achieve generality, a generic approach is proposed and has been adopted in the derivation of governing algebraic equations from general conservation laws covering channel geometry, polymer flow speed, equivalent radius in a pipe, material properties, power consumption and heat transfer. The model makes no use of empirical factors or correlation. The validity of the new model has been assessed by comparison with published experimental results. Good agreement was achieved with respect to its ability to predict (a) the solid‐bed width profile; (b) the axial pressure profile and (c) the temperature and pressure of the melt pool at the extruder exit. Furthermore, the model can predict other information including the solid‐bed velocity in the axial direction and the power consumption. The work has demonstrated the potential of a fast track approach to designing helical extruder screws, while maintaining a level of accuracy comparable with more complex 3D models but without the penalty of computational efforts.     

Transport processes and feasible operating domain in a twin‐screw polymer extruder

The flow of a polymer and the associated heat transfer in a fully intermeshing, co‐rotating twin screw extruder are investigated numerically. The control volume technique is used for numerical modeling and simulation, considering both Newtonian and non‐Newtonian fluids. The velocity distributions in the screw channel are compared with experimental resultlsf and good agreement is obtained. Owing to limitations arising from the physical aspects of the problem, the numerical results show that not all operating conditions are feasible. A feasible domain, in terms of screw speed and mass flow rate, in which the extruder operation is satisfactroy, is obtained for pure starch. To improve the applicable range of this model, an axial formulation is adopted for the translation region that characterizes the domain away from the intermeshing zone of the extruder. This model yields results consistent with the earlier down‐channel model while the feasibility region is extended towards lower mass flow rates. For the upper limit, a physicdal restriction arises in terms of the maximum flow rate for a pressure rise in the extruder. Thus, the model can be used for simulating a wide range of operating conditions while retaining the appropriate physical behavior of the process.     

同向双螺杆挤出机的停留时间分布及填充度

引 言 双螺杆挤出机在高分子材料加工中已被广泛地应用于聚合物共混改性、反应挤出及高分子可控降解等各个方面[1].但先前对挤出过程研究较少,一般仅停留在"黑箱"型经验操作的层面,主要以定性的机械设计为主.     

The effects of kneading block design and operating conditions on distributive mixing in twin screw extruders

A mixing limited interfacial reaction between polymer tracers was used to directly measure the distributive mixing performance of a co‐rotating twin screw extruder during melt‐melt blending of polypropylene. The reaction between the polymer tracers, which are low molecular weight succinic anhydride and primary amine terminally functionalized polymer chains, was followed using Fourier‐Transform Infrared Spectroscopy (FT‐IR). Experiments were completed to determine the effects of flow rate, screw speed, and kneading block design on the distributive mixing performance and the residence time distribution (RTD). The only RTD variable that was significantly affected by the experimental factors was the average residence time. Distributive mixing with neutral and reverse kneading blocks was controlled by the average residence time, the fully filled volume, and the shear rate. Conversely, the mixing performance of a forward kneading block did not follow the same trends.     

Application of ultrasound in the determination of fundamental extrusion performance: Residence time distribution measurement

By means of new probe design and rapid data acquisition, we have succeeded in in‐line ultrasonic monitoring of residence time distribution (RTD) at the melting, mixing, and pumping zones as well as at the die exit of a Werner & Pfleiderer 30‐mm twin‐screw extruder by mounting the ultrasonic probes on the extruder barrel over the screw elements and at the die. The experimental systems were LDPE, CaCO₃‐filled LDPE, and a Kraton/LDPE blend. The ultrasonic data at each of the extruder functional zones are presented. The ultrasonic results have been used to evaluate an opical RTD measurement method by using an optical sensor side by side with one ultrasonic probe at the mixing zone of the extruder. The comparison of the ultrasonic and optical results has shown that the presented ultrasonic technique could be a good complement to the optical technique in the monitoring and understanding of RTD during polymer extrusion processes.     

Computation of starch cationization performances by twin‐screw extrusion

A theoretical model for the cationization of plasticized wheat starch in a modular seIf‐wiping co‐rotating twin screw extruder was developed. Our objective was to build a model which would be able to predict the evolution of the cationization reaction along the screws, in relation with the processing conditions and the geometry of the twin screw extruder. Based on previous studies on reactive extrusion modeling, the present model takes into account the interactions occurring between the flow conditions encountered in the extruder and the kinetics of the reaction. It allows one to predict the influence of operating parameters such as reagent concentrations, feed rate, screw speed, and barrel temperature on the reaction extent. Depending on conditions, degrees of substitution in the range 0.01–0.05 are obtained, with efficiencies between 30 and 90%. A good agreement is found between theoretical results and experimental measurements, allowing future use of the model for optimization and scale‐up purposes. POLYM. ENG. SCI., 47:112–119, 2007. © 2007 Society of Plastics Engineers     

Steady and transient flow of a non‐Newtonian chemically reactive fluid in a twin‐screw extruder

The flow of chemically reactive non‐Newtonian materials, such as bio‐polymers and acrylates, in a fully intermeshing, co‐rotating twin‐screw extruder is numerically investigated. A detailed study of the system transient behavior is carried out. The main transient aspects, including response time, variation of system variables, and instability of operation, are studied for both single‐ and twin‐screw extruders, since single‐screw extruder modeling closely approximates the region away from the intermeshing zone in a twin‐screw extruder. The effect of a time‐dependent variation in the boundary conditions is studied. The coupling due to conduction heat transfer in the screw barrel is found to be very important and is taken into account for single‐screw extruders. In the absence of this conjugate coupling, the response time is much shorter. Several other interesting trends are obtained with respect to the dependence of the transient response on the materials and operating conditions. Steady state results are obtained at large time. The calculated velocity distributions in the screw channel are compared with experimental results in the literature for steady state flow and good agreement has been obtained. The calculated results for transient transport agree with the few experimental observations available on this system. Chemical reaction, leading to chemical conversion of the material, is also considered and the resulting effects on the flow and transport determined. These results will be useful in the design, control and optimization of polymer extrusion processes.     

Numerical simulation and experimental study of pressure and residence time distribution of triple‐screw extruder

Three‐dimensional flow field of triangle arrayed triple‐screw extruder (TTSE) in different feed rates, screw speeds and screw configurations were simulated by POLYFLOW. Polypropylene processing by TTSE was tested to validate the numerical simulation. The reliability of simulation was tested directly and indirectly by comparing the axial pressure difference and residence time distribution (RTD) separately. The results show that the axial pressure differences from the simulations and experiments were in high agreement. The simulated and experimental RTD curves show the same trend, and so are the simulated and experimental average residence times. These results prove the reliability of simulation and its guidance to the experiment. POLYM. ENG. SCI., 55:156–162, 2015. © 2014 Society of Plastics Engineers     

单螺杆挤出机中非牛顿流体层流混合停留时间表征

基于有限差分数值模拟技术,提出了计算非牛顿流体在单螺杆挤出机内停留时间分布的半解析方法,得到了不同操作参数下的停留时间分布,该分布可用来表征聚合物熔体在加工过程中的混合情况.结果表明：半解析方法能够反映由流体的非牛顿性所导致的耦合流场及压力反流对混合的影响,能更真实地反映聚合物熔体在单螺杆挤出机内的混合程度.