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.     

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     

Visual observation and numerical studies of N2 vs. CO2 foaming behavior in core‐back foam injection molding

We investigated , by visual observation and numerical calculations , the foaming behavior of polypropylene within a foam injection mold cavity with the environmentally benign physical blowing agents nitrogen (N₂) and carbon dioxide (CO₂) . An 85‐ton core‐back injection‐molding machine with temperature and pressure monitoring systems as well as a high‐pressure view cell was used for the investigation . The experiments showed a prominent difference in bubble nucleation and growth between N₂ and CO₂ injection foaming . Even when the weight concentration of N₂ dissolved in polymer was one‐third that of CO₂ , N₂ injection foaming provided a bubble number density that was 30 times larger and a bubble size that was one‐third smaller compared to CO₂ injection foaming . Classical bubble nucleation and growth models developed for batch foaming were employed to analyze these experimental results . The models reasonably explained the differences in injection foaming behavior between N₂ and CO₂ . It was clearly demonstrated by both experiments and numerical calculations that N₂ provides a higher number of bubbles with a smaller bubble size in foam injection molding compared to CO₂ as a result of the lower solubility of N₂ in the polymer and the larger degree of super‐saturation . POLYM. ENG. SCI., 2011. ©2011 Society of Plastics Engineers     

Microcellular PVC

Novel microcellular PVC foams with a very homogenous cell distribution and cell densities ranging from 10⁷ to 10⁹ cells/cm³ have been created using carbon dioxide as the nucleating gas. Microcellular foams with relative densities (density of foam divided by the density of unfoamed polymer) ranging from 0.15 to 0.94 have been produced. It was found that the bubble nucleation density has and Arrhenius-type dependence on temperature, while the average bubble diameter is relatively independent of the foaming temperature. A majority of the cell growth was found to occur in the early stages of foaming.     

Influence of Stress Whitening Pretreatment on Cell Structure,Foaming Behavior,and Mechanical Properties of AN/MAA Copolymer Foam

Stress whitening pretreatment on expandable acrylonitrile (AN)/methacrylic acid (MAA) copolymer was adopted to reduce the cell size of high-performance AN/MAA copolymer foam. The article studied the influence of stress whitening on cell structure and mechanical properties of AN/MAA copolymer foam, observed foaming behavior of stress- whitened copolymer by hot stage optical microscopy, and discussed its bubble nucleation mechanism. The results indicate that stress-whitening pretreatment makes the cell size of corresponding copolymer foam reduce sharply when stress whitening occurs. The cell size of copolymer foam with the density of 32 kg/m³ and 75 kg/m³ reduces from 1.07 mm to 0.37 mm and from 0.59 mm to 0.076 mm, respectively. It also causes residual fragmental films in cells. The defects created by stress whitening work first as a bubble nucleus, then expand and combine together as cells. Stress whitening creates new interface between gas and polymer phase and new volume of gas phase, reduces the change of interface free energy and volume free energy during bubble nucleation, and improves the bubble nucleation rate. The foaming phenomenon of stress whitened copolymer is in line with the defect nucleation mechanism. However, stress whitening pretreatment reduces the mechanical properties of final foam because of residual fragmental films.     

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     

热固性聚氨酯泡沫成核机理的研究

用自制的一套在线显微观测系统研究了热固性聚氨酯泡沫合成初期的气泡成核机理,探讨了聚氨酯发泡过程中搅拌速率(剪切力)、固体成核剂及反应前体系中溶解的气体量等工艺参数对气泡成核过程的影响。通过研究发现,热固性聚氨酯泡沫的成核机理为空气分散成核,在反应原料中添加固体成核剂、增加反应前体系中溶解的气体量以及提高物料的搅拌速率等都可以在一定程度上促进成核。     

Study of microcellular foaming of polystyrene aided with 45 kHz of ultrasound waves energy

ABSTRACT

In the microcellular foam plastic processing, cellular formation stage was being an essential stage since the nucleation and growth of the cell take place within. Based on classical nucleation theory, diminution of the free energy for nucleation, exponentially lead to an increase in the nucleation rate. This can be done by increasing the super-saturation level which achieved by heating the gas-saturated polymer. Hence, the advance is taken out by utilizing the ultrasound wave simultaneously with heating for foaming Polystyrene-scCO₂, which, not only to keep the super-saturation degree but also reduce the nucleation barrier. In this work, foaming was conducted under 45 kHz of ultrasound and varying the foaming temperature after saturating polystyrene with scCO₂. The results demonstrate, that foaming under ultrasound, the expansion ratio attained up to 1.5 fold, increase along with the heating temperature. Higher cell densities obtained with ultrasound applied at 50°C, however only slight difference can be seen, which about 10¹⁰–10¹¹ cell/cm³. From the cell size distribution results, cell distributed around 0.5–3.5 µm, with or without ultrasound applied for 60 and 70°C, Meanwhile at 50°C of foaming, the lowest cell size obtained with the aid of ultrasound in the range of 0.3–2.4 µm.     

CO2-原油体系发泡特性实验研究

为研究CO₂驱油田分离器内泡沫层产生及消除机理,设计了一套高压溶气原油泡沫测试系统,采用降压法研究了CO₂-原油体系的发泡特性。利用高速摄像机对泡沫产生至衰变的演变过程进行了记录,总结分析了不同降压阶段的气泡行为,研究了降压速率和搅拌速率对原油发泡特性的影响规律。研究发现,随压力降低,稳定存在气泡的直径增大,气泡位置上移,发泡行为更加剧烈;降压速率增加对降压阶段的发泡行为无明显影响,但会加剧稳定工作压力下的发泡行为;在转速小于等于120 r/min的条件下,搅拌速率增加会加剧降压阶段的发泡行为,但会加速稳定工作压力下的泡沫衰变。     

聚丙烯挤出发泡中的关键技术——发泡体系的性能和发泡机理研究

从聚丙烯挤出发泡体系的性能包括聚丙烯熔体的黏弹性、发泡剂的溶解度和扩散系数、聚丙烯的结晶行为和成核剂的性能以及聚丙烯挤出发泡的气泡成核机理和气泡增长机理系统介绍了聚丙烯挤出发泡中的一些关键技术。研究表明：具有显著应变硬化行为和高熔体强度的长链支化聚丙烯是获得优质PP发泡材料的前提；发泡剂的溶解度和扩散系数、聚丙烯的结晶行为和成核剂的种类和性能对发泡材料的泡孔密度、泡孔尺寸和泡孔尺寸分布有显著影响；气泡成核和气泡增长机理对于聚丙烯挤出发泡的配方设计、工艺确定和设备选型具有极其重要的意义。     

Modeling nanoporosity development in polymer films for low‐k applications

The bubble growth dynamics of a polymer supersaturated with CO₂ have been modeled for micron‐size films after nucleation. The model equations are based on the shell model of Arefmanesh, Advani, and Michaelides in which a nucleated bubble is surrounded by a finite concentric shell of polymer supersaturated with gas. Bubbles grow by mass transfer of dissolved gas from this shell. The model is extended to allow for diffusion of dissolved gas out of the shell in addition to diffusion into the bubble. A parametric analysis is performed to examine the effects of film thickness, temperature, diffusivity at the T_g and Henry's law constant. POLYM. ENG. SCI., 45:640–651, 2005. © 2005 Society of Plastics Engineers     

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     

The rate of gas evolution at electrodes—II. An estimate of the efficiency of gas evolution on the basis of bubble growth data

In Part I [Electrochim. Acta29, 167 (1984)] it was found from concentration data that at gas-evolving electrodes only a fraction of the dissolved gas formed is transformed into bubbles adhering to the electrode. The finding being contrary to the established view is now checked and confirmed by use of an independent method, namely by an analysis of available bubble growth data. Furthermore, the existence of two concentration differences controlling mass transfer of dissolved gas to the bulk of electrolyte and to adhering bubbles, respectively, is confirmed. Evidence is given of their interdependence.     

Four stages of the simultaneous mass and heat transfer during bubble formation and rise in a bubbly absorber

We studied nonisothermal absorption of a solvable gas from growing at an orifice and rising bubble when the concentration level of the absorbate in the absorbent is finite (finite dilution of absorbate approximation). It is shown that simultaneous heat and mass transfer at all stages of bubble growth and rise in a bubbly absorber can be described by a system of generalized equations of nonstationary convective diffusion and energy balance. Solutions of diffusion and energy balance equations are obtained in the exact analytical form. Coupled thermal effects during absorption and absorbate concentration level effect on the rate of mass transfer are investigated. It is found that the rate of mass transfer between a bubble and a fluid increases with the increase of the absorbate concentration level. The suggested approach is valid for high Peclet, Prandtl and Schmidt numbers. It is shown that for the positive dimensionless heat of absorption K thermal effects cause the increase of the mass transfer rate in comparison with the isothermal case. On the contrary, for negative K thermal effects cause the decrease of the mass transfer rate in comparison with the isothermal case. The latter effect becomes more pronounced with the increase of the concentration level of the absorbate in the absorbent. Theoretical results are consistent with the experiments of Kang et al. (Int. J. Refrigeration 25 (2002) 127) for absorption from ammonia gas bubbles rising in water and aqueous ammonia solutions.     

Mass transfer at a rotating ring—cone electrode and its use to determine supersaturation of gas evolved

The rotating ring-cone electrode (rrce) is a useful electrode assembly to study electrochemical reactions, in particular, when gas bubble formation occurs. The aim of this study is to characterize the rate of mass transfer from the bulk to the cone of a rrce, to determine its collection efficiency, N, in the presence or absence of gas bubble formation, and to investigate its usefulness for determination of the oxygen supersaturation at an oxygen-evolving electrode. The mass transfer coefficient for the cone of a rrce increases linearly with increasing rate of oxygen evolution, while N declines sharply with increasing rate of oxygen evolution on the cone. In the absence of gas bubble formation N is determined by the rrce geometry factors except the cone angle. The rrce can be used successfully to determine the supersaturation concentration of oxygen on an oxygen-evolving electrode. The absorption of dissolved oxygen by bubbles during the transport of supersaturated solution from the cone to the ring will be, however, a rather complicating factor.     

发泡塑料成型气泡膨胀热动力问题浅析

分析了发泡塑料气泡膨胀的热动力问题,从热动力学的角度阐明了气泡膨胀的条件、气泡膨胀的方向,分析得出气泡膨胀的动力是气液两相间的压强差,说明了气液两相间的质量传递和热量传递的根本原因,为进一步研究气泡膨胀的热动力学问题提供了理论基础。     

Visualization of bubble dynamics in foam injection molding

This article presents a visualization study on nonisothermal bubble growth and collapse in the foam injection molding process (FIM). Observation study can give more insight to the bubble growth in foaming process, especially in the challenging injection foaming process. In this study, besides the growth of bubbles, collapse of the bubbles was also observed which could provide knowledge to the final foam morphology. Cell growth vs. time was recorded and analyzed using a software‐equipped high speed camera. To investigate the cell collapse, various holding pressure was exerted on the gas‐charged molten polymer. The amount of holding pressure had noticeable effect on the rate of bubble collapse. © 2010 Wiley Periodicals, Inc. J Appl Polym Sci, 2010     

An extrusion die with rollers for foaming polymers

Operation of a flat slot die with rollers for the extrusion foaming of polymers, which has been originally designed by Benkreira et al. (Int. Polym. Proc., 19, 111 (2004)), is considered. The rotation of rollers makes it possible to independently control shear rate inside the die, in the bubble nucleation zone, thus influencing the cell density. In experimental studies of low‐density polyethylene foaming, the influence of the roller rotation speed on the cell density at variable isobutane and talc concentrations and die outlet area has been determined. Based on the fluctuational nucleation theory, a simple model is proposed for estimating the number density of supercritical nuclei formed at the nucleation stage and evaluating the cell density in the foam with allowance for bubble coalescence effects. POLYM. ENG. SCI., 54:96–109, 2014. © 2013 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     

Change in the critical nucleation radius and its impact on cell stability during polymeric foaming processes

The critical radius of cell nucleation is a function of the thermodynamic state that is uniquely determined by the system temperature, system pressure, and the dissolved gas concentration in the polymer/gas solution. Because these state variables change continuously during the foaming process, the critical radius varies simultaneously despite the traditional concept that it is a fixed thermodynamic property for a given initial state. According to classical nucleation theory, the critical radius determines the fate of the bubbles. Therefore, the change in the critical radius during foaming has a strong impact on the stability of foamed cells, especially in the production of microcellular or nanocellular foams. In this study, the continuous change in the critical radius is theoretically demonstrated under atmospheric pressure while bubbles are generated and expanded by the decomposition of a chemical blowing agent. The experimental results observed from the visualization cell are used to support the theoretically derived concept. Sustainability of the nucleated bubbles is also discussed by comparing the bubble size to the critical radius.