Internal Mixers Research Articles

Simulation of Free Surface Flow in Partially Filled Internal Mixers

Abstract Internal mixers used in rubber processing and other industries are always partially filled. This results in the establishment of multiple random free surfaces in the flow field generated inside these mixers. Therefore successful mathematical modelling of internal mixing process depends on the development of efficient techniques for the reliable simulation of complex free surface flows. Various interface tracking and boundary capturing methods have been used in the past to model this kind of flow regimes. In particular, in recent years the well-known volume of fluid (VOF) method has been frequently used to model a variety of processes involving free surface and moving boundary flows. Both Eulerian and Lagrangian frameworks can be adopted in the VOF scheme to simulate free surface regimes. Under realistic flow conditions, however, the straightforward application of the technique in both frameworks may yield inaccurate results unless elaborate solution strategies are used to avoid errors. In many cases the use of such elaborate schemes requires excessive computational costs and effort or the solution scheme becomes complex and inflexible. In this paper we describe a relatively simple free surface tracking method based on the application of the VOF method in an Eulerian framework. In this scheme the flow field inside a partially filled internal mixer is treated as a two-phase system consisting of incompressible and compressible phases. The sections filled with the fluid which is being mixed are always regarded as an incompressible phase. The parts which are filled with air (or voids in some applications) form the second phase in the present two-phase flow analysis. The latter phase is treated as a compressible or an incompressible fluid (or pseudo fluid in the case of voids) depending on the value of the pressure calculated at each time step for the sections which contain it. We show that free surface flow of highly viscous fluids in partially filled internal mixers can be very successfully simulated by this method.

Modeling the transient flow of rubber compounds in the dispersive section of an internal mixer with slip-stick boundary conditions

The aim of this article is to describe the development of a mathematical model for the simulation of the flow of polymer melts inside internal mixers. The rheological behavior of the polymeric fluid is assumed to be described by the Carreau equation. The flow regime is considered to be non-isothermal. The set of the governing equations are solved using the finite element method for both steady-state and transient conditions. In the steady-state case, the flow equations are solved by the penalty method using the standard Galerkin technique. Petrov-Galerkin schemes based on both consistent and inconsistent streamline upwinding methods are employed to solve the energy equation and the obtained results are compared. Transient velocity, pressure, and stress fields are modeled using implicit θ method. In addition to implicit θ method, two versions of the Taylor-Galerkin approach are used to solve the transient energy equation. Slip-stick on the solid walls, encountered in the flow of viscous fluids, is incorporated in the model by the use of Navier's slip conditions. We describe two new methods for the inclusion of this condition in the working equation. Our simulations yield the velocity field, distribution of pressure, stress and temperature in the steady state and the variations of these parameters with respect to time under transient conditions. As an example of the applicability of the developed model, a typical mixing problem which involves convection of carbon black with flowing rubber in a domain representative of the section under the blade of a tangential rotor mixer is simulated. Concentration profiles of carbon black in the rubber matrix in this case is obtained by the solution of carbon mass continuity equation in conjunction with the flow model. This solution gives the distribution of filler volume fraction at different mixing times in the mixer. Comparison of the obtained results with the available experimental data gives some indication of the validity of the model. © 1997 John Wiley & Sons, Inc. Adv in Polym Techn 16: 45–68, 1997

FINITE ELEMENT MODELLING OF FREE SURFACE VISCOELASTIC FLOWS WITH PARTICULAR APPLICATION TO RUBBER MIXING

Internal mixers are used extensively in industry for mixing the components of rubber compounds. In these operations, in order to achieve effective mixing, the mixer chamber is always partially filled. This inevitably results in the appearance of multiple free surfaces in flow fields inside rubber mixer chambers. Mathematical modelling of such a flow regime is not a simple task and requires a great deal of effort. Traditional free surface flow-modelling techniques, which are mainly based on the use of volume-of-fluid or pseudo-density approaches in an Eulerian framework, are not flexible enough to cope with this problem. In this paper we describe a new method for the numerical modelling of free surface flows. In this method the pseudo-density approach is extended to a special Lagrangian framework along the trajectories of the fluid particles. We show that the developed scheme can very effectively simulate viscoelastic free surface flows encountered in rubber-mixing processes.

Rubber processing: technology, materials, and principles

Overview and Rubber Materials Flow Characteristics Internal Mixers and Mixing Continuous Mixers Extrusion: Screw Pumps Extrusion: Dies and Post Die Equipment Calendering Molding.

Predicting the effect of viscosity ratios on the mixing of polymer blends using the boundary element method

AbstractMixing or blending two or more fluids of different viscosities is an important and complex issue in the polymer industry. Simulating these types of processes leads to a better understanding of the flow phenomena that take place during mixing. The boundary element method is ideal to simulate mixing flows, because of the large deformations and moving boundary nature of internal batch mixers and extruders. This paper presents a boundary element simulation of the flow of multi‐viscous polymer blends inside extruders and internal mixers. In addition, the governing equations, boundary integrals, and their numerical implementation for creeping flows are presented. The simulation is used to predict the mixing quality of polymer blends in realistic mixing processes. A model describing the relationship of drop strain to matrix strain as a function of viscosity ratio is also presented. The flow simulation results are in good agreement with analytical and experimental results.

Simulating the flow of multi-domain polymer blends during mixing using BEM

Mixing or blending two or more fluids of different viscosity is an important and complex issue in the polymer industry. Simulating these types of processes leads to a better understanding of the flow phenomena that take place during mixing. The boundary element method is ideal to simulate mixing flows, due to the large deformations and moving boundary nature of internal batch mixers and extruders. This paper presents a boundary element simulation of the flow of multi-viscous polymer blends inside extrudersand internal mixers. In addition, the governing equations, boundary integrals and their numerical implementation for creeping flows are presented. The simulation is used to predict the mixing quality of polymer blends in realistic mixing processes. The flow simulation results are in good agreement with analytical and experimental results.

Comparison of Four-Flighted and Two-Flighted Internal Mixer Rotors Using Cylindrical Coordinate Hydrodynamic Lubrication Theory

Abstract Internal mixers have played a key role in the polymer industry. Internal mixers with four-flighted rotors are attracting more and more attention today. In this paper, we apply a new model based on cylindrical coordinate hydrodynamic lubrication theory for internal mixers to various rotor designs. Numerical techniques were used to carry out the calculations of the pressure field, mean flux field, and various mixing characteristic parameters. Comparisons were made for both four-flighted and two-flighted rotor designs. This was done assuming a fully filled mixing chamber. The simulation effort is important for the understanding of mixing mechanisms in internal mixers and to provide a basis for the rational design of internal mixers.

Simulation of 3-Dimensional Flow in Internal Mixers

Abstract The design of internal mixers for the rubber industry has traditionally been based on the basis of intuition rather than a knowledge of the fluid mechanics of motions in the internal mixer. In recent years, efforts have been made to numerically simulate the flow and mixing characteristics in internal mixers. The simulation effort is important for the understanding of mixing mechanisms in the internal mixer, and furthermore, to provide a basis for rational design. In this paper, we develop a new model based on cylindrical coordinate hydrodynamic lubrication theory for internal mixers. This allows full consideration of curvature in an internal mixer. Numerical techniques are used to carry out the calculations of the pressure field and flux field for various rotors described in the patent literature. This is done for a Newtonian fluid in a fully filled mixing chamber. This type of calculation is of key importance in the design of flight arrangements on internal mixer rotors.

Simulating Polymer Mixing Processes Using the Boundary Element Method

Abstract The mixing of plastic into filled and unfilled polymer blends has been an important issue in the polymer industry. Processing difficulties with these polymers have been encountered in the mixing quality as well as in the thermal degradation due to viscous heating. Mixing often occurs as an element of the processing step, e.g., inside single and twin screw extruders used in the fabrication of final parts or sheets, and inside internal mixers such as the Banbury type mixer. Quantifying the mixing inside an extruder or an internal mixer and predicting the thermal degradation due to viscous heating is an extremely difficult task. A better understanding of the mixing process and control of viscous heating will lead to optimal parts and may eventually allow us to increase the relative amount of fillers within the material. This paper presents a boundary element simulation of the flow of filled and unfilled polymer blends inside extruders and internal mixers. First, the general equations that govern such flows are shown. The boundary integral equation and the fundamental solutions are then formulated followed by the numerical implementation and logistics of the simulation. After the theoretical background is presented, a numerical example is given. The paper then shows how the simulation was used to analyze the flow inside a single screw extruder and internal batch mixers. Such a simulation can be used to eliminate some of the tedious trial-and-error tasks that are typically performed in the early stages of material synthesis and can also be used by manufacturers of mixing equipment when optimizing the geometries of cavities and mixing heads to achieve optimum mixing with reduced viscous heating. This research will significantly increase our knowledge of the behavior of filled and unfilled polymer blends and expand our understanding of the complex phenomena that take place during their mixing process.

Distributive Mixing Characteristics of Batch Internal Mixers

Abstract The distributive mixing characteristics of three internal mixers are examined: a Parrel BR Banbury (1.6 L), a Farrel F40 Banbury (40 L), and a Francis Shaw K1 Intermix (5.5 L). The former two machines have two-wing tangential rotors while the latter has intermeshing rotors. The distribution of sulfur in mixed batches of an EPDM compound and an SBR compound, as measured by curemeter tests on samples taken from random locations within each batch, is used to quantify distributive mixing. The dominant influence on sulfur distribution is total rotor revolutions and a maximum of 20 rotor revolutions is adequate for distribution of powder sulfur in each mixer. The effects on distribution of rotor speed, rubber compound rheology, and mixer size are insignificant.

Determining the components of mixing energy when preparing rubber compounds in instrumented internal mixers

AbstractAn experimental procedure has been developed to assess the various components of the mixing energy when preparing carbon black filled rubber compounds. A microprocessor based instrument developed for laboratory mixers allows the measurement and recording of all the relevant parameters of the operation, which are stored on diskette, loaded in a Lotus 123 spreadsheet, and further processed with the appropriate macro‐programs. Using compounds based either on ethylene‐propylene rubber, EPDM, or natural rubber, NR, and constant level of different carbon blacks, experiments were made using single pass mixing procedures, typical of factory processes. The position of the ram during the process has been identified as an important parameter of the process, and a method to correct the actual mixing energy by the effective batch volume has consequently been developed. With this correction and the data treatment described, it is possible to split the overall mixing energy into its various components, i.e., the energy to masticate the rubber alone, the energy to fragment and disperse the filler, and the extra mastication energy due to the presence of the filler. The energy to fragment and disperse various types of carbon black is dependent on the structure and the particle size of the filler considered. Depending on the compounding formulation, 65 to 80% of the total mixing energy is associated with the mastication of the pure gum, 15 to 20% accounts for the extra mastication energy due to the presence of the filler, and 5 to 15% is needed to fragment and disperse the filler.

Development of Internal-Mixer Technology for the Rubber Industry

Abstract The early rubber industry was largely based on mixing with two-roll mills. The coming of the pneumatic-tire industry associated with the rise in popularity of the automobile brought increasing production and large quantities of fine particles and poisonous vulcanization accelerators. This made necessary the introduction of internal mixers into the rubber industry by the second decade of the 20th century. This paper treats the development of internal mixer technology from its origins in the 19th century to the late 1980's, largely through critically following the patent literature. There seems to be no other critical review of the development of internal mixer technology, and this manuscript is unique. Briefly, the technology development we will describe is as follows: There were two conflicting design approaches, one based upon a single-rotor masticator devised by Thomas Hancock in the early 19th century and a second based upon two nonintermeshing counterrotating rotors which were championed by Paul Pfleiderer later in that century and manufactured by his firm, Werner and Pfleiderer. As late as the mid 1920's, machines based on both the single rotor and two nonintermeshing rotor designs competed with each other for the internal-mixer market. The insight, perseverance, intensity, and dedication of Fernley H. Banbury and the Birmingham Iron Foundry (later merged into Farrel-Birmingham) brought about the design which proved to be the paradigm of the industry. Innovation, however, continued in internal-mixer technology. The most striking new development of the post-Banbury period was the invention and application of intermeshing counter-rotating rotor mixers in 1934 by Rupert Cooke of Francis Shaw and Company. Werner and Pfleiderer developed and worked with many internal-mixer designs and in time began to manufacture both nonintermeshing- and intermeshing-rotor machines. In the 1950's and 1960's, Kobe Steel and Pomini began to manufacture internal mixers as Farrel-Birmingham licensees. This period also saw developments of nonintermeshing-rotor internal mixers. The basic Banbury design maintained its position and its manufacturer, Farrel-Birmingham (later Farrel), devised improvements of it. Innovations in the design were also made from the late 1970's by Kobe Steel, now operating independently. Pomini also began operating independently, manufacturing not only nonintermeshing machines but a unique intermeshing-rotor machine with variable clearance between the rotors. In recent years, we have seen the development of increasingly improved control systems for the internal mixer.

Scale-up Effect in Internal Mixers

Abstract In the development of a new polymer and a new compound, mixing equipment plays an important role. However, the properties of a compound tend to vary depending on the size and shape of the equipment used and a means to obtain the same compound by a small scale laboratory mixer as the one obtained by a large scale mixer has been longed for a long time. As a rubber compound is characterized by the physical properties, they are affected both by the dimensions and shape of the equipment and the mixing conditions. Recently, we developed a laboratory mixer generally following the designs of FH Banbury with exchangeable rotors and mixing chamber blocks which enable us to investigate the influences of the shape of equipment as well as the mixing conditions. In analysing rubber mixing, we found that the following factors should be taken into account, that is, unit-work which is the applied energy to the unit volume of the material during mixing, Mooney viscosity of the compound, bound rubber which is the amount of polymer unextractable from the compound by a solvent, and weight average molecular weight of polymer extractable by a solvent. If the values of the four factors are close enough for the two compounds obtained by different mixers of different size and shape, one may regard them as the same compounds. Furthermore, we experimentally measured the four factors for the compounds of typical formulations of three species of commercially available rubbers, that is, styrene butadiene rubber, ethylene propylene rubber and butadiene, and expressed the values of the factors as functions of mixing conditions and the parameters of rotor shapes by means of multiple regression analysis. Among the rotor parameters, the following showed significant effects: tip clearance, tip width, total bulkiness and wing overlap ratio. As for the mixing conditions, mixing time, rotor speed and mixing temperature were dominant. Using the functions obtained by the above mentioned method for the laboratory scale mixer, we tried to find the combinations of rotor shapes and mixing conditions that reproduced the compound mixed by large scale mixers. The optimum parameters of a laboratory mixer for the reproduction of the mixing of an industrial mixer were found to be larger rotor tip clearance, larger rotor tip width, larger wing overlap ratio, higher mixing temperature, and higher rotor speed than those of proportionally reduced dimensions and comparable conditions.

Non-Newtonian and Non-Isothermal Modeling of 3D-Flow in an Internal Mixer

Abstract In previous work we have applied hydrodynamic lubrication theory to simulate 3-dimensional flow of a polymer melt or elastomer in an internal mixer. That study presumed isothermal Newtonian flow in a flattened out mixing chamber. In the present paper, we take into consideration both non-Newtonian flow properties of the melt/elastomers and increase in temperature due to viscous dissipation heating. We consider the influence of non-Newtonian viscosity on flow patterns in the internal mixer. Viscous dissipation heating in the internal mixer is also modelled. It is shown that large scale internal mixers tend to operate adiabatically while small scale machines are close to isothermal. Temperature-time profiles are predicted for laboratory and large scale internal mixers.

Dynamic Modelling of Internal Mixers Using System Identification Techniques

Abstract Dynamical modelling techniques are presented that facilitate the derivation of transfer function models between key inputs and outputs of internal mixing processes. Tests to model the mastication of natural rubber in a Francis Shaw Intermix at two levels of fill-factor are described. The derived models will form the basis for closed-loop control strategies.

Simulation of flow in compounding machinery: Internal mixers and modular corotating intermeshing twin‐screw extruders

AbstractHydrodynamic lubrication theory has been applied to analyze flow in internal mixers and twin‐screw extruders. Fluid motions in mixing regions are interpreted as being due to coupling of drag flow and pressure gradients. Pressure fields and mean flow patterns have been computed. Distributive and dispersive mixing are interpreted in terms of computed fluid fluxes in the processing machinery.

On the Design of Internal Mixers

A number of variables affect the performance of an internal mixer. This has led, at least to some extent, to a state of the art as far as the design of internal mixers is concerned. The present contribution discusses some design issues in the light of some recent findings. Based on these findings a scale-up rule is sug gested.

Development of polymer blend phase morphology during processing

AbstractWe investigate the mechanics of formation of polymer blends both from the view of (i) the technology and flow characteristics in batch and continuous compounding machinery as well as from (ii) the mechanistic perspective of the formation and evolution of dispersed phases. Special attention is given to internal mixers and to intermeshing co‐rotating twin screw extruders. The role of interfacial tension and viscosity ratio in affecting phase morphology is described. We also discuss the development of polymer chain orientation in the different components of an immiscible polymer blend during processing.

Possibilities of formation or modification of polymers by means of chemical reactions during processing (polymer processing)

AbstractThe trends for polymeric engineering materials are marked by the search for defined thermomechanical, plastic‐elastic stability of dimension, and surface properties. This trend is caused by the demands for higher usage values of the polymers and more efficient processing technologies. The greatest chances are granted to the chemical modification and reactive compounding of known polymers to reach the aims of this development. Thermodynamically, most of the polymers are incompatible with each other and no sufficient disperse distribution is reached by only physical mixing. During the last 10 years a good compatibility at the interfaces has been found as one supposition and the influence of the viscosity of the polymer components and of the shear rate in the mixing machine as a further supposition to reach a fine‐dispersed distribution. Polymer composites with fibres and fillers are a further importent group of materials. The properties of composites are also determined by the interactions in the interfaces, by the dispersity of the fibres and fillers, and by the physical properties of the interfaces. Polymer‐analogous reactions, polymer blends, and polymer composites with and without low molecular reactants in the melt are decisively influenced by the parameters of the compounding machine. The quality of mixing, distribution of the residence time and of the shear rate, and the temperature profile of the reaction mixture are essential criterions for the course of the reaction. Continuous and quasi continuous technologies as, e. g., extruders and internal mixers are preferred. The lecture will deal with the present state and technical possibilities. Polymer syntheses in screw extruders are a new trend for the future. All these possibilities offer prospective chances of development.

A Dispersive Mixing Testing Apparatus

Abstract The dispersion process of agglomerated soldis, such as carbon-black, into rubbers and plastics is still not understood to a satisfactory extent. Dispersive mixing is commonly carried out in roll mills, internal mixers and continuous intensive mixers. It is accomplished by repeated passage of the mixture, through converging-tight clearance high stress regions, of the mixers. The key design and operational variables are the geometry of this region, the stress history of the fluid element, and the passage distribution function. A laboratory apparatus was designed and built to enable a systematic study of the effect of these variables on mixing. The apparatus, and experimental results are described. Results verify that the number of passages is a dominant variable in dispersive mixing, and proves the utility of the apparatus to study the dispersive mixing process.