Numerical simulation of polymer foaming process in extrusion flow

Computer simulations of polymer foaming processes in extrusion flow have been carried out in order to improve current understanding of viscoelasticity and bubble growth effects on die-swelling in the production of polymer foam. The linear and non-linear viscoelastic materials functions of a commercial low density polyethylene (LDPE) melt have been extracted by fitting its rheometric data with constitutive models including a simple viscoelastic model (SVM), the exponential Phan-Thien–Tanner (EPTT) model and the double convected pom–pom (DCPP) model. Simulations of LDPE melt under extrusion flow without foaming show that the predictions of the die-swell by the SVM are in reasonably good agreement with the results obtained from the EPTT and DCPP models. By comparison of the simulation results of LDPE foaming in extrusion flow using the Bird–Carreau model and the SVM, a cooperative effect of polymer viscoelasticity and bubble growth on the die-swell has been quantified. The numerical results also show that the density of polymeric foam decreases significantly with the increasing concentration of foaming agent, and that the combination of the SVM and bubble growth model can account for some essential physics of polymer foaming process in extrusion flow.     

Grundlagen der Blasenbildung an Einzelporen und Lochplatten

Basics on Bubble Formation at Single Pores and at Porous Plates Many processes in biotechnology (e.g., gas supply for fermentation vessels) and in process engineering (e.g., foaming with membranes) require the knowledge of how bubbles are formed at pores and at porous plates. Bubble build‐up at and release from the pores are both complex processes due to the constant change in bubble size, shape, and compressibility. The relevant literature to these processes is summarized here, and the bubble formation and bubble release processes in stationary and moving media are described. The factors that influence bubble formation and movement are deduced from the forces that act on a forming bubble. Empirical approaches from the literature are presented, which estimate the bubble size in dependence of the process parameters. Bubble formation depends on the one hand on the gas flow through the pores, on the other hand one has to distinguish between bubble formation in stationary and in moving media.     

Numerical simulation of bubble growth in viscoelastic fluid with diffusion of dissolved foaming agent

Viscoelastic simulations of bubble growth in polypropylene (PP) physical foaming were performed. A multimode Phan‐Thien Tanner (PTT) model was used to analyze the dynamic growth behavior of spherically symmetric bubbles with the diffusion of a foaming agent (CO₂). Changes in the dissolved foaming agent concentration in the polymer and in the strain of the polymer melt surrounding the bubbles were simulated with the Lagrangian FEM method. The simulation technique was validated by comparison with the bubble growth data, which were experimentally obtained from visual observations of the PP/CO₂ batch foaming system. The simulation results demonstrated that the strain‐hardening characteristic of polymer does not strongly affect the bubble growth rate. The linear viscoelastic characteristic is more influential, and the relaxation mode around 0.01 s is the most important factor in determining the bubble growth rate during the early stage of foaming. A multivariate analysis for the simulation results was also carried out. This clarified that bubble nucleus population density, surrounding pressure, initial dissolved foaming agent concentration, and diffusion coefficient are more important factors than the viscoelastic characteristics. POLYM. ENG. SCI., 45:1277–1287, 2005. © 2005 Society of Plastics Engineers     

Modelling of the continuous foaming operation by dimensional analysis

In this study, a dimensional analysis of the continuous foaming operation by whipping was performed. Newtonian model fluids were formulated with controlled rheology and interfacial properties. The viscosity has been modified by changing the dilution of glucose syrup and surface tension has been modified by using two different surfactant species (whey protein and sucrose ester). Foams have been produced on an instrumented industrial rotor–stator mixer by varying the rotation speed, flow rates and pressure. An image analysis method which makes possible to characterize accurately the bubble sizes was performed on each samples. A dimensional analysis allowed to describe in a general way the foaming operation with dimensionless ratios and also enabled to weigh the magnitude of each operating parameter. A model which predicts bubble size, depending on process parameters and those related to the products has been established. This model offers a new definition of capillary number. The major influence of this number provides information on the mechanisms involved in the process. However, the approach also shows that other phenomena affect the bubble size.     

Modeling particle inflation from poly(amic acid) powdered precursors. II. Morphological development during bubble growth

The morphological development of cellular polyimide microstructures from poly(amic acid) powders has been shown to depend on the processing conditions throughout the inflation process and the morphological characteristics of the precursor particles. In an earlier publication the authors presented a numerical study of the preliminary stages prior to particle inflation when the processing temperature is below the glass transition temperature, T_g. In the present article, a second numerical scheme is presented for behavior above T_g in which bubble growth is modeled to account for the effect of multiple phenomena in the final stages of morphological development. The bubble growth kinematics and subsequent cessation of growth are predicted as a function of process parameters and material properties. Morphological characteristics of the precursor particles have also been shown to influence the kinematics of inflation. These results provide a clearer understanding of the solid‐state foaming processes for polyimide cellular materials. POLYM. ENG. SCI., 47:572–581, 2007. © 2007 Society of Plastics Engineers.     

超临界CO_2微孔发泡制备聚乳酸/磷酸三钙多孔材料

利用超临界二氧化碳(sc-CO2)微孔发泡方法制备聚乳酸/磷酸钙(PLA/TCP)多孔材料,通过扫描电子显微镜(SEM)观察TCP颗粒分散和泡孔形态。结果表明,TCP质量分数为1 wt%和3 wt%时,微米级TCP颗粒均匀分布在PLA基体中,在发泡过程中起到异相成核的作用,减小泡孔尺寸同时增加泡孔密度。当TCP含量为5 wt%时,TCP颗粒出现团聚,异相成核作用减弱,泡孔密度下降。随着发泡温度升高,泡孔尺寸增大的同时泡孔壁变薄甚至破裂,发泡温度对泡孔密度影响不大。增加发泡压力,泡孔的数量急剧增加,同时泡孔的尺寸减少,泡孔壁变厚。     

Research on formation mechanisms and control of external and inner bubble morphology in microcellular injection molding

This study investigates the formation mechanisms and control of external and inner bubble morphology in MIM. First, the related theories about foaming and filling flow are analyzed. Second, the assumptions for the formation of inner bubble morphology, external bubble morphology, and the compact skin layer in MIM process are proposed based on theoretical analysis. Finally, experiments of MIM process are conducted to verify the theoretical assumptions. In addition, gas counter pressure (GCP) and rapid mold heating and cooling (RMHC) technology are used for control of bubble morphology. It is found that foaming process in MIM can be divided into foaming during filling and foaming during cooling. Foaming during filling produce oriented and deformed bubbles while foaming during cooling produce spherical or polygonal bubbles. As the bubbles formed by foaming during filling can reach melt flow front, they will be pushed to the cavity surface where they are stretched further and frozen to generate the silver or swirl marks. The compact skin layer is formed due to the redissolution of the gases within bubbles into polymer melt and also restraint of foaming by high cavity pressure. GCP and RMHC are two effective methods for controlling external and inner bubble morphology. POLYM. ENG. SCI., 55:807–835, 2015. © 2014 Society of Plastics Engineers     

Polymer foaming with chemical blowing agents: Experiment and modeling

An experimental and theoretical analysis of the polypropylene foaming process using three different chemical blowing agents (CBA) was performed. A simple experiment was designed to analyze the foaming process of polypropylene (PP)/CO₂ system under two different pressure conditions. The expansion ratio and final foam structure was measured both by direct observation and from optical measurements and image analysis, showing a good agreement. A single bubble simulation based on relevant differential scanning calorimetry and thermo‐gravimetrical analysis experiments, assuming each CBA particles as a nucleation site and accounting for gas diffusion in the surrounding polymer matrix has been built. The sensitivity of the model to physical and processing parameters has been tested. The calculation results are compared to the experiments and open the route to a simplified method for evaluating the efficiency of CBA. POLYM. ENG. SCI., 55:2018–2029, 2015. © 2014 Society of Plastics Engineers     

Desorption Kinetics of Volatile in Condensed Mode PolyethyleneProcess

In this paper the desorption kinetics of volatile in condensed mode polyethylene process is studied through experiments. It is found that though the residual volatile in particles at the later stage of desorptlon accounts for a relatively small portion of the total quantity, the desorptinn of this part of volatile requires much longer time than at the earlier stage. For high requirement of devolatilisation, the total time needed will be predominately determined by the residual amountof volatile in particles. Temperature has greater effect on the desorption rate than other influence factors, especially in the later period of desorptinn. A model is proposed to calculate the volatile deaorption rate for condensed mode polyethylene process.     

Improving the stability of polylactic acid foams by interfacially adsorbed particles

Polymers such as poly(lactic acid) (PLA), which have poor melt strength, are difficult to foam due to severe cell coalescence during foaming. We show that addition of a few percent of polytetrafluoroethylene (PTFE) particles can stabilize PLA foams against bubble coalescence and collapse. The particles and a chemical blowing agent, were dispersed into the PLA by extrusion, and then foamed by heating. The PTFE‐containing foams remained stable even when the foams were held under molten conditions for extended periods. Foam stability is attributed to an interfacial mechanism: due to their low surface energy, the PTFE particles adsorb on the inner surface of the foam bubbles at a high surface coverage, and endow the bubbles with an interfacial “shell” that prevents coalescence. This mechanism resembles the particle‐stabilization of Pickering emulsions in oil/water systems. Particle adsorption at the interface is a necessary condition for using this approach, and hence this approach is most likely to be successful if the particles have a low surface energy and the polymer has a high surface tension. The approach of using interfacially adsorbed particles can be broadly generalized, and offers the opportunity of foaming various polymers with low melt strength, or for expanding the processing window within which foaming can be conducted. POLYM. ENG. SCI., 56:9–17, 2016. © 2015 Society of Plastics Engineers     

Migration of a single gas bubble in water during the formation of stable gas-hydrate crust on its surface

A theoretical model of gas-hydrate formation during the migration of the methane bubble in water under thermobaric conditions of hydrate stability has been considered. Numeric solutions were obtained and analyzed for two limiting cases when the rate of formation of the hydrate crust on bubble surface is constrained by the intensity of heat removal, which is released during hydrate-formation process by the surrounding water or the diffusive resistance of gas hydrate crust against the transfer of hydrate-forming components. A comparative analysis of the numeric results with the experimental data showed that the diffusive transfer of hydrate-forming components through the crust most adequately described the process of hydrate-particle growth that was observed in experiments during the ascent of methane particles in seawater. The conditions of the best agreement between the theoretical and experimental data on changing of radius of gas-hydrate particle allowed numeric estimates to be obtained for values of the reduced coefficient of gas and water diffusion through the hydrate crust.     

蒸汽发泡与传统发泡方式对TPU发泡效果的影响

采用超临界流体间歇式微孔发泡技术制备了超轻热塑性聚氨酯弹性体（TPU）颗粒,利用扫描电子显微镜等研究了以水蒸气、热空气、水、甘油4种不同发泡介质对发泡行为的影响。结果表明,高温水蒸气发泡、烘箱发泡、油浴发泡、水浴发泡的最佳发泡时间分别为50、180、30、15 s左右;最佳发泡温度分别为120、115、75、80 ℃左右;从发泡颗粒的外观、颗粒及泡孔结构的均匀性上来看,高温水蒸气发泡优于其他几种方式。     

On degradation of chemical solvents for bulk removal of CO2

Chemical solvent degradation during bulk removal of CO₂ has been studied for aqueous solutions of methyldiethanolamine (MDEA) and triethanolamine (TEA) promoted by piperazine (PIP) and morpholine (MOR), and for 40% aqueous solutions of diethanolamine (DEA). These solvents are either used commercially or have good commercial potential. Physical properties of the degraded solutions were measured. The study has been extended to determine the foaming characteristics of the solutions. The effectiveness of granular and powdered activated carbon in suppressing foaming was studied. The data generated by using accelerated degradation tests are of considerable interest to process engineers in the gas treating industry.     

Dynamically enhanced membrane foaming

Foamed food products like chocolate mousse, ice cream or fresh cheese are increasingly popular due to their soft and creamy sensory properties. Their perception, stability and flow behavior strongly depend on gas fraction and bubble size distribution. Foam processing research focuses on developing new optimized processes and material systems to achieve small mean bubble size and narrow size distribution.In this work, we present a new dynamically enhanced membrane foaming process. This foaming device basically consists of two concentric cylinders: the inner cylinder is rotated with circumferential velocities up to , the outer cylinder is fixed. Thus, a shear field is created in the narrow annular gap. The membrane can either be mounted to the inner or outer cylinder. Gas is pressed through the membrane and is detached as small bubbles by the acting flow shear stresses. The comparison of rheological and microstructural analysis of foams to results on bubble breakup in simple shear flow and on detachment of bubbles from the pore of a rotating membrane proved that the detachment of small bubbles from the membrane is the dominating bubble formation process in the dynamically enhanced membrane foaming process. Compared to conventional rotor-stator foaming devices, the dynamically enhanced membrane foaming process leads to significantly smaller mean bubble sizes at higher gas volume fractions and to reduced size distributions widths.     

Conventional and nanometric nucleating agents in poly(ϵ‐caprolactone) foaming: Crystals vs. bubbles nucleation

The aim of this article was to investigate the nucleating ability of different nucleating agents for the foaming of poly(ε‐caprolactone), a biodegradable, semicrystalline polymer. In particular, the efficiency of the nucleating agent in inducing the formation of the gaseous phase has been compared to the efficiency in inducing the formation of the crystalline phase. In effect, in foaming of semicrystalline polymers, bubble nucleation and crystal nucleation are concurrent and somehow interacting phenomena. Here, these two aspects have been evidenced and clarified. Foams were prepared by using a batch process with the pressure quench method, with nitrogen and carbon dioxide as the blowing agents. Conventional and novel nucleating agents were used: talc has been compared to several novel nanometric particles of different geometries and dimensions, such as titanium dioxide and alumina powders, exfoliated and intercalated clays, and carbon nanotubes. Foam densities and morphologies, in terms of number of cells per initial unit volume, were measured and found to depend both on crystalline phase nucleation and gaseous phase nucleation. In fact, the different nucleating agents, depending on shape, dimension, and surface functionalization, selectively nucleated the crystallites and/or the bubbles, affecting, respectively, bubble growth (and, hence, final foam density) and bubble nucleation (and, hence, cell number density—morphology). POLYM. ENG. SCI., 2008. © 2007 Society of Plastics Engineers     

Water based blowing agents for rubber extrusion

Physiologically hazardous chemical blowing agents are state of the art for the foaming of extruded rubber profiles. Water is a potential alternative to these blowing agents and is incorporated into rubber compounds in the form of water-leaded hygroscopic substances such as carbon blacks, silica, or hydrates. To achieve an optimum foaming result, the water desorption and cross-linking reaction has to be coordinated. In thermogravimetric investigations it is found that the inertia of the evaporation process plays an important role in water desorption mechanisms. It turned out that manual conditioning of the hygroscopic fillers with water is not reproducible. As a consequence, measurement uncertainties in characterization resulted, so that statistical proof of the expected effects on water desorption due to the specific properties of the fillers (e.g., silanol group density, specific surface area) could not be provided. However, carbon blacks are less suitable than silica due to the lower desorption temperature. The precipitated silica Ultrasil 360 with a relatively high pH-value showed higher water desorption rates than the other silica. The desorption temperature can reproducibly be adjusted as required by a suitable choice of hydrate. Since the absolute amount of water in the rubber compound is crucial to the foaming behavior during vulcanization Karl Fischer titration is used to determine the water content of a polar and a nonpolar rubber compound is determined over several weeks. Depending on the climatic conditions during storage, large deviations from the amount of incorporated water occur especially for polar rubber compounds such as nitrile butadiene rubber.     

The effect of dispersed elastomer particle size on heterogeneous nucleation of TPO with N2 foaming

Blending polypropylene (PP) with elastomeric modifiers provides a simple method of improving polymer's impact strength. Such PP/elastomer blends are commonly called thermoplastic polyolefin (TPO) blends. Developing TPO materials suitable for foaming is of great interest because they can be applied in high-volume markets such as the automotive industry. For immiscible polymer blends such as TPO, it has been often noted that the dispersed particles can act as cell nucleating agents, thereby enhancing heterogeneous nucleation. However, little work has been done to assess the effects of blend morphology on the nucleation behavior. Furthermore, the effects of elastomer dispersion on TPO foamability are still unknown. In this work, TPO blends with different blend morphologies were prepared by controlling the viscosity ratio between the blending components. Experimental results from both batch foaming and extrusion foaming processes with nitrogen (N₂) indicate that the foam structure is influenced by the size and the number density of the dispersed particles.     

木质活性炭自燃性质及其影响因素研究

对6种木质活性炭自燃性质的影响因素进行了研究。研究表明活性炭的临界自燃温度与其制造工艺和设备有关。挥发分(碳氢氧化合物)、氧含量、氢含量和表面含氧官能团及粒度是影响活性炭临界自燃温度的主要因素。磷酸法活性炭临界自燃温度最低(180℃),水蒸气法活性炭由于经过1000℃活化过程,在试验范围内无自燃性质。另外,平板炉制造的粉状活性炭比回转炉制造的粉状活性炭的临界自燃温度高。     

Features of the motion of gel particles in a three-phase bubble column under foaming and non-foaming conditions

Features of the motion of gel particles in a three-phase bubble column with non-foaming and foaming gas–liquid systems,determined by using experiments of radioactive particle tracking(RPT),have been compared.The tracer used is a gel particle which resembles typical immobilized biocatalyst.The tracer trajectory is analyzed to extract relevant information for design purposes.The solid velocity field,turbulence parameters,dispersion coefficients,mixing times and flow transitions are determined and compared.The presence of foam significantly affects many quantified parameters,especially within the heterogeneous flow regime.The hydrodynamic stresses are reduced in the presence of foam,especially close to the disengagement.The dispersion coefficients also decrease,and the solid mixing time is only slightly affected by the presence of foam.Gas holdup,inferred both from RPT experiments and from gamma ray scanning,is higher for foaming systems and leads to a shift in the transition gas velocity towards higher values.     

The motion mechanism and characteristic of bubble in a pseudo-2D tapered fluidized bed

The different carbon nanotube (CNT) particles (^@A and ^@V) were bed materials in the pseudo-2D tapered fluidized bed (TFB) with/without a distributor. A detailed investigation of the motion mechanism of bubbles was carried out. The high-speed photography and image analysis techniques were used to study bubble characteristic and mixing behavior in the tapered angle of TFB without a distributor. The fractal analysis method was used to analyze the degree of particles movement. Results showed that an S-shaped motion trajectory of bubbles was captured in the bed of ^@V particles. The population of observational bubbles in the bed of ^@V particles was more than that of ^@A particles, and the bubble size was smaller in the bed of ^@V particles than that of ^@A particles. The motion mechanism of bubbles had been shown to be related to bed materials and initial bed height in terms of analysis and comparison of bubble diameter, bubble aspect ratio and bubble shape factor. Importantly, compared to the TFB with a distributor, the TFB without a distributor had been proved to be beneficial to the CNT fluidization according to the study of bubble characteristic and the degree of the particle movement. Additionally, it was found that the mixing behavior of ^@V particles was better than ^@A particles in the tapered angle of TFB without a distributor.