Theoretical analysis of residence time distribution functions and strain distribution functions in plasticating screw extruders

The residence time distribution (RTD) function in a single screw plasticating extruder was theoretically calculated. The calculation is based on the solids conveying, melting, and melt conveying models in extruders. The screw channel is divided into small axial increments and the path of each exiting fluid particle is followed from hopper to die. In addition to the residence times the total shear deformation or strain imposed on the fluid particles was also calculated. This together with the RTD function has led to the definition and calculation of the strain distribution function (SDF). This function is proposed for quantitative characterization of the mixing performance of screw extruders as well as other laminar mixers. Some simple idealized batch and continuous laminar mixers are analyzed in terms of the SDF. Finally, the effect of extruder operating conditions and screw design on the RTD and SDF were investigated by computer simulations.     

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.     

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.     

The concept of conversion distribution in reactive processing

A new concept of conversion distribution applied to the continuous chemical modification and polymerization of polymers in a twin screw extruder was discussed. The kinetics and the residence time distribution function (RTD) are two undissociable parameters in reactive extrusion because their combination reflects the degree of homogeneity of the modified polymer at the die die exit of the extruder. A function G defining the distribution of the modification rate allowed us to evaluate the distribution of the extent of the conversion around the mean conversion. This study has underlined the predominant role of the kinetics on the structural homogeneity of the modified product. This new concept was developed, within a framework of reactive processing, from previous works on chemical modification of polymers and polycondensation in corotating twin screw extruder. © 1996 John Wiley & Sons, Inc.     

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.     

Residence time distribution in non-intermeshing counter-rotating twin-screw extruders

This paper deals with the residence time distribution (RTD) in a non-intermeshing counter rotating twin screw extruder. The RTDs were measured in three vent zones of the extruder sparately, and in the adjacent zones combined, using a soluble dye as the tracer. Assuming that the RTDs in the adjacent zones are independent of each other, the overall RTD was also calculated using a previously developed statistical theory. The theory has also confirmed the consistency of the present measurements. A predictive RTD model for the non-intermeshing twin screw extruder, based on the flow analysis of the individual screw zones and their statistical superposition, was also developed. The predictions are in good agreement with experiment.     

Modeling of a cokneader for the manufacturing of composite materials having absorbent properties at ultra‐high‐frequency waves. Part 1: Modeling of flow from residence time distribution investigations

The purpose of this study is to gain better understanding of flow patterns and mixing conditions in a particular single‐screw extruder: the Buss Cokneader. To this end, the residence time distribution (RTD) of the polymer was investigated experimentally for different combinations of the operating variables (i.e. feed rate, screw rotation speed). The measurement of RTD used a standard stimulus‐response technique. Two kinds of tracer were used: free anthracene and anthracene grafted on the polymer. It was shown that only the second could characterize the actual flow of the polymer in the extruder. It does not perturb the flow and has the same rheological behavior as the studied fluid. Thanks to the RTD data, a model of the extruder based on the combination of ideal reactors, such as continuous stirred tank reactors or plug flow reactors, was finally set up. The establishment of relationships between model parameters and extrusion conditions allowed the prediction of RTD with good agreement.     

Residence time distribution in a twin screw extruder

The residence time distribution (RTD) in a fully intermeshing, corotating twin screw extruder was determined with a stimulus-response technique. In addition to varying three process parameters (i.e. throughput, screw rotational speed, and barrel temperature), two screw configurations were also studied: one containing four kneading block mixing sections, and the other consisting only of regular screw bushings. Although screw configuration was an important variable, it was found that for both configurations the throughput had the largest effect on RTD. The screw rotational speed was second in importance, and the barrel temperature change produced no effect. A fluid mechanical model based on the fluid flow in a partially-filled rectangular channel was used to explain the experimentally observed dependence of RTD on the process parameters. Reaction engineering approaches were adopted to compare the RTD results of two screw configurations with two idealized flows.     

Effects of screw configurations on the grafting of maleic anhydride grafted low-density polyethylene in reactive extrusion

The effects of screw configurations, that is, the staggering angles and disc widths of the kneading blocks, on grafting reactive extrusion for maleic anhydride grafted low-density polyethylene were investigated in a corotating twin-screw extruder. Samples were collected from three positions along the screw and the die exit. The grafting degree (GD) of the specimens was evaluated by titration. It was found that the kneading block configurations had a significant influence on the grafting reactive extrusion. In addition, another three groups of extrusion experiments were performed to explore the intrinsic relationship between the GD, the degree of fill in the screw channel, the residence time distribution (RTD), and the mixing intensity in various screw configurations. The experimental results indicated that the location of the melting endpoint significantly affected the position at which the reaction began; the degree of fill, RTD, and mixing performance of the screw played important roles in the grafting reaction. The reverse kneading blocks with a narrow disc width, which had a high degree of fill and good mixing capacity, enhanced the increase in GD along the screw during the reactive extrusion. © 2008 Wiley Periodicals, Inc. J Appl Polym Sci, 2008     

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.     

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.     

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.     

Measurements of residence time distribution for the peroxide degradation of polypropylene in a single-screw plasticating extruder

Measurements of the residence time distribution (RTD) in a single-screw plasticating extruder were carried out during experimental studies of the peroxide-initiated controlled chemical degradation of polypropylene (PP). A radioactive tracer method was employed, and the effect of screw speed, temperature, and reaction on the RTD was examined. An increase of the peroxide concentration resulted in a broader distribution whereas an increase of the extrusion temperature was found to result in a narrower distribution. Use of low screw speeds simply increased the time delay through the extruder without affecting considerably the breadth of distribution. Results obtained from the present experiments were compared with several theoretical models.     

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.     

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.     

Numerical Simulation of Extrusion Characteristics for Co-rotating Tri-Screw Extruder

The flow of polyethylene melt in new tri-screw extruder was simulated using the finite element method (FEM). A special study of flow in central region was performed by analysis of the velocity, pressure, and resident time distribution (RTD). The extrusion characteristics of tri-screw extruder, namely the abilities of material conveying, mixing, and power consumption, were compared with those of twin screw extruder. The results showed that there was circumfluence in central region but no stagnation in it. Tri-screw extruder had better operative abilities and high productivity ratio than twin screw extruder in the aspect of material conveying and mixing.     

Functionalization of PVC by grafting of plasticizing group in a twin screw extruder

Substitution reactions are an appropriate way to attach chemical functions to polymer chains for improving properties and to diversify the application of polymer materials. The stereoselective substitution of chlorine atoms affords a useful way to plasticize polyvinychloride (PVC) by attaching appropriate plasticizing functions (ester group) such as isooctylthiosalicylate. Thus, the substitution of chlorine atoms of PVC by reactant bearing plasticizing groups was carried out in a continuous mixing apparatus such as a twin screw extruder. This continuous chemical engineering process taking place in the extruder is studied as the function of the residence time distribution (RTD) measured by a UV method. This function combined with the kinetics of the chemical reaction allows to define a new function G as the distribution of the extent of conversion by analogy with the RTD function.     

单螺杆挤出机压力-转速闭环控制系统传递函数研究

通过机理分析法求取了单螺杆挤出机的传递函数——机头压力与螺杆转速之间的动态关系，并通过系统辨识法对其结果进行了验证。结果表明单螺杆挤出机的传递函数是一个比例环节。利用此结果和闭环系统中其他环节的传递函数，给出了挤出机压力-转速闭环控制系统的数学模型。     

非啮合双螺杆挤出过程停留时间分布实验研究

通过对非啮合双螺杆挤出过程常规螺纹纹元件螺杆组合及引入轴向循环段的螺杆组合下的停留时间的实验研究，分析了轴向循环段的引入对非啮合双螺杆过程中停留时间及其分布的影响。     

Numerical nonisothermal flow analysis of non-Newtonian fluid in a nonintermeshing counter-rotating twin screw extruder

A simulation technique for nonisothermal flow analysis of non-Newtonian fluid in a nonintermeshing counter-rotating twin screw extruder was developed by modifying the flow analysis network (FAN) method. The local shear viscosity in the flow field was calculated by an iteration method combing the three types of mean shear rate functions. The modified Cross model and an Arrhenius-type function for temperature dependence were also introduced. Streamlines in the flow field are represented by computing the movements of fluid particles based on the flux fields. The computed residence time from the streamlines led us to solve the energy equation by replacing the coordinate system. The profiles of pressure, shear rate, shear viscosity, temperature, and residence time were simulated. The influence of operating and geometrical parameters on the screw characteristics are discussed. Further, residence time distribution (RTD), strain distribution function (SDF), and interfacial area growth are predicted from the computation of streamlines to analyze the mixing capabilities of the extruder.