An extrusion process for manufacturing microcellular plastics is presented. In the past, microcellular structures have been produced in batch processes by using a thermodynamic instability of a polymer/gas system. In order to utilize such a thermodynamic instability in a continuous extrusion process, a large amount of gas must be dissolved quickly in a molten plastic flowing in the machine, and a rapid drop in the gas solubility must be induced in the flowing polymer/gas solution. Since the solubility of a gas in a polymer is a sensitive function of pressure, a thermodynamic instability for producing a microcellular structure can be induced by rapidly lowering the pressure. This paper presents a means for continuously forming the polymer/gas solution at an industrial processing rate and a means of nucleating microcells in the polymer/gas solution using a nozzle. Finally, a process model for controlling the cell morphology is presented by identifying the key parameters that control microcellular foaming in a continuous process. The experimental results agree with theoretical analyses, confirming the fact that the processing pressure strongly affects the microcellular foaming process through its effects on the amount of gas dissolved in the polymer and the magnitude of the pressure drop in the nucleation device.

Filamentary extrusion of microcellular polymers using a rapid decompressive element

Publisher Summary Mixing and dispersion of viscous fluids—blending in the polymer processing literature—is the result of complex interaction between flow and events occurring at drop length-scales: breakup, coalescence, and hydrodynamic interactions. Similarly, mixing and dispersion of powdered solids in viscous liquids is the result of complex interaction between flow and events—erosion, fragmentation and aggregation—occurring at agglomerate length scales. Important applications of these processes include the compounding of molten polymers and the dispersion of fine particles in polymer melts. The modeling of mixing processes has undergone exciting progress in the past few years. Computations have reached maturity and exploitation of concepts and results in the context of realistic devices is now a reality. However, the advances have been restricted to single-phase fluids. Further research is needed to gain advancements in the dispersion of solids and liquids in viscous flows.

Mixing and Dispersion of Viscous Liquids and Powdered Solids

Numerical characterization of low Reynolds number flow in the Kenics static mixer

The development of multiphase liquid-liquid morphologies during mixing at small Reynolds numbers has been modeled. The mixing process is divided into (i) stretching of dispersed drops. (ii) breakup of the liquid threads formed, and (iii) coalescence of the final droplets upon collision. Rules and criteria of the distinct processes are presented and combined to a general 2-zone mixing model simplifying the flow field into a sequence of alternating “strong and weak zones.” In a “strong zone,” dispersed drops and threads are stretched unless their radius is too small; meanwhile, the stretching threads might break up into droplets. In the subsequent “weak zone,” the remaining threads may disintegrate while any drops present may coalesce. After passing a number of zones, stretching, breakup, and coalescence lead to a dynamic equilibrium that could be considered as the “final” morphology. Using the 2-zone mixing model, the influence of material parameters and processing conditions on the morphology has been studied. Interestingly, increasing either viscosity (dispersed or continuous phase) yields a finer morphology due to the delay of thread breakup, allowing for further stretching and suppression of coalescence.

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Dynamics of liquid-liquid mixing : a 2-zone model

Previous experimental studies have revealed that the mixing efficiencies of widely used continuous processors such as the single and twin screw extruders depend on the types of screw elements, which are utilized. It is generally recognized that the basic single screw extruder and the fully-fighted sections of the fully-intermeshing co-rotating twin screw extruders are not efficient mixers, in contrast to the specialized mixing elements such as the kneading discs used in co-rotating twin screw extruders. However, no simulation techniques were available to characterize quantitatively and rigorously the mixing efficiencies of continuous processors. In this study, we have solved the three-dimensional equations of conservation of mass and momentum, and utilized various tools of dynamics to analyze the mixing occurring in single and co-rotating twin screw extruders. It is shown that simulation methods can indeed capture the relative differences in the mixing mechanisms of continuous processors like the single and twin screw extruders. The ability to distinguish quantitatively between the distributive mixing capabilities of various continuous processors should facilitate numerical testing of new continuous mixer designs, optimization of operating conditions and geometries of existing mixers and the material-specific design of new mixers.

Mechanisms of mixing in single and co-rotating twin screw extruders

An expression is derived for the increase in mixedness due to an arbitrary deformation of a material. For mixtures having initial orientation this expression is a function of the principal values of the strain tensor and the orientation of the fluid. For mixtures without initial orientation, this expression is simply a function of the principal values of the strain tensor. Mixing in pure shear, simple shear, and pure elongation is determined. The rate of mixing for each of these deformations in steady flow is derived. A comparison of these rates of mixing with the energy consumed in the deformation shows that simple shear flow is a very inefficient way to accomplish mixing. For the example cited, five orders of magnitude greater energy is required to accomplish mixing in shear flow as opposed to extensional flows.

Theory of laminar mixing

A discussion of the effect of deformation on mixing leads to reorientation of fluid interfaces as a proposed mechanism for special “mixing sections” in single screw extruders. Based on the kinematics of mixing it is shown how a mixing section can greatly decrease the amount of work necessary to accomplish extensive mixing through orienting the fluid more favorably for mixing by subsequent shear. Mathematical development quantitatively describes favored configurations of mixing sections. An upper bound for the mixing performance of a simple model of an extruder with special sections is shown to be similar to turbulent mixing. Based on this theory the key actions of the special sections are identified.

Theory of mixing sections in single screw extruders

Consideration of the basic equation for mixing in plane strain laminar flow shows that mixing can proceed much more rapidly than has been commonly accepted. While linear rates of mixing have been predicted previously, exponential rates of mixing are possible. An upper bound for, the rate of mixing in plane strain laminar flow is shown to be an exponential. The geometry of the flow which produces this most rapid mixing is shown to be plane strain extensional flow, sometimes called pure shear flow, with all interfaces aligned normally to the smallest principle axis of the deformation.

An upper bound on the performance of plane strain mixers

Simple quantitative mixing experiments in well-defined deformations clearly demonstrate the validity of previously derived equations relating deformation and mixing. A simple mixture of black and white polyethylene is studied by direct measure of striation thickness. The well-known linear relationship in simple shear is demonstrated. By using a simple method for uniform reorientation, the second power relationship in shear once interrupted, the third power relationship in shear twice interrupted and the fourth power relationship in shear interrupted three times are demonstrated. In uniaxial elongational mixing of a silicone fluid, exponential dependence of mixing on strain is demonstrated.

Lewis Erwin

Papers

Theory of laminar mixing

Theory of mixing sections in single screw extruders

An upper bound on the performance of plane strain mixers

Experiments in extensive mixing in laminar flow. I. Simple illustrations