Volume 5, Issue 3

A mathematical model for simulating flow in batch and continuous twin rotor mixers and extruders is presented. The model is a lumped parameter model based on the Flow Analysis Network (FAN) method.

An attempt has been made to predict flow behavior of the rub bery material in an internal mixer by means of finite element analysis. For the convenience of analysis, a simplified model for the mixer and some assumptions were introduced. The model consists of a circular cylinder and a rotor with uniform cross sectional shape along the axis which rotates around the axis located at the center of the cylinder. Rubbery material fills the void between the cylinder and the rotor. The assumptions are: the material is a power law liquid, the material is incompressible, and the viscosity is large enough to allow laminar flow.

A modified laboratory mixer (Banbury-type; batch volume is 250 cm 3 ) with transparent front windows was used to observe the flow of silicone rubber. A pair of specially designed rotors was used in order to estimate the influence of rotor design upon the behavior of silicone rubber. Five parameters were picked up in designing the rotors. The rotor consists of a number of thin plates of identical shape. The plates are designed so that they can construct a double-winged rotor. By assembling the plates properly, the angles of twist of longer and shorter wings and lengths of wings can be varied, i. e. the overlap ratio of longer and shorter wings can be controlled. The rotor tip clearance is also variable. Batch homogenization times were measured with torque and unit-work for all experiments, observing the flow of silicone rubber through the front window at the same time. The torque and unit-work increase as rotor tip clearance decreased and as overlap ratio of wings increased. The twist angle of wings had little influence on torque and unit-work. The batch homogenization time became shorter with increases of rotor tip clearance, overlap ratio of wings and twist angle of wings and with the decrease of rotational speed ratio.

A fluid dynamics analysis package – FIDAP using the finite element method was implemented to simulate the flow patterns in a Banbury mixer. A number of different geometries were selected to represent the dynamic motion of the rotors during a repeated mixing cycle. The simulation results were then used to characterize the flow field in terms of a parameter quantifying the elongational flow components. The influence of design and processing variables on the flow characteristics as well as on the average shear rate were analyzed.

Correlation between state of dispersion and mechanical properties is obtained and failure mechanisms from falling weight impact tests are discussed. The state of dispersion is characterized for calcium carbonate filled polypropylene model composites by using a scanning electron microscope. A dispersion index is defined in terms of the fraction of agglomerates of the filler remained in the composites. Improvement of dispersion uplifts tensile strength and more prominently falling weight impact strength. It is pointed out that an initial failure in the falling weight impact test rises at the agglomerate existing near the loading point. Falling weight impact strength is found to be dependent upon the distance from loading point to failure initiation point where the agglomerate exists. This explains the dependency of impact strength on the state of dispersion and a large sample deviation often observed in the falling weight impact test.

An improved form of the numerical FAN method of Tadmor, Broyer, and Gutfinger for solving hydrodynamic lubrication theory problems in flow through molds and dies has been developed. The new procedure takes into consideration transverse shearing in two rather than only one direction. It is also applied to the class of problems considered by Szydlowski, Brzoskowski, and White which involved applying this technique to situations when one surface is stationary and the other moves, such as in screw sections of extruders.

The feasibility of the continuous and direct conversion from latex to wet crumb through the coagulation process in an extruder has been demonstrated through this work. The coagulation efficiency in the extruder has been largely governed by temperature. The maximum rate of increase of the first and the second moments of the particle size distribution of the coagulated latex occur in the neighborhood of the polymer glass transition temperature. The particle densities showed no longer a one-to-one relationship to the specific surface typical of the batch coagulation experiments, as the material coagulated in the extruder did not reach the same degree of equilibrium. Although the basic trends remained the same as in the batch coagulation experiments, the addition of residence time distribution, inherently associated with the extruder operation, introduced some significant changes into the coagulation process.

The flow of Newtonian fluids in a (modular) tangential counter-rotating twin screw extruder is analyzed using hydrodynamic lubrication theory and a modified Flow Analysis Network Method. The flow in systems with (i) forward puming screws and (ii) backward pumping screw pairs is investigated. For forward pumping screw elements we analyze the extent of back flow between the screws for different levels of screw flight staggering. The ratio of backflow to net flow is the highest when the flight staggering angle is 180°. The computed flow fields of backward pumping screw elements shows backward helical flow along the screw channel and forward flow between the screws. Screw characteristic curves of backward pumping screw elements are shifted by a factor of 2 Δp/L Q=0 from the forward pumping screw characteristic curves. The flow and pumping characteristics of modular systems have also been considered.

This paper presents a mathematical-physical model for tightly intermeshing co-rotating twin screw extruders which describes the throughput and pressure characteristics of these extruders in the sections filled with molten plastic. With the equations that have been compiled, it is possible to calculate pressure profiles and back-pressure lengths for individual sections of isothermal and two-dimensional flow with non-Newtonian melts, making allowance for the screw geometry and for the parameters of relevance to the process. A comparison of the results supplied by the formulated theory and those obtained from the experiment shows that good computed results are obtained for various materials and different points of operation, although no allowance is made for the leakage flow that occurs in reality.