Porous Hydrogels: Present Challenges and Future Opportunities

In this feature article, we critically review the physical properties of porous hydrogels and their production methods. Our main focus is nondense hydrogels that have physical pores besides the space available between adjacent cross-links in the polymer network. After reviewing theories on the kinetics of swelling, equilibrium swelling, the structure-stiffness relationship, and solute diffusion in dense hydrogels, we propose future directions to develop models for porous hydrogels. The aim is to show how porous hydrogels can be designed and produced for studies leading to the modeling of physical properties. Additionally, different methods that are used for making hydrogels with physically incorporated pores are briefly reviewed while discussing the potentials, challenges, and future directions for each method. Among kinetic methods, we discuss bubble generation approaches including reactions, gas injection, phase separation, electrospinning, and freeze-drying. Templating approaches discussed are solid-phase, self-assembled amphiphiles, emulsion, and foam methods.

Characterization of Distributive Mixing in Polymer Processing Equipment using Renyi Entropies

A new method for characterization of distributive mixing in processing equipment, based on Renyi entropies, was developed. This method was applied to a twin-flight single screw extruder, in which tracer positions were determined through computer simulations of the flow field. The various entropies were calculated using particle concentrations in equal area domains of the mixer. Renyi entropies, which are function of a parameter β, were calculated for extruders of different lengths. We discuss the merit of using Renyi entropies for different values of β by pointing to the different mixing characteristics they probe. The relative Renyi entropy varies between 0 and 1 and represents a measure of distributive mixing quality, with 1 corresponding to perfect mixing and 0 corresponding to poorest mixing. We compare this new method of distributive mixing characterization to traditional ones based on the concepts of Scale and Intensity of Segregation, and the calculations based on Pairwise Correlations and Correlation Sums. The results show good agreement between the relative Renyi entropy and the traditional methods. Other advantages of the Renyi entropy such as reduced calculation time and geometric independence are discussed. For the case of a twin-flight single screw extruder, it is shown that a longer extruder is not necessarily more beneficial to distributive mixing.

Porous hollow fibers with controllable structures templated from high internal phase emulsions

A technique to fabricate hollow fibers with porous walls via templating from high internal phase emulsions (HIPEs) has been demonstrated. This technique provides an environmentally friendly process alternative to conventional methods for hollow-fiber productions that typically use organic solvents. HIPEs containing acrylate monomers were extruded into an aqueous curing bath. Osmotic pressure effects, manipulated through differences in salt concentration between the curing bath and the aqueous phase within the HIPE were used to control the hollow structures of polyHIPE fibers. The technique was used to produce porous fibers (with millimeter-scale diameters and micronscale pores) having a hollow core (with a diameter of 50%-75% of the fiber diameter). Two potential applications of the hollow fibers were demonstrated. In vitro drug release studies using these hollow fibers show a controlled release profile that is consistent with the microstructure of the porous fiber wall. In addition, the presence of pores in the walls of polyHIPE fibers also enable size-selective loading and separation of functional materials from an external suspension.

Catalyst-Free Mechanochemical Recycling of Biobased Epoxy with Cellulose Nanocrystals

Mechanochemical vitrimerization, as a method to recycle cross-linked thermosets by converting the permanent network into a recyclable and reprocessable vitrimer network, inevitably requires a catalyst to accelerate the bond exchange reactions. Here, we demonstrate a catalyst-free approach to achieve the recycling of a cross-linked biobased epoxy into high-performance nanocomposites with cellulose nanocrystals (CNCs). CNCs provide abundant free hydroxyl groups to promote the transesterification exchange reactions while also acting as reinforcing fillers for the resultant nanocomposites. This technique introduces an effective way to fabricate high-performance thermoset nanocomposites based on recycled polymers in an ecofriendly way, promoting the recycle and reuse of thermosets as sustainable nanocomposites for different applications.

Cellulose Nanocrystals: Accelerator and Reinforcing Filler for Epoxy Vitrimerization

The novel vitrimerization concept of converting permanently cross-linked networks of thermoset polymers into dynamic exchangeable networks often relies on transesterification reactions. Transesterification exchange reactions, for example, in epoxy vitrimers, are usually contingent on equivalent ratios of hydroxyl to ester groups and large amounts of catalysts to achieve proper dynamic exchange capability. In general, postconsumer epoxy cured with anhydrides contains very few hydroxyl groups in the network, and it is challenging to convert it into efficient dynamic networks by vitrimerization. Here, we demonstrate that introducing cellulose nanocrystals as feedstock of external hydroxyl groups in the mechanochemical vitrimerization process could improve the exchange reaction rate as well as the thermomechanical properties of the vitrimerized epoxy. This work offers an effective way to recycle and reprocess postconsumer epoxy/anhydride waste with inherent low ratios of hydroxyl to ester groups into higher value-added vitrimer nanocomposites.

Vitrimerization: Converting Thermoset Polymers into Vitrimers

Thermoset polymers with permanently cross-linked networks have outstanding mechanical properties and solvent resistance, but they cannot be reprocessed or recycled. On the other hand, vitrimers with covalent adaptable networks can be recycled. Here we provide a simple and practical method coined as "vitrimerization" to convert the permanent cross-linked thermosets into vitrimer polymers without depolymerization. The vitrimerized thermosets exhibit comparable mechanical properties and solvent resistance with the original ones. This method allows recycling and reusing the unrecyclable thermoset polymers with minimum loss in mechanical properties and enables closed-loop recycling of thermosets with the least environmental impact.

Design Strategy for Porous Composites Aimed at Pressure Sensor Application

Flexible and highly sensitive pressure sensors have versatile biomedical engineering applications for disease diagnosis and healthcare. The fabrication of such sensors based on porous structure composites usually requires complex, costly, and nonenvironmentally friendly procedures. As such, it is highly desired to develop facile, economical, and environment-friendly fabrication strategies for highly sensitive lightweight pressure sensors. Herein, a novel design strategy is reported to fabricate porous composite pressure sensors via a simple heat molding of conductive fillers and thermoplastic polyurethane (TPU) powders together with commercially available popcorn salts followed by water-assisted salt removal. The obtained TPU/carbon nanostructure (CNS) foam sensors have a linear resistance response up to 60% compressive strain with a gauge factor (G_F ) of 1.5 and show reversible and reproducible piezoresistive properties due to the robust electrically conductive pathways formed on the foam struts. Such foam sensors can be potentially utilized for guiding squatting exercises and respiration rate monitoring in daily physical training.

Stretchable elastomer composites with segregated filler networks: effect of carbon nanofiller dimensionality

Electrically conductive elastomer composites (CECs) have great potential in wearable and stretchable electronic applications. However, it is often challenging to trade off electrical conductivity and mechanical flexibility in melt-processed CECs for wearable electronic applications. Here, we develop CECs with high electrical conductivity and mechanical elasticity by controlling the segregated networks of carbon nanofillers formed at the elastomer interface. The carbon nanofiller dimensionality has a significant influence on the electrical and mechanical properties of thermoplastic polyurethane (TPU) composites. For instance, 3D branched carbon nanotubes (carbon nanostructures, CNSs) have a very low percolation threshold (Φ _C = 0.01 wt%), which is about 8-10 times lower than that of 1D carbon nanotubes (CNTs) and 2D graphene nanosheets (GNSs). Besides, the TPU/CNS system has a higher electrical conductivity than other fillers at all filler contents (0.05-2 wt%). On the other hand, TPU/CNT systems can retain high elongation at break, whereas for the TPU/GNS systems elongation at break is severely deteriorated, especially at a high filler content. Different electrical and mechanical properties in the TPU-based CECs enable potential applications in flexible conductors/resistors and stretchable strain sensors, respectively.

Biomimetic Water-Responsive Self-Healing Epoxy with Tunable Properties

As dynamic cross-linking networks are intrinsically weaker than permanent covalent networks, it is a big challenge to obtain a stiff self-healing polymer using reversible networks. Inspired by the self-healable and mechanically adaptive nature of sea cucumber, we design a water-responsive self-healing polymer system with reversible and permanent covalent networks by cross-linking poly(propylene glycol) with boroxine and epoxy. This double cross-linked structure is self-healing due to the boroxine reversible network as well as showing a room-temperature tensile modulus of 1059 MPa and a tensile stress of 37 MPa, on a par with classic thermosets. The dynamic boroxine bonds provide the self-healing response and enable up to 80% recovery in modulus and tensile strength upon water contact. The system shows superior adhesion to metal substrates by comparison with the commercial epoxy-based structural adhesive. Besides, this system can change modulus from a stiff thermoset to soft rubber (by a factor of 150) upon water stimulus, enabling potential applications of either direct or transform printing for micro/nanofabrication. Moreover, by incorporating conductive nanofillers, it becomes feasible to fabricate self-healing and versatile strain/stress sensors based on a single thermoset, with potential applications in wearable electronics for human healthcare.

Interface Design Strategy for the Fabrication of Highly Stretchable Strain Sensors

Simultaneously achieving high piezoresistive sensitivity, stretchability, and good electrical conductivity in conductive elastomer composites (CECs) with carbon nanofillers is crucial for stretchable strain sensor and electrode applications. Here, we report a facile and environmentally friendly strategy to realize these three goals at once by using branched carbon nanotubes, also known as the carbon nanostructure (CNS). Inspired by the brick-wall structure, a robust segregated conductive network of a CNS is formed in the thermoplastic polyurethane (TPU) matrix at a very low filler fraction, which renders the composite very good electrical, mechanical, and piezoresistive properties. An extremely low percolation threshold of 0.06 wt %, currently the lowest for TPU-based CECs, is achieved via this strategy. Meanwhile, the electrical conductivity is up to 1 and 40 S/m for the composites with 0.7 and 4 wt % CNS, respectively. Tunable piezoresistive sensitivity dependent on CNS content is obtained, and the composite with 0.7 wt % filler has a gauge factor up to 6861 at strain ε = 660% (elongation at break is 950%). In addition, this strategy also renders the composites' attractive tensile modulus. The composite with 3 wt % CNS shows 450% improvement in Young's modulus versus neat TPU. This work introduces a facile strategy to fabricate highly stretchable strain sensors by designing CNS network structures, advancing understanding of the effects of polymer-filler interfaces on the mechanical and electrical property enhancements for polymer nanocomposites.

Dielectric Properties of Bio-Based Diphenolate Ester Epoxies

Thermoset bio-based diglycidyl ether of diphenolate esters (DGEDP) exhibit comparable mechanical properties as petroleum-derived diglycidyl ether of bisphenol A (DGEBA), whereas DGEDP is derived from levulinic acid, a safe and readily renewable feedstock. To determine the potential replacement of DGEBA as dielectric materials, a series of DGEDP-esters (i.e., methyl, ethyl, propyl, and butyl esters) were synthesized and studied. Broadband dielectric spectroscopy revealed that DGEDP-propyl has the highest dielectric constant in the series, comparable to DGEBA. Differences in the dielectric properties of DGEDP-esters is attributed to the interplay of segmental, small local, and side-chain motions on one hand and free volume and steric hindrance on the other.

Modeling compressive behavior of open-cell polymerized high internal phase emulsions: effects of density and morphology

The compressive behavior of poly(HIPE) foams was studied using the developed micromechanics based computational model. The model allowed identifying the morphological parameters governing the foam compressive behavior. These parameters comprise: (i) foam density, (ii) Sauter mean diameter of voids calculated from the morphological analysis of the polydispersed microstructure of poly(HIPE), and (iii) polymer/strut characteristic size identified as the height of the curvilinear triangular cross-section. The model prediction compared closely with the experiments and considered both the linear and plateau regions of the compressive poly(HIPE) behavior. The computational model allows the prediction of structure-property relationships for poly(HIPE) foams with various relative densities and open cell microstructure using the input parameters obtained from the morphology characterization of the poly(HIPE). The simulations provide a pathway for understanding how tuning the manufacturing process can enable the optimal foam morphology for targeted mechanical properties.

Effect of Curing Rate on the Microstructure and Macroscopic Properties of Epoxy Fiberglass Composites

Curing rates of an epoxy amine system were varied via different curing cycles, and glass-fiber epoxy composites were prepared using the same protocol, with the aim of investigating the correlation between microstructure and composite properties. It was found that the fast curing cycle resulted in a non-homogenous network, with a larger percentage of a softer phase. Homogenized composite properties, namely storage modulus and quasi-static intra-laminar shear strength, remained unaffected by the change in resin microstructure. However, fatigue tests revealed a significant reduction in fatigue life for composites cured at fast curing rates, while composites with curing cycles that allowed a pre-cure until the critical gel point, were unaffected by the rate of reaction. This result was explained by the increased role of epoxy microstructure on damage initiation and propagation in the matrix during fatigue life. Therefore, local non-homogeneities in the epoxy matrix, corresponding to regions with variable crosslink density, can play a significant role in limiting the fatigue life of composites and must be considered in the manufacturing of large scale components, where temperature gradients and significant exotherms are expected.

Synergistic Effects in Thermoplastic Polyurethanes Incorporating Hybrid Carbon Nanofillers

In this study thermoplastic polyurethane (TPUs) nanocomposites incorporating carbon nanotubes (CNTs) and graphene nanoplatelets (GNPs) were prepared via melt blending and compression molding and CNT dispersion was optimized by using non-covalent surface modification (surfactant). Filler dispersion was further improved by combining two fillers with different geometric shape and aspect ratio in hybrid filler nanocomposites. Synergistic effects were observed in the TPU-GNP-CNT hybrid composites, especially when combining GNP and CNT at a ratio of 6 : 4, showing higher tensile modulus and strength with respect to the systems incorporating individual CNTs and GNPs at the same overall filler concentration. This improvement was attributed to the interaction between CNTs and GNPs limiting GNP aggregation and bridging adjacent graphene platelets thus forming a more efficient network. Hybrid systems also exhibited improved creep resistance and recovery ability. Morphological analysis carried out by scanning electron microscopy (SEM) indicated that the hybrid nanocomposite presented slightly smaller and more homogeneous filler aggregates. The well-dispersed nanofillers also favored higher phase separation in TPU, as indicated by atomic force microscopy (AFM), resulting in a better microstructure able to enhance the load transfer and maximize the mechanical and viscoelastic properties.

THERMOGRAVIMETRIC ANALYSIS OF THE KINETICS OF THE REACTION OF ALKOXYSILANE WITH SILICA

The surface functionalization of silica by alkoxysilane can improve its dispersion into polymers by beneficially modifying interparticle and particle–polymer interactions. Thermogravimetric analysis (TGA) has been used to study the kinetics of binding a bifunctional alkoxysilane onto silica over the temperature range of 50 to 110 °C. Derivative TGA curves of the reacted silica show distinct peaks, which correspond to the alkoxysilane bound to one or two surface silanol sites. Binding at two silanol sites is postulated to occur in a two-step series reaction model. An Arrhenius analysis for the alkoxysilane binding reactions shows that the activation energies of the two reaction steps are similar, which is expected because the alkoxysilane contains two identical binding groups. This work demonstrates the suitability of the TGA technique to investigate the reaction kinetics for modifying the surface of silica.

THERMOGRAVIMETRIC ANALYSIS OF THE KINETICS OF BOUND-RUBBER FORMATION ON SURFACE-MODIFIED SILICA

Thermogravimetric analysis (TGA) has been used to study the kinetics of bound-rubber formation on the surface of silica modified with a bi-functional alkoxysilane coupling agent (CA) over the temperature range of 110 to 150 °C. The bound-rubber formation is attributed to the direct binding of a polymer chain with a number of nonpolar interactive sites provided by the CA molecules on the silica surface. A kinetic model developed for the reaction process suggests that the bound-rubber morphology is altered at temperatures above 110 °C.

Modeling of the Torque Requirements for the Mixing and Dispersion of Silica into Rubber

A model for the evolution of torque requirements in the batch mixing of silica agglomerates in styrene-butadiene rubber has been developed. The analysis considers the rheology of suspensions as modeled by the Krieger-Dougherty equation but with modifications so that it can apply to a wider range of solids loading, and combines that with a separate model that expresses the kinetics of the dispersion of silica agglomerates. The model shows good agreement with the trends of experimental data, and thus can be used to make predictions about torque requirements for compounding commercial grades of silica into rubber, as related to dispersion, under practical mixing conditions.

Chaotic Features of Flow in Polymer Processing Equipment-Relevance to Distributive Mixing

The dominant distributive mixing mechanism in polymer processing is convection. Convection, involving movement of fluid elements from one spatial location in the system to another, results in the creation of interfacial area. Length stretch distributions can be used as a measure of distributive mixing efficiency. We have studied the dynamics of distributive mixing in single and tangential twin screw extruders by means of tracking the evolution of particles originally gathered as clusters. Length stretch distributions and the dynamics of the average length stretch indicate that the tangential twin screw extruder is a better mixing device by comparison with the single screw extruder. The chaotic features of flow in these devices, studied by means of Poincaré sections and Lyapunov exponents, correlate well with the distributive mixing efficiency of the equipment.

Influence of Design on Mixing Efficiency in a Variable Intermeshing Clearance Mixer

The Variable Intermeshing Clearance (VIC) mixer possesses the unique feature of the ability to change the inter-rotor clearance during the compounding process. To improve the mixing performance of the VIC mixer new designs are proposed. A fluid dynamics analysis package-FIDAP, using the finite element method was employed to simulate the flow behavior in the VIC mixer. The problem of time dependent flow boundaries was solved by selecting a number of sequential geometries with 20 degree increments to represent a complete mixing cycle. Dispersive mixing was evaluated in terms of both the shear stress distribution and the elongational flow components generated in the flow field. Distributive mixing was studied numerically by means of tracking the evolution of particles originally gathered as clusters. Our studies indicate that the new design of an enlarged chamber gives overall better dispersive and distributive mixing performance than the traditional VIC. The VIC mixer with both an enlarged chamber and wider rotor blades design shows poorer dispersive mixing but better distributive mixing capability. The effect of inter-rotor clearance on mixing efficiency is also discussed.

Distributive Mixing in an Axial Discharge Continous Mixer

The axial discharge continuous mixer-LCMAX 40, which combines the features of a continuous mixer and the co-rotating twin screw extruder, was analyzed in this work for its distributive mixing efficiency. We analyzed the distributive mixing performance for various rotor configurations. Four designs with either alternating or block arrangements of pushing and counter-pushing units were investigated. A fluid dynamics analysis package-FIDAP, based on the finite element method was used to model the flow behavior of a power law model fluid. Distributive mixing was quantified using particle distributions along the axial distance. Residence time distribution (RTD) functions were calculated and found to reveal interesting information related to design features. The influence of design on the evolution of the particle path length and shear strain distribution was also discussed. The counter-pushing units and their arrangements were found to play an important role in distributive mixing.

Numerical Simulations and Experiments in a Double-Couette Flow Geometry

Modeling of batch and continuous twin rotor mixers, widely used in polymer processing, is a challenging computational problem. One approach to understand the mechanics of flow in twin rotor mixers is to simplify the geometry of the rotors by using cylindrical rotors. This geometry is referred to as the double-Couette geometry. Advantages of the double-Couette geometry are a simple symmetrical mesh design and no time-dependent flow boundaries. In this work, we used the double-Couette geometry to study the mechanics of flow and mixing efficiency in laminar and turbulent flow regimes. Flow visualization experiments utilizing a fluorescent dye were carried out in a transparent flow cell. A fluid dynamics analysis package—FIDAP, based on the finite element method, was used for the flow simulations in laminar and turbulent flow regimes. Numerical results showed good agreement with the experimental data. We attempted a qualitative comparison for distributive mixing efficiency in laminar and turbulent flow regimes in light of the spreading of a tracer line (dye) in the matrix. The analysis pointed out to differences in the mixing mechanisms encountered in different flow regimes.

Modeling and Experimental Study of the Flow in a Simplified Cavity Transfer Mixer

The Cavity Transfer Mixer (CTM) was primarily designed as a distributive mixing device to be used as an add-on unit to existing extruders. Understanding the flow patterns and characteristics within the CTM is of fundamental importance for a proper design and optimum processing. Due to the complex geometry and the transient characteristics of the flow, solving for the flow patterns in the CTM is not an easy task. However, some of the design features of the CTM can be reproduced in a simplified device which will allow more detailed experimental and numerical investigation. In this work such a simplified device was built and used to reveal some of the features of the flow patterns and the influence of one design parameter (cavity shallowness) on the dispersive mixing efficiency.

A Study of Distributive Mixing in Counterrotating Twin Screw Extruders

Counterrotating twin screw extruders are widely used for compounding, devolatilization, blending, and reactive extrusion. A fluid dynamics analysis package-FIDAP, using the finite element method, was implemented to simulate the 3-D, isothermal flow patterns in intermeshing and tangential counterrotating twin screw extruders. The rheology of the fluid was described by a power-law model. We developed a framework to evaluate the distributive mixing efficiency. The dynamics of distributive mixing were studied numerically by means of tracking the evolution of particles originally gathered as clusters. The extent or goodness of mixing was characterized in terms of length stretch, pairwise correlation function and volume fraction of islands. The length stretch reflects the capability of the mixer to spread particles away from their neighbors initially present in the same cluster. The pairwise correlation function characterizes the global distribution of particles in the mixing region. The volume fraction of islands quantifies the regions void of minor component and provides the local analysis of mixing. This framework can then be used to differentiate among various operating conditions or various designs of the same type of equipment.

Two-Dimensional Dynamic Study of the Distributive Mixing in an Internal Mixer

Distributive mixing in an internal mixer was studied numerically by means of tracking the evolution of the distance between pairs of particles in the mixing chamber. The distributions of these pairwise distances are reported in terms of the probability density function of a pairwise correlation function. In conjunction with this descriptive technique, a dynamic particle-tracking algorithm for two dimensions has been developed to study the dynamics of mixing in the mixer. We also propose a parameter e to monitor the extent of mixing. This general approach represents the first attempt of this kind to address directly the goodness of mixing. A total of five operating modes was considered. Three of them have even speed ratio of 60 rpm and rotors positioned at 90–90, 90–180, 90–270 relative to the horizontal axis, respectively. The remaining two have uneven speed of 60 rpm/40 rpm and rotors positioned at 90–90, 90–270 relative to the horizontal axis, respectively. For each operating mode, a complete period is represented as a sequence of snap shots (72 for even speed and 216 for uneven speed) and the flow field for each snap shot was calculated by means of FIDAP. Based on our proposed framework, we were able to demonstrate clearly that the anti-symmetric configuration (90–270) is the best operating mode among the three even speed cases and the configuration (90–180) is the worst. The performance of the uneven speed cases fell in between the even speed cases.

Analysis of Agglomerate Rupture in Linear Flow Fields

A dispersive mixing model focusing on the rupture of agglomerates as the step that primarily determines the dynamics of the mixing process was developed and analyzed. Rupture is predicted to occur when hydrodynamic forces exerted on the outer surface of the agglomerate exceed cohesive forces binding the agglomerate together. Agglomerates are modeled as clusters of aggregates bound by van der Waals forces. The magnitude and orientation of the rupturing hydrondynamic force depend on the local stress field in the fluid. Cleavage of the agglomerate is predicted to occur at the mid-plane of the agglomerate where the effects of hydrodynamic tension is the largest. Under the assumption that parent agglomerates and their fragments have the same shape, the kinetics of the rupture process is found to be independent of the absolute size of the agglomerate. Following from this is the result that the dispersion process is governed by flow dynamics, i.e., a minimum value of flow strength, which depends on the geometry of the bulk flow field, is required for rupture of the agglomerate. Agglomerate rupture was investigated in four flow geometries: simple shear; pure elongation; uniaxial extension, and biaxial extension. The efficiency of each flow geometry is compared on the basis of power and time requirements to achieve a given degree of dispersion.

Analysis of Mixing Performance in a VIC Mixer

The VIC mixer is an intermeshing internal mixer, whose unique feature is its ability to vary the clearance between the two rotors. The flow field in the chamber of an internal mixer is difficult to analyze due to the complex geometry and transient character of the flow. Here, a fluid dynamics analysis package – FIDAP, using the finite element method was employed to simulate the flow patterns in a VIC 1.9 mixer. A 3D flow analysis was carried out for the whole mixing chamber. The problem of time dependent flow boundaries was solved by selecting a number of sequential geometries to represent a complete mixing cycle. The flow field was characterized in terms of velocity profiles, pressure contours, shear stresses generated and a parameter λ quantifying the elongational flow components. The last two parameters are the most important ones in analyzing dispersive mixing efficiency. Distributive mixing was studied numerically by means of tracking the evolution of particles originally gathered as clusters. The pairwise correlation function and the particle concentration were used to quantify the degree of mixing. The dynamic average flow field characteristics based on the particle tracking were also calculated. The effect of changing gap size on dispersive and distributive mixing was investigated.

3D Flow Field Analysis of a Banbury Mixer

Banbury mixers are widely used in polymer processing. The flow field in the chamber of an internal mixer is difficult to analyze due to the complex geometry and transient character of the flow. In this work, a fluìd dynamics analysis package – FIDAP, using the finite element method was employed to simulate the flow patterns in a BB-2 type Banbury mixer. A 3D flow analysis was carried out for the whole mixing chamber. The problem of time dependent flow boundaries was solved by selecting a number of sequential geometries to represent a complete mixing cycle. The flow field was characterized in terms of velocity profiles, pressure contours, shear stresses generated and a parameter λ quantifying the elongational flow components. The last two parameters are the most important ones in analyzing mixing efficiency. The influence of processing conditions (rpm, speed ratio, and initial relative position of the two rotors) on the flow characteristics was analyzed. The flow results from the 3D model were also compared with results previously obtained from a 2D model.

3-D Flow Simulations of a Cavity Transfer Mixer

The Cavity Transfer Mixer (CTM) was primarily designed as a distributive mixing device to be used as an add-on unit to existing extruders. In determining the CTM overall mixing efficiency as well as its potential use for various applications, the flow patterns/characteristics within this mixer must be well understood. In this work, a fluid dynamics analysis package – FIDAP – using the finite element method was employed to simulate the flow patterns in a CTM with 3 rows and 6 cavities per row. A 3-D, isothermal flow analysis for a Newtonian fluid was carried out. The flow field was characterized in terms of velocity profiles, average shear stresses and a parameter λ quantifying the elongational flow components. The influence of processing variables on the flow characteristics was also discussed. The simulation results show good agreement with the experimental data.

Observation and Analysis of Carbon Black Agglomerate Dispersion in Simple Shear Flows

Experiments aimed at detecting agglomerate dispersion were performed in a rotating concentric cylinder device mounted in a light scattering monophotometer. The dispersion of carbon black agglomerates suspended in various media (e.g. water, squalene, poly (dimethyl siloxane)) was inferred by measuring changes in turbidity under the application of a controlled simple shear field. In a given suspension the turbidity was observed to be constant for shear rates less than a threshold value. At shear rates in excess of this value, the turbidity was observed to increase monotonically in time to a steady state value. The effects of particle size and fluid viscosity on the critical shear rate necessary to induce agglomerate breakage were examined. Also, the change in the nature of the agglomerate size distribution upon shearing was studied. The results obtained indicate that the breakup of highly structured agglomerated solids such as carbon black does not proceed by a halving process. Also, the initial breakup process was observed to be irreversible.

Flow Field Characterization in a Banbury Mixer

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.

Dynamics of Filler Size and Spatial Distribution in a Plasticating Single Screw Extruder – Modeling and Experimental Observations

A model of agglomerate break-up, incorporating both rupture and erosion, is employed to predict the dynamics of filler size distribution in a plasticating single screw extruder. Filler spatial distribution along the extruder length was also ascertained and direct comparison of experimental and computational data proved to be satisfactory. The method was also used to investigate the effect of material properties, operating conditions and extruder geometry on the dynamics of agglomerate dispersion along a single screw extruder. Generally, dispersion levels were primarily governed by the magnitude of the hydrodynamic stresses developed in the extruder and the residence time in the melt.

Modeling of Agglomerate Dispersion in Single Screw Extruders

A model for solid agglomerate dispersion in single screw extruders is proposed. The model combines numerical simulations of flow patterns in the metering section of a single screw extruder with a Monte Carlo method of clusters rupture and erosion mediated by a local fragmentation number. Particle size distributions and Shannon entropy are used for mixing characterization. The model is quite general and can be adapted for different polymer-additive systems as well as for different processing equipment.