Numerical and experimental studies of bubble growth during the microcellular foaming process

A new experimental technique for studying the dynamics of bubble growth in thermoplastics using scanning electron microscopy is developed. The influence of temperature, saturation pressure, molecular weight, and the nature of physical blowing agent are investigated. The experimental results show that, the above, process variables control the growth of foams during processing. The existing Newtonian model for the growth of a single bubble in an infinite amount of polymer has been modified to account for the non-Newtonian effects by modeling the polymer as a power law fluid. The experimental data has been compared with the appropriate viscoelastic cell model which considers the growth of closely spaced spherical bubbles during the foaming process. The simulation results indicate that the predictions of the cell model are in qualitative agreement with the trends of the experimental data and the quantitative agreement is reasonable. The cell model also gives an equilibrium radius which agrees with the experimental data. Other viscous models do not predict the equilibrium radius of the bubble and underpredict the experimental data.     

Numerical simulation for bubble growth during supercritical CO2 foaming epoxy resin process based on chemorheology

The bubble growth process of epoxy resin foams has been evaluated through a combination of numerical simulation and chemorheology. It was discovered that rheological properties play an essential role in forecasting bubble growth during supercritical CO₂ epoxy resin foaming. Time–cure superposition was conducted revealing that shear storage modulus increased from 10⁻³ to 10⁶ Pa during the curing reaction process. The complex viscosity increased up to 10⁵ Pa s and the characteristic relaxation time increased up to 53.1 s with the curing degree. The epoxy resin with high rigid modulus could effectively inhibit bubble growth. Furthermore, the simulation results indicated that the bubble growth process for epoxy resin foams was influenced by both the CO₂ content and CO₂ plasticization on rheology properties.     

Beyond classical theory: Predicting the free energy barrier of bubble nucleation in polymer foaming

Based on the Gibbs‐Tolman‐Koenig formalism, we considered the Tolman correction to the free energy barrier of bubble nucleation in polymer‐gas binary mixtures. For this class of systems, the correction may be estimated with a reasonable accuracy using experimentally accessible macroscopic thermodynamic quantities only. Although the Tolman correction is applicable only in the low supersaturation regime, a simple ansatz regarding the supersaturation dependence of the Tolman length can be made to extend the usefulness of this approach and to yield the free energy barrier that vanishes at the mean‐field spinodal as demanded by thermodynamic considerations. © 2013 American Institute of Chemical Engineers AIChE J, 59: 3042–3053, 2013     

Determination of modified polyamide 6's foaming windows by bubble growth simulations based on rheological measurements

Reactive extrusion was used to modify virgin polyamides 6 (v-PA6) and to prepare chain extended PA6 (CE-PA6) and long-chain branched PA6 (LCB-PA6) for the melt foaming process. This was done using a twin-screw extruder and the following modifiers: a chain extender ADR-4368 and a branching agent maleic anhydride grafted polypropylene. A reaction mechanism was proposed to explain the chain extension and long-chain branching reactions and was verified by the Fourier transform infrared spectroscopy data. The analysis of the gel permeation chromatography data showed that LCB-PA6 presented a strong increase in the molecular weight and in the dispersity index. Moreover, the rheological properties of the v-PA6 and modified PA6 resins were characterized by a dynamic shear test. The LCB-PA6 compared with CE-PA6 showed much higher shear viscosity and longer characteristic relaxation times, indicating the presence of an LCB structure. A uniaxial elongation test showed that the LCB-PA6 had the highest melt viscosity and melt strength as well as most obvious strain-hardening behavior. A high-pressure differential scanning calorimeter under compressed CO₂ was used to investigate the PA6's crystallization properties so as to analyze its minimum temperature of foaming windows. The melt foamability of the CE-PA6 and the LCB-PA6 was verified by batch melt foaming experiments with CO₂ as the blowing agent and maximum temperature of foaming windows was also quantitatively determined by numerical simulation of bubble growth based on the rheological measurements. The results showed that the LCB-PA6 foams had a smaller cell diameter, a larger cell density, a greater expansion ratio, and wider foaming temperature window than the CE-PA6. © 2019 Wiley Periodicals, Inc. J. Appl. Polym. Sci. 2019 , 136, 48138.     

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     

Experimental and numerical studies on the effects of pressure release rate on number density of bubbles and bubble growth in a polymeric foaming process

A simulation of simultaneous bubble nucleation and growth was performed for a batch physical foaming process of polypropylene (PP)/CO₂ system under finite pressure release rate. In the batch physical foaming process, CO₂ gas is dissolved in a polymer matrix under pressure. Then, the dissolved CO₂ in the polymer matrix becomes supersaturated when the pressure is released. A certain degree of supersaturation produces CO₂ bubbles in the polymer matrix. Bubbles are expanded by diffusion of the dissolved CO₂ into the bubbles. The pressure release rate is one of the control factors determining number density of bubbles and bubble growth rate.To study the effect of pressure release rate on foaming, this paper developed a simple kinetic model for the creation and expansion of bubbles based on the model of Flumerfelt's group, established in 1996 [Shafi, M.A., Lee, J.G., Flumerfelt, R.W., 1996. Prediction of cellular structure in free expansion polymer foam processing. Polymer Engineering and Science 36, 1950-1959]. It was revised according to the kinetic experimental data on the creation and expansion of bubbles under a finite pressure release rate. The model involved a bubble nucleation rate equation for bubble creation and a set of bubble growth rate equations for bubble expansion. The calculated results of the number density of bubbles and bubble growth rate agreed well with experimental results. The number density of bubbles increased with an increase in the pressure release rate. Simulation results indicated that the maximum bubble nucleation rate is determined by the balance between the pressure release rate and the consumption rate of the physical foaming agent by the growing bubbles. The bubble growth rate also increased with an increase in the pressure release rate. Viscosity-controlled and diffusion-controlled periods exist between the bubble nucleation and coalescence periods.     

Plasticization of soy protein polymer by polyol-based plasticizers

Soy protein isolate (SPI) was mixed with four polyol-based plasticizers and molded into plastics using a hot press. The plasticized SPI powder was evaluated for denaturation temperatures and denaturation enthalpies. The SPI plastics were studied for mechanical properties, glass transition temperatures, storage modulus, morphology, and water absorption. Thermal properties of the SPI plastics with propylene glycol were depressed to the largest degree, and the plastics with glycerol showed the largest strain at break, whereas plastics with 1,3-butanediol gave the highest tensile strength. The morphology of the fractured surface on the SPI plastics changed from brittle fracture for the unplasticized SPI to ductile fracture for the plasticized SPI. Water absorption of all the plasticized SPI plastics was lower than that of the unplasticized SPI plastics.     

Experimental observations and modelling relating to foaming and bubble growth from pentane loaded polystyrene melts

This paper is concerned with microstructure and kinetics relating to bubble growth within a pentane loaded molten polystyrene sample and the work is of relevance to the commercial foaming of polymers achieved by pressure release at the exit of an extruder. Optical experiments were carried out using a Multipass Rheometer to follow the time evolution for melting pentane loaded polystyrene beads. Two protocols were followed and one resulted in the formation of a single melt phase. With subsequent pressure release, the growth kinetics of bubbles were followed together with rheological measurements. A modified Newtonian model incorporating gas diffusion was developed and compared with the experimental data. Good matching of data could be achieved using realistic values of parameters and the model was able to predict early stage growth conditions. The model, as presented, still has many simplifications, however it does form the basis for further refinement.     

Experimental and numerical studies on bubble dynamics in nonpressurized foaming systems

This work explores the influence of rheological properties on polymer foam development in nonpressurized systems. To understand the complex contributions of rheology on the mechanism of bubble growth during different stages of foam processing, visualization studies were conducted by using a polymer‐foaming microscopy setup. The evolving cellular structure during foaming was analyzed for its bubble surface density, bubble size, total bubble projected area, and bubble size distribution. Morphological analysis was used to determine the rheological processing window in terms of shear viscosity, elastic modulus, melt strength and strain‐hardening, intended for the production of foams with greater foam expansion, increased bubble density and reduced bubble size. A bubble growth model and simulation scheme was also developed to describe the bubble growth phenomena that occurred in nonpressurized foaming systems. Using thermophysical and rheological properties of polymer/gas mixtures, the growth profiles for bubbles were predicted and compared to experimentally observed data. It was verified that the viscous bubble growth model was capable of depicting the growth behaviors of bubbles under various processing conditions. Furthermore, the effects of thermophysical and rheological parameters on the bubble growth dynamics were demonstrated by a series of sensitivity studies. POLYM. ENG. SCI., 54:1947–1959, 2014. © 2013 Society of Plastics Engineers     

Effect of polymer properties on bubble growth in polymer–paperboard composites

Foamed paperboard is a composite material used in thermally insulated food packaging and beverage containers. The paperboard is sandwiched between a layer of low‐density polyethylene and a barrier layer, and the low‐density film is foamed through heating. The moisture inside the paperboard vaporizes and serves as the driving force for creating the foam. The bubble growth on the paper surface has been tracked with high‐speed photography. The number of generated bubbles has been found to depend on the number of pores on the surface of the paperboard; there is little or no dependence on the properties of the polymer, at least across the range of properties studied. In contrast, the thickness of the foam is relatively insensitive to the paperboard properties but has a strong dependence on the thickness of the initial polymer film, the nature of the polymer, and the speed at which it is extruded onto the paperboard. It is believed that some of these variations arise from differences in the degree of adhesion between the polymer and the paperboard. © 2008 Wiley Periodicals, Inc. J Appl Polym Sci, 2008     

Surface tension effects in gas bubble dissolution and growth

The influence of surface tension upon the dissolution and growth of a stationary, isolated gas bubble in a fluid is examined. It is demonstrated that for small gas undersaturation of the liquid, surface tension corrections for bubble dissolution are significant for nearly the entire period of bubble dissolution. Also, it is shown that for slight supersaturation of the liquid, when bubble growth occurs, surface tension corrections are non-negligible too. Furthermore, comparisons are made with the quasi-stationary results which seem to indicate that surface tension corrections are of greater significance than convective corrections for small undersaturations. In the case of large undersaturations surface tension corrections are only of importance when the radius of the bubble is small.     

Hydrodynamic studies with foaming and non-newtonian solutions in bubble columns

Experiments were conducted in 0.05 m ID and 0.23 m ID by 3 m tall bubble columns to study the effect of surfactants and viscosity of liquid medium on gas hold-up and Sauter mean bubble diameter. The addition of n-butanol (0.5 and 1 wt.%) to water leads to the formation of foam and consequently produces higher gas hold-ups. The foam could be eliminated completely with the addition of a sufficient quantity (0.5 wt.%) of carboxymethyl cellulose to the aqueous alcohol solution. In the absence of foam, gas hold-ups were similar to those obtained with pure liquids. Sauter mean bubble diameters, obtained using the dynamic gas disengagement technique, increase with viscosity of liquid medium.     

Bubble nucleation in nonpressurized polymer foaming systems

The mechanism of bubble nucleation in the foaming process under atmospheric pressure is investigated in the present study. The experimental observations using a plastic‐foaming visualization setup revealed two stages of nucleation, primary nucleation in interstitial regions and secondary nucleation in the polymer melt, which followed the sintering and densification of the polymer matrix. Statistical analysis of the evolving cellular structure during the nucleation stage was used to study the significance of rheology on the behavior of polymer materials during the nucleation. The role of viscosity on the nucleation rate was also investigated theoretically by using a modified form of the classical nucleation theory and it was verified with the experimentally observed data. POLYM. ENG. SCI., 54:1201–1210, 2014. © 2013 Society of Plastics Engineers     

Impact of approximating the initial bubble pressure on cell nucleation in polymeric foaming processes

According to the classical nucleation theory, the free energy barrier for bubble nucleation, and thereby the nucleation rate, are functions of the initial bubble pressure, P_bubble,0. In almost all of the previous studies that have used computer simulations to investigate polymeric foaming processes, the value of P_bubble,0 has been approximated using the saturation pressure, P_sat. This article employs the thermodynamic equilibrium condition and the Sanchez–Lacombe (SL) equation of state (EOS) to determine the value of P_bubble,0. It is shown that using P_sat to approximate P_bubble,0 may lead to significant overestimations of the nucleation rate and the final cell density. © 2007 Wiley Periodicals, Inc. J Appl Polym Sci 104: 902–908, 2007     

Effect of microcellular foaming on the fracture behavior of ABS polymer

In this work, the properties of microcellular ABS were studied. Foamed samples exhibited a solid skin/foamed core structure, with some elongated cells in the flow direction, while spherical cells were mostly observed in the transversal direction. The flexural modulus, flexural strength, and fracture toughness K_Ic decreased with the density. However, the Crack Tip Opening Displacement (CTOD) was found to increase with the foaming ratio. The evolution of the mechanical properties and fracture toughness was well described by prediction models considering the skin/core morphology of these microcellular materials. Foaming increased the anisotropic behavior of the material, due to the cell elongation caused by the fountain flow during injection. © 2015 Wiley Periodicals, Inc. J. Appl. Polym. Sci. 2016 , 133, 43010.     

致孔法制备新型CMCTS-g-PAA大孔高吸水树脂

在过硫酸铵的引发下,使丙烯酸在羧甲基壳聚糖的分子链上接枝聚合,以N,N’-亚甲基双丙烯酰胺为交联剂,并加入NaHCO₃为致孔剂,制得具有大孔结构的羧甲基壳聚糖接枝聚丙烯酸（CMCTS-g-PAA）高吸水性树脂。采用Voigt模型成功地对树脂的溶胀动力学进行了模拟,并确定了模型中的各参数在高吸水树脂溶胀过程中的意义。通过溶胀动力学及SEM的表征,研究讨论了致孔剂的加入量,致孔剂加入时间与聚合物的凝胶过程的配合等因素对所合成树脂的表面形貌和吸水速率的影响。     

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.     

基于聚合物发泡过程参数模拟的冰箱门体成型层分析

针对制冷类产品中隔热发泡层结构的设计问题,分析聚合物发泡过程的物理特性,提出了基于发泡过程参数演化的发泡层结构仿真模型,用于指导相关冰箱门体结构优化设计。结合聚合物发泡工艺的理论过程分析,提取并分析发泡层结构相关联的物理参数演化规律,提出其相应函数表达。通过文献调研及发泡工艺实际模拟实验,分别获取其相关物理参数的统计数据及实际表达,并基于CFD-UDF构建了发泡过程仿真模型,用于冰箱门体结构模拟分析。最后,结合某款冰箱门体结构,分析其发泡层成型状态及过程参数,验证了该发泡过程CFD-UDF仿真模型的有效性。     

Effect of branched PP content on the physical properties and cell growth during foaming of TPOs

Linear/branched PP blends at various ratios were used as the matrix for thermoplastic olefin (TPO) compounds, containing an ethylene–octene copolymer dispersed phase. A detailed investigation of the physical properties of these blends revealed that addition of branched PP (BPP) resulted in improved stiffness and flexural properties. Given that the phase morphology of the blends and the interfacial tension between their components remained virtually unaffected, these improvements are attributed to the higher stiffness of the BPP‐containing matrices. Talc‐filled TPOs containing branched PPs exhibited further improvements in the stiffness and flexural properties. An investigation into the bubble growth process during foaming using a batch foaming simulation system revealed that the presence of BPP resulted in a slight delay in cell nucleation, whereas the rate of bubble growth was not significantly altered. © 2008 Wiley Periodicals, Inc. J Appl Polym Sci, 2008