A simulation of simultaneous bubble nucleation and growth was performed for polyurethane/CO2 physical foaming process. The single-factor and comprehensive effects of viscoelastic properties, Henry’s constant, CO2 diffusion coefficient and surface tension on the cell morphology were numerically analyzed. The results show that the cell density of PU foam (N0) increases and its average cell diameter (Dv) reduces with increased Henry’s constant and slower gas diffusion. Both N0 and Dv reduces with the curing degree (α). In addition, the effects of α and foaming conditions on the cell structure were experimentally investigated. With an increase of α at foamable range, Dv decreases continuously and N0 increases first and then declines. With increasing saturation pressure and depressurization rate or decreasing temperature, N0 increases and Dv reduces. There is an intrinsic correlation between the simulated and experimental variables, and the results of the simulation and experiment are generally consistent.
Di MaioEKiranE.Foaming of polymers with supercritical fluids and perspectives on the current knowledge gaps and challenges. J Supercrit Fluid2018; 134: 157–166.
2.
GwonJGKimSKKimJH.Sound absorption behavior of flexible polyurethane foams with distinct cellular structures. Mater Design2016; 89: 448–454.
3.
ItoASembaTTakiK, et al. Effect of the molecular weight between crosslinks of thermally cured epoxy resins on the CO2-bubble nucleation in a batch physical foaming process. J App Polym Sci2014; 131: 40407.
4.
YangZLiuTHuD, et al. Foaming window for preparation of microcellular rigid polyurethanes using supercritical carbon dioxide as blowing agent. J Supercrit Fluid2019; 147: 254–262.
5.
EngelsHWPirklHGAlbersR, et al. Polyurethanes: versatile materials and sustainable problem solvers for today's challenges. Angew Chem Int Ed Engl2013; 52: 9422–9441.
6.
EckertCAKnutsonBLDebenedettiPG.Supercritical fluids as solvents for chemical and materials processing. Nature1996; 383: 313–318.
7.
BaoJBLiuTZhaoL, et al. A two-step depressurization batch process for the formation of bi-modal cell structure polystyrene foams using scCO2. J Supercrit Fluid2011; 55: 1104–1114.
8.
LiD-CLiuTZhaoL, et al. Foaming of linear isotactic polypropylene based on its non-isothermal crystallization behaviors under compressed CO2. J Supercrit Fluid2011; 60: 89–97.
9.
ChenJLiuTYuanWK, et al. Solubility and diffusivity of CO2 in polypropylene/micro-calcium carbonate composites. J Supercrit Fluid2013; 77: 33–43.
10.
HuDYanLLiuT, et al. Solubility and diffusion behavior of compressed CO2 in polyurethane oligomer. J Appl Polym Sci2019; 136: 47100.
11.
HopmannCLatzS.Foaming technology using gas counter pressure to improve the flexibility of foams by using high amounts of CO2 as a blowing agent. Polymer2015; 56: 29–36.
12.
FerklPKrškováIKosekJ.Evolution of mass distribution in walls of rigid polyurethane foams. Chem Eng Sci2018; 176: 50–58.
13.
TakiK.Experimental and numerical studies on the effects of pressure release rate on number density of bubbles and bubble growth in a polymeric foaming process. Chem Eng Sci2008; 63: 3643–3653.
14.
Pérez-TamaritSSolórzanoEMoksoR, et al. In-situ understanding of pore nucleation and growth in polyurethane foams by using real-time synchrotron X-ray tomography. Polymer2019; 166: 50–54.
15.
BlanderMKatzJL.Bubble nucleation in liquids. AIChE J1975; 21: 833–848.
16.
LeungSNParkCBXuD, et al. Computer simulation of bubble-growth phenomena in foaming. Ind Eng Chem Res2006; 45: 7823–7831.
17.
LeungSNWongAWangLC, et al. Mechanism of extensional stress-induced cell formation in polymeric foaming processes with the presence of nucleating agents. J Supercrit Fluid2012; 63: 187–198.
18.
LiYYaoZChenZH, et al. Numerical simulation of polypropylene foaming process assisted by carbon dioxide: bubble growth dynamics and stability. Chem Eng Sci2011; 66: 3656–3665.
19.
TakiKTabataKKiharaS-i, et al. Bubble coalescence in foaming process of polymers. Polym Eng Sci2006; 46: 680–690.
20.
TakiKNakayamaTYatsuzukaT, et al. Visual observations of batch and continuous foaming processes.J Cell Plast2003; 39: 155–169.
21.
AzimiHJahaniD.The experimental and numerical relation between the solubility, diffusivity and bubble nucleation of supercritical CO2 in polystyrene via visual observation apparatus. J Supercrit Fluid2018; 139: 30–37.
22.
ShafiMFlumerfeltR.Initial bubble growth in polymer foam processes. Chem Eng Sci1997; 52: 627–633.
23.
ShafiMJoshiKFlumerfeltR.Bubble size distributions in freely expanded polymer foams. Chem Eng Sci1997; 52: 635–644.
24.
SunYUedaYSuganagaH, et al. Experimental and simulation study of the physical foaming process using high-pressure CO2. J Supercrit Fluid2016; 107: 733–745.
25.
DeviDARajuKAminabhaviT.Synthesis and characterization of moisture‐cured polyurethane membranes and their applications in pervaporation separation of ethyl acetate/water azeotrope at 30°C. J Appl Polym Sci2007; 103: 3405–3414.
26.
Al-MoameriHZhaoYGhoreishiR, et al. Simulation blowing agent performance, cell morphology, and cell pressure in rigid polyurethane foams. Ind Eng Chem Res2016; 55: 2336–2344.
27.
SeoDYounJR.Numerical analysis on reaction injection molding of polyurethane foam by using a finite volume method. Polymer2005; 46: 6482–6493.
28.
NiyogiDKumarRGandhiKS.Modeling of bubble-size distribution in water and Freon co-blown free rise polyurethane foams. J App Polym Sci2014; 131: 40745.
29.
ArefmaneshAAdvaniSG.Diffusion-induced growth of a gas bubble in a viscoelastic fluid. Rheol Acta1991; 30: 274–283.
30.
FengJJBerteloCA.Prediction of bubble growth and size distribution in polymer foaming based on a new heterogeneous nucleation model. J Rheol2004; 48: 439–462.
31.
ShafiMALeeJGFlumerfeltRW.Prediction of cellular structure in free expansion polymer foam processing. Polym Eng Sci1996; 36: 1950–1959.
32.
KumarV.Process synthesis for manufacturing microcellular thermoplastic parts: a case study in axiomatic design. Boston: Massachusetts Institute of Technology, 1988.
33.
BaoJBLiuTZhaoL, et al. Oriented foaming of polystyrene with supercritical carbon dioxide for toughening. Polymer2012; 53: 5982–5993.
34.
MacoskoCWMilleDR.A new derivation of average molecular weights of nonlinear polymers. Macromolecules1976; 9: 199–206.
35.
YounJRParkH.Bubble growth in reaction injection molded parts foamed by ultrasonic excitation. Polym Eng Sci1999; 39: 457–468.
36.
DimierFSbirrazzuoliNVergnesB, et al. Curing kinetics and chemorheological analysis of polyurethane formation. Polym Eng Sci2004; 44: 518–527.
37.
LucioBFuenteJLDL.Kinetic and thermodynamic analysis of the polymerization of polyurethanes by a rheological method. Thermochim Acta2016; 625: 28–35.
38.
MalkinSAYBolgovSABegishevVP, et al. Evolution of viscoelastic properties of polyurethane in the course of curing. Rheol Acta1992; 31: 345–350.
39.
Zhou ChenYZTaoLZhimeiX, et al. Polyurethane isothermal curing reaction reinforced by high pressure carbon dioxide. Chem React Eng Technol2018; 34: 334–341.
40.
O'BrienDJMatherPTWhiteSR.Viscoelastic properties of an epoxy resin during cure. J Compos Mater2001; 35: 883–904.
41.
HuDLyuJXLiuT, et al. Solvation effect of CO2 on accelerating the curing reaction process of epoxy resin. Chem Eng Process2018; 127: 159–167.
42.
XuZMJiangXLLiuT, et al. Foaming of polypropylene with supercritical carbon dioxide. J. Supercrit Fluid2007; 41: 299–310.
