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.     

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     

Prediction of cellular structure in free expansion of viscoelastic media

A systematic model is presented for a free expansion polymer foaming process that includes simultaneous nucleation and bubble growth. An influence volume approach, which couples nucleation and bubble growth, is used to account for the limited supply of dissolved gas. The melt rheology is described using the Larson viscoelastic model. The initial conditions are obtained at the upper bound of critical cluster size under conditions of elastic deformation. The resulting set of equations are solved using a combination of numerical techniques. A parametric study is conducted to examine the effects of key process variables on bubble growth, nucleation, and final bubble size distribution. It shows that the factors influencing nucleation and growth affect the ultimate bubble sizes and their distribution. The Gibbs number, a dimensionless measure of the barrier to overcome for nucleation, has the strongest impact on the cellular structure of the foam. © 1998 John Wiley & Sons, Inc. J Appl Polym Sci 67:1353–1368, 1998     

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     

The effect of bubble size on oil-water separation efficiency for a novel oil-water separation column

Bubble size is a key factor in froth flotation for oil-water separation. In this paper, the bubble size which impacts on oil removal efficiency for a novel oil-water separation column was researched systematically. The bubble size distribution was researched by using the photographic method and Matlab software. In addition, several operating parameters which impact on the bubble size were investigated, including circulating pressure, aeration rate, and the foaming agent. Based on the results of experimental data and image analysis, the frother consumption and aeration rate has important influence on the bubble size. The bubble size can be controlled by adjusting the operation conditions including the circulating pressure, aeration rate, and the frother consumption. The optimum operating conditions for the oil-water separation column were determined. Furthermore, the mathematical model of oil removal efficiency for the oil-water separation column was established.     

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 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.     

PP/改性纳米CaCO3/AC复合挤出发泡体系泡孔形态预测模型的研究

以AC发泡剂对聚丙烯(PP)/改性纳米CaCO3发泡体系进行挤出发泡,对发泡体系进行单因素轮换法实验,通过观察纵截面泡孔形态,分析各工艺参数对泡孔形态的影响规律,利用正交实验与实验统计软件相结合的方法对实验数据进行回归,得到泡体平均直径、泡孔面积比的预测模型,并进行了实验验证.通过模型预测最佳的加工参数范围,可对实验和...     

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。     

吹气发泡法制备闭孔泡沫铝发泡过程的三维数值模拟

吹气发泡法制备闭孔泡沫铝的过程实质上是搅拌流场中复杂的两相流动过程,应用计算流体力学方法分析由倾斜轴倾斜叶片引起的发泡熔池内气液两相强旋湍流流动过程. 在双流体模型基础上引入多重参考系法描述搅拌两相流场,通过分析相间相互作用及湍流模型进行封闭. 解气泡数密度函数的输运方程来分析气泡聚合和破碎引起的气泡尺寸变化. 应用体积积分的方法,计算平均及局部气含率及气泡直径. 考察了桨叶转速及气体流率对气泡直径及其分布的影响. 结果显示,气含率随桨叶转速和气体流率增加而增大;气泡直径随气体流率增加而增大,随桨叶转速增大而减小.     

Theoretical and visual study of bubble dynamics in foam injection molding

This article presents an experimental observation and a theoretical prediction of bubble dynamics in foam injection molding process with a main focus on the cell collapse phenomenon under pressure. Using a visualizing setup, cell growth behavior under a nonisothermal condition was monitored. In conjunction with the growth behavior, dynamics of cell collapse under different pressures and the effect of growing time on collapse behavior and final cell size were studied. Theoretical simulation of bubble behavior included power law model, which predicted bubble dynamics during foaming process. The results show that collapse phenomenon strongly depends on both exerted holding pressure and growth time. The presented model can also give a reasonable prediction of growth and collapse of cells and could give insight to control of cell size in injection foaming process. POLYM. ENG. SCI., 2010. © 2009 Society of Plastics Engineers     

Visual observation and numerical studies of polymer foaming behavior of polypropylene/carbon dioxide system in a core‐back injection molding process

Thermoplastic foaming within a mold cavity was visualized as it was conducted in an 85‐ton core‐back injection‐molding machine. The core‐back molding process moved a section of the mold just after injecting a molten polymer into the cavity, quickly reducing the pressure to enhance the bubble nucleation. The foaming behavior during core‐back was observed directly through the glass windows of the mold. In the experiments, impact copolymer polypropylene was foamed with carbon dioxide. The effects of the gas concentration and the core‐back rate on bubble nucleation and growth were investigated. It was experimentally confirmed that the bubbles disappeared when the cavity was fully packed and that bubble nucleation occurred when the mold plate was moved and the cavity pressure dropped. Faster core‐back rates and higher gas concentrations increased the number of bubbles while decreasing their size. To analyze the experimental results, a bubble nucleation and growth model was employed that was based on batch foaming. The numerical results were a reasonable representation of the experiments, and this study demonstrated the applicability of the conventional free foaming model to the industrial core‐back molding process. Many aspects of the foaming in the core‐back molding aresimilar to the behaviors observed by batch foaming. POLYM. ENG. SCI., 2011. © 2011 Society of Plastics Engineers     

影响泡沫玻璃泡径因素的数学分析

在实验的基础上应用数学分析方法,建立了较理想的泡沫玻璃的泡径和发泡剂粒径及发泡温度间的函数关系,对设计泡沫玻璃新品种有一定参考价值。     

Numerische Berechnung physikalischer Schäumungsprozesse auf unterschiedlichen Größenskalen

A simulation method for numerical calculation of physical foaming processes is presented. A micro‐scale model is used to predict the time‐dependent change in foam volume by describing the growth of a single foam bubble as a function of given process conditions. In order to visualize the three‐dimensional foam expansion at the macro scale, the calculated growth dynamics is integrated into a simulation model based on the finite volume method. The calculation procedure is validated using discontinuous and continuous foam experiments.     

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.     

Bubble growth model and its influencing factors in a polymer melt under nonisothermal conditions

Traditionally, in order to simplify the bubble growth process in a polymer melt, an isothermal model is typically used. In fact, the temperature of the polymer melt is changing during the foaming process. In order to accurately study the growth mechanism of bubbles in polymer melts, we build a physical and mathematical model of bubble growth in a polymer melt under nonisothermal conditions. The parameters of pressure, zero-shear viscosity, relaxation time, Henry's constant, diffusion coefficient, and surface tension were determined. The fourth-order Runge–Kutta method was used to solve the nonisothermal bubble model in the polymer melt. A computational program is developed to find the dimensional change during the bubble growth process, and the correctness of the model is verified. The nonisothermal growth mechanism of and factors influencing bubbles in the polymer melt are analyzed. Combined with the design of experiment (DOE) analysis method, the transfer function of the bubble radius and the maximum growth rate of bubbles with the process parameters were obtained, such as cooling rate, system pressure, and gas concentration. The results show that system pressure has the most significant effect on bubble growth. At the same time, a bubble growth prediction model is built, which can be used to predict the growth of bubbles. Through optimization analysis, it can be used to control the growth of bubbles. © 2018 Wiley Periodicals, Inc. J. Appl. Polym. Sci. 2019 , 136, 47210.     

Bubble growth mechanism in carbon foams

The present work is a numerical study to predict the growth mechanism of a non-spherical bubble assisted for a carbon foam fabrication process. An approach for two dimensional non-spherical mass-diffusion controlled bubble growth in an isothermal Newtonian liquid of infinite extent is considered. Using the two dimensional unsteady form of the equations governing the conservation of mass and momentum, bubble growth is solved as a function of time using a fixed-grid sharp interface finite volume method. A comparative study is performed by considering previous cases of study and shows good agreement, which reflects the validity of the present model. A parametric study highlighting the effects of the non-spherical growth of the bubble is performed in order to emphasize how controlled bubble growth can be achieved. In each case a change in a particular parameter resulted in a distinct change of the bubble shape.     

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     

Open-celled microcellular foaming and the formation of cellular structure by a theoretical pattern in polystyrene

An open-celled structure was produced using polystyrene and supercritical carbon dioxide in a novel batch process. The required processing conditions to achieve open-celled structures were predicted by a theoretical model and confirmed by the experimental data. The theoretical model predicts that at least a saturation pressure of 130 bar and a foaming time between 9 and 58 s are required for this system to produce an open-celled structure. The foaming temperature range has been selected to be higher than the polymer glass transition temperature yet not higher than a temperature limit where the gas starts leaving the system. The experimental results in the batch foaming process verified the model substantially. The SEM pictures showed the presence of pores between the cells, and the mercury porosimetry test results verified the overall open-celled structure. Experimental results also showed that by increasing the saturation pressure and the foaming temperature, there was a drop in the time required for open-celled structure formation. At saturation pressure of 130 bar, foaming temperature of 150 °C and a foaming time of 60 s, open-celled microcellular polystyrene foams were obtained using supercritical CO₂ in the batch process. Based on the results, a schematic diagram, depicting the process of foam structure formation from nucleation to bubble coalescence and gas escape from polymer, was proposed. Theoretical calculations showed that by increasing foaming time, cell size was increased and cell density was reduced and the experimental results verified this prediction.     

采用压力脉动信号分析法对三相流化床流型划分的研究

本文采用床层压力脉动信号的计算机在线分析方法进行了并流三相流化床流型转变过程的研究.为了查明操作条件(气速、液速)和颗粒物性(密度、粒径)对转变过程的影响,进行了一系列的实验工作.最后得到在空气-水-颗粒的三相流化体系内,从气泡合并区向气泡分散区转变的判别式:在R_(eg)p_(?)/p_l·(D_T/d_p)~(-1.589)·Fr_g~(-0.1)≥1.01×10~5条件下如果Re_(lc)(U_(mf)~(?)/U_(mf)~())~(0.388)·Re_U_(mf)~(?)~(-0.461)·((p_(?)-p_l)/p_l)~(-0.478)≥13.4则流化床处于分散区操作,反之,则处于合并区操作状态.