Analysis of Polymer Flow in a Stepped Parallel Bore Coating Unit by Power Law

Polymer flow for a continuum coating in a stepped parallel bore pressure unit was simulated where the flow is dependent on the wire velocity, geometry of the unit, and the properties of the polymer melt. In a hydrodynamic wire coating process the pulling action of the solid continuum through a circular cross-section stepped parallel or conical orifice filled with polymer melt generates hydrodynamic pressure as well as polymer coating on the continuum. In this paper a mathematical model was developed for the pressure distribution within a stepped parallel bore pressure unit. Results were also obtained for different wire speeds in terms of the changes in viscosity, shear rate, shear stress, and drawing force within the unit. Theoretical hydrodynamic pressure and drawing force results have been compared with the experimental results from literature.     

Studies on wire coating extrusion. I. The rheology of wire coating extrusion

Wire coating extrusion was studied, both experimentally and theoretically, using a pressure-type die. For the experimental study, a wire coating apparatus of laboratory scale was constructed, consisting of a pay-off device, extruder, cross-head and pressure-type die, cooling trough, and take-up device. The materials used were low- and high-density polyethylenes and thermoplastic rubber. The following measurements were taken during the experiments: (1) the axial pressure profiles in the die, (2) melt flow rate, and (3) take-up speed. The measurements were then used to determine the effect of the rheological properties of the polymers on the performance of the wire coating operation. It was found that a reduction in axial pressure gradient and a reduction in the recoverable elastic strain of a molten polymer at the die exit can be realized as the speed of the wire is increased. For the theoretical study, using a power-law model, the equations of motion were solved numerically to predict the volumetric flow rate as functions of the pressure gradient in the die and the rheological properties of the polymer being extruded. Solution of the system equations permitted us to predict the velocity profile and shear stress distributions of a molten polymer inside a pressure-type wire coating die.     

Studies on wire coating extrusion. II. The rheology of wire coating coextrusion

An experimental and theoretical study of wire coating coextrusion through a pressure-type die was carried out. For the experimental study, the wire coating apparatus employed was the same as that described in Part I of this series (14), except for the newly constructed coextrusion die. The die was provided with three melt pressure transducers along the axial direction, which permitted us to determine the pressure gradient in the die. It was found that a reduction in pressure gradient was realized when a lower viscosity polymer was coextruded with a high viscosity polymer. The materials used for the coextrusion were combinations of low-density polyethylene, high-density polyethylene, polystyrene, and two different commercially available thermoplastic rubbers (UniRoyal TPR-1900 and Shell Kraton G 2701). The use of a high shrinking (crystalline) polymer inside a low shrinking (amorphous) polymer was found to give rise to distorted coatings (non-circular cross section of the coated wire). The interface between the coextruded layers was examined under a magnifying lens, and it was found that under certain processing conditions, the interface was highly irregular. Experimental correlations were obtained to explain the onset of an unstable interface in terms of the rheological properties of the individual components being coextruded, and of the processing variables. It was found that interfacial instability occurs when the shear stress and the viscosity ratio (also elasticity ratio) of the two components at the interface exceed certain critical values. For the theoretical study, using a power-law model, the equations of motion were solved numerically to predict the volumetric flow rate as functions of the pressure gradient in the die and the rheological properties of the polymers being coextruded. Solution of the system of equations permitted us to predict the velocity profile and shear stress distributions of two molten polymers inside a pressure-type wire coating coextrusion die. Comparisons were made between the experimental and theoretically predicted volumetric flow rates. The comparison was found to be reasonably good with certain systems. The discrepancy between the experimentally obtained and the theoretically predicted volumetric flow rates was attributed to interface migration and interfacial instability.     

Stability of buoyancy-driven convection in directional solidification of a binary melt

In directional solidification, compositional convection can be driven by an unstable density gradient in the melt. In this paper convective instabilities in liquid and mushy layers during solidification of a horizontal binary melt are analyzed by using the propagation theory. The self-similar stability equations are used to examine the boundary-mode and mushy-layer-mode of convection. The effects of velocity conditions at the liquid-mush interface on the onset of convection are discussed. The critical Darcy-Rayleigh number for the convection in the mushy layer decreases with increasing the temperature of a cooled boundary. This paper is presented on the occasion of professor Chang Kyun Choi’s retirement from the school of chemical and biological engineering of Seoul National University.     

A theoretical analysis of non-isothermal flow in wire-coating co-extrusion dies

A theoretical study of non-isothermal superimposed flow of two polymer melts in wire coating co-extrusion dies has been carried out. Numerical methods have been employed to solve the coupled momentum- and energy-balance equations. Various combinations of three polymers—namely, high density polyethylene (HDPE), polystyrene (PS) and low density polyethylene (LDPE) have been studied and least squares curve fitted quadratic polynomials have been used for constitutive equations for all three polymers in non-Newtonian high shear rate regions. A multitude of thermal and mechanical boundary conditions can be treated by this algorithm. It was found that temperature and velocity profiles in the die depend significantly on the arrangement of the polymers. Maximum temperature rise has been noted to increase sharply with wire velocity but it can be reduced by increasing the die radius. When the thickness of the outer layer is increased from zero, the shear stress at the wall undergoes a dramatic change (if the viscosities of the polymers are different) at small values of the flow rate ratio and it reaches an asymptotic value at large values of flow rate ratio. It was also found that viscosity ratio at the interface can be reduced by changing the initial temperatures of the liquids. It was observed in some cases that large errors in the calculation of rheological and thermal variables for this problem can be made if temperature rise due to viscous dissipation is not considered.     

A level set based immersed boundary method for simulation of non-isothermal viscoelastic melt filling process

In this work, the polymer melt filling process is simulated by using a coupled finite volume and level-set based immersed boundary (LS-IB) method. Firstly, based on a shape level set (LS) function to represent the mold boundary, a LS-IB method is developed to model the complex mold walls. Then the non-isothermal melt filling process is simulated based on non-Newtonian viscoelastic equations with differ-ent Reynolds numbers in a circular cavity with a solid core, and the effects of Reynolds number on the flow patterns of polymer melt are presented and compared with each other. And then for a true polymer melt with a small Reynolds number that varies with melt viscosity, the moving interface, the temperature distributions and the molecular deformation are shown and analyzed in detail. At last, as a commonly used application case, a socket cavity with seven inserts is investigated. The corresponding physical quantities, such as the melt velocity, molecular deformation, normal stresses, first normal stress differ-ence, temperature distributions and frozen layer are analyzed and discussed. The results could provide some predictions and guidance for the polymer processing industry.     

The effect of melt compressibility on a high-speed wire-coating process

The effects of melt compressibility on a wire-coating process have been investigated, assuming that the compressible behavior of a polymeric melt obeys the Spencer-Gilmore equation of state. The compressible model is distinctly different from the incompressible model in two ways: (1) it has substantially lower pressure build-up within the die, and (2) the location of the maximum velocity is closer to the traveling wire position. As a result, the velocity profile within the die may change from a parabolic shape to a shape somewhat similar to that observed in a drag-flow case; and the shear stress generated by the fluid on the moving wire is no longer constant. Calculations indicate that the effect of melt compressibility during wire coming may not be neglected if the wire speed Ls greater than 50 cm/s (100 ft/min). In addition, the relationships between processing parameters and product coating thickness for both compressible and incompressible fluids are quite different.     

Dynamics of air drawing in the melt blowing of nonwovens from isotactic polypropylene by computer modeling

The dynamics of stationary air drawing in the melt blowing of nonwovens were determined on the basis of a single‐filament model in a thin‐filament approximation that accounts for polymer viscoelasticity, heat of viscous friction in the polymer bulk, and surface energy. Predetermined distributions of the air velocity and temperature along the melt blowing axis were assumed. Axial profiles of the polymer velocity, temperature, elongation rate, filament diameter, tensile stress, and extrapressure were computed for the melt blowing of isotactic polypropylene. The effects of the air‐jet velocity, die‐to‐collector distance, and polymer molecular weight are discussed. We predicted that the filament attenuation and velocity at the collector located in the air‐drawing zone would increase with increasing die‐to‐collector distance. The air‐drawing zone was shorter for higher air velocities and lower molecular weights. No online crystallization was predicted before the achievement of the collector, and melt bonding of the filament in the web should have occurred during cooling on the collector, accompanied by spherulitic crystallization. Significant online extrapressure in the filament was predicted in the case of supersonic air jets as resulting from polymer viscoelasticity, which could have led to longitudinal splitting of the polymer into subfilaments. © 2010 Wiley Periodicals, Inc. J Appl Polym Sci, 2011     

Hydrodynamic Pressure Distribution Within a Complex Geometry Coating Unit

When a wire is pulled through a stepped parallel or conical gap, which is filled with a viscous fluid, a very high pressure is generated. The pressure is termed hydrodynamic pressure and can facilitate the coating of wire. In this paper analytical equations have been developed for predicting the pressure distribution within a combined unit, taking account of the changes in the viscosity and the shear rate of the polymer melt during the coating process. A finite difference type approach has been employed to obtain solutions for these equations. The change in the viscosity due to variations in pressure within the unit as well as the change in shear rate in the tapered part due to change in gap between the wire and the unit have been taken into account. Theoretical results are obtained for different wire speeds in terms of the pressure distributions within the unit. These results are compared with experimental results obtained from the literature.     

微孔塑料挤出快速降压口模的数值模拟

应用FLUENT软件对微孔塑料连续挤出成型过程中的快速降压口模内的熔体流动进行数值模拟,经过简化及边界处理,分别研究了微孔塑料在不同CO2浓度、不同流量和不同温度条件下微孔塑料连续挤出过程中快速降压口模中的压力和速度分布情况。结果表明:压力降随熔体温度和CO2浓度的升高而降低,随熔体流量的升高而增大。导管中的速度也几乎均匀分布,在毛细管人口处中心线速度突然增大。熔体流量和CO2浓度的变化对口模压降和口模速度的影响比较大,而温度的变化对其影响要小得多。     

Finite element analysis of wire coating

A general-purpose finite element program has been used to simulate the flow of polymers through wire-coating dies. The analysis includes Newtonian and power-law fluids. The effect of normal stresses was examined through a simple viscoelastic constitutive equation, Nonisothermal wire coating was studied to obtain the temperature field within the melt. The effect of a slip condition at the solid boundaries was also examined. The determination of the coating melt free surface was carried out through an iterative procedure. The finite element solution provides details about the existence and extent of recirculation regions, about hot spots due to viscous dissipation, and also captures the stress singularities present at the impact of the melt with the wire and at the exit from the die. Pressure distribution, maximum temperature rise, haul-off wire tension, maximum wire tension, and stresses at the wire surface and die wall are also presented.     

Surface-Tension-Driven Flow in a Glass Melt

Motion driven by surface tension gradients was observed in a vertical capillary liquid bridge geometry in a sodium borate melt. The surface tension gradients were introduced by maintaining a temperature gradient on the free melt surface. The flow velocities at the free surface of the melt, which were measured using a tracer technique, were found to be proportional to the applied temperature difference and inversely proportional to the melt viscosity. The experimentally observed velocities were in reasonable accord with predictions from a theoretical model of the system.     

An optimization method with experimental validation for the design of extrusion wire coating dies for a range of different materials and operating conditions

The objective of this article is to determine a wire coating‐hanger melt distributor geometry to ensure a homogenous exit velocity distribution that will best accommodate a wide material range and multiple operating conditions (i.e., die wall temperature and flow rate change). The computational approach incorporates finite element (FE) analysis to evaluate the performance of a die design and includes a nonlinear constrained optimization algorithm based on the Kriging interpolation and sequential quadratic programming algorithm to update the die geometry. Two optimization problems are then solved, and the best solution is taken into account to manufacture the optimal distributor. The Taguchi method is used to investigate the effect of the operating conditions, i.e., melt and die wall temperature, flow rate and material change, on the velocity distribution for the optimal die. In the example chosen, the wire coating die geometry is optimized by taking into account the geometrical limitations imposed by the tool geometry. Finally, the FE analysis and optimization results are validated by comparison with the experimental data obtained with the optimal die. The purpose of the experiments described below is to investigate the effect of material change. POLYM. ENG. SCI., 2012. © 2012 Society of Plastics Engineers     

充模过程的Level Set两相流模拟

采用Level Set两相流方法模拟了熔体充模过程,避免了处理复杂的边界以及用Ghost方法将熔体内的速度值外推到熔体外的情况。分别对型腔水平中面与垂直中面的充模过程进行了模拟。讨论了不同注射速度、不同注射口数量以及不同Reynolds数对充模过程的影响,得出了不同时刻各种情况下熔体界面的位置与充模过程刚结束时型腔内的压力分布,分析了熔体在型腔内运动的不同阶段的特点及形成不同阶段的原因。结果表明,在注射口宽度与型腔宽度相差不大的情况下,如果采用中低速充模,则整个充模运动过程以比较平稳的扩展性运动为主,充模较完全,熔体不发生破裂,制件效果较好。充模速度越大,熔体达到平稳流动的时间越短,充模过程越短。数值模拟结果与实验结果一致,同时表明Level Set两相流方法在求解拓扑性质发生较大变化问题时具有很大的优势。     

Network numerical simulation of two-dimensional nonlinear micropolar hydrodynamics in a Darcian porous medium

The two-dimensional steady-state boundary layer flow of an incompressible micropolar fluid in a Darcian porous medium is studied theoretically and computationally. The governing parabolic partial differential equations are reduced to dimensionless form by using a set of transformations, under appropriate boundary conditions. A network simulation method (NSM) solution is presented. Translational velocities (U, V) are found to increase with a rise in Darcy number (Da) and to increase and decrease, respectively, with a rise in micropolar parameter (Er), i.e., Eringen number (ratio of micropolar vortex viscosity to Newtonian viscosity). Micro-rotation is increased with increasing Er and Da values. Translational velocity gradient, ∂U/∂Y and micro-rotation gradient, ∂Ω/∂Y both increase with Darcy number; however, they are both found to decrease with increasing micropolar parameter, Er. The present study finds applications in polymer flows in filtration systems, chemical engineering, biorheology of porous tissue and plastic sheet processing.     

Wire Melt Electrospinning of Thin Polymeric Fibers via Strong Electrostatic Field Gradients

Here, a novel melt electrospinning method to produce few‐micron and nanometer thick fibers is presented, in which a polymer‐coated wire with a sharp tip is used as the polymer source. The polymer coating is melted via Joule heating of the source wire and extracted toward the target via electrostatic forces. The high viscosity and low charge density of polymer melts lower their stretchability in melt. The method relies on confining the Taylor cone and reducing initial jet diameter via concentrated electrostatic fields as a means to reduce the diameter of fibers. As a result, the initial jet diameter and the final fiber diameter are reduced by an order of magnitude of three to ten times, respectively, using wire melt electrospinning compared to syringe‐ and edge‐based electrospinning. The fiber diameter melt electrospun via this novel method is 1.0 ± 0.9 µm, considerably thinner than conventional melt electrospinning techniques. The generation of thin fibers are explained in terms of the electrostatic field around the wire tip, as obtained from finite element analysis (FEA), which controls the size and shape of the melt electrospun jet.     

Effect of viscous dissipation on the temperature of the polymer during injection molding filling

During injection molding, viscous dissipation changes the temperature distribution by playing the role of an energy source, which affects heat transfer rates. Understanding the effect of the viscous dissipation assists the designing of the cooling system in injection molding process. In this article, the effect of the viscous dissipation on the temperature distribution throughout a rectangular channel for different polymers at different inlet velocities and temperatures is studied. A cross type rheological model depending on the temperature and pressure is assumed for polymer materials polystyrene (PS) and polypropylene (PP). The evolution of the flow velocity inside the channel is presented. The quantity of heat added due to viscous dissipation to the polymer is also calculated up to different positions through the channel. A numerical finite volume code for the simulation of polymer melt flow in a channel is used and a validation of this numerical code is presented. POLYM. ENG. SCI., 2008. © 2008 Society of Plastics Engineers.     

矩形薄腔中聚合物熔体非等温注气充填的数值模拟

采用五参数Cross粘度模型,利用有限元和控制体积法对矩形薄腔中聚合物熔体非等温注气充填过程中不同时刻的气泡边界、熔体前沿、熔体压力场、温度场和速度场等进行了数值模拟,结果表明:气泡主体边界平行于模壁方向生长,其前沿总是先向中心线附近移动,再向中心线两边移动;熔体压力在气泡周围某一区域内保持不变且等于气压;对于充模时间很短的情况,除气泡附近外,温度在各处相差不大。     

基于浓度/速度场测量的吸收过程液相传质系数

针对矩形流道内气、液流体的并流吸收传质过程,分别应用实时激光全息干涉术和激光多普勒速度仪对不同气、液流速下液相内近界面浓度分布与速度分布进行了实验观测.结果表明,边界层内浓度分布呈指数下降,流速越大梯度越陡,且速度边界层厚度要大于浓度边界层厚度.建立了通过物料衡算求算液相传质系数的方法.得到了不同条件下平均液相传质系数,并与Whiteman’s双膜理论的计算结果进行了比较.     

Melt spinning and characterization of hollow fibers from poly(4-methyl-1-pentene)

In this article, the melt spinning behavior of poly(4-methyl-1-pentene) (PMP) hollow fibers (HF) is examined. The melt spinning trials are carried out on a pilot scale melt spinning plant with different settings while a 10-hole 2c-shaped spinneret is used. It is found that the winding speed mainly affects the outer fiber diameter. The influence of different melt spinning parameters is investigated, in particular temperatures, take-up velocities, and the use of quench air. For this purpose, the shape and crystalline structure of the fibers are analyzed using a light microscope, a scanning electron microscope, and wide-angle X-ray scattering. The shape of the fibers is mainly influenced by the temperature settings in the melt spinning process. As a reasonable lower limit, a melt spinning temperature of 280°C is identified. Concerning the crystallinity, a saturation going along with a slight reduction of the polymer chain orientation is observed at elevated take-up velocities.