Multi-scale modelling of expanding polyurethane foams: Coupling macro- and bubble-scales

Ferkl, Pavel; Karimi, Mohsen; Marchisio, Daniele; Košek, Juraj

doi:10.1016/j.ces.2016.03.040

Cited by 33 publications

(32 citation statements)

References 19 publications

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“…The numerical simulation of bubble growth and stability during polymer foaming is based on the well‐known cell model . Some assumptions in this model and the principles of transfer processes (i.e., momentum transfer, mass transfer, and etc.)…”

Section: Numerical Simulation Of Bubble Growth Dynamics and Stabilitymentioning

confidence: 99%

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

Chen

Liu

et al. 2019

J of Applied Polymer Sci

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Reactive extrusion was used to modify virgin polyamides 6 (v-PA6) and to prepare chain extended PA6 (CE-PA6) and longchain 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 CO 2 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 CO 2 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.

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Section: Numerical Simulation Of Bubble Growth Dynamics and Stabilitymentioning

confidence: 99%

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

Chen

Liu

et al. 2019

J of Applied Polymer Sci

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“…In other words, the initial amount of blowing agent is soluble in the reacting mixture and it immediately evaporates once it reaches the supersaturated concentration in the mixture. This could be remedied by integrating a meso-scale model for bubbles growth due to evaporation of blowing agents into this modeling platform, an example of such an approach is presented elsewhere (Ferkl et al, 2016).…”

Section: Macro-scale Cfd Modelmentioning

confidence: 99%

“…For instance, we applied a simplified diffusion controlled model for the bubble growth rates. However, later we addressed this by coupling a detailed bubble-scale model with the macro-scale CFD code and showed the benefits of applying a multiscale approach on the accuracy of the numerical predictions (Ferkl et al, 2016).…”

Section: Introductionmentioning

confidence: 99%

Bridging the gap across scales: Coupling CFD and MD/GCMC in polyurethane foam simulation

Karimi

Marchisio

Laurini

et al. 2018

Chemical Engineering Science

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This work presents a multi-scale approach to reacting and expanding polyurethane (PU) foams modeling and simulation. The modeling strategy relies on two pillars: an atomistic model (molecular dynamics (MD)/Grand Canonical Monte Carlo (GCMC)) that provides liquid mixture density and reactant solubility and a continuum model (CFD) in which the expansion characteristics of the foam is modeled exploiting the results of the atomistic simulations. The resulting coupled model is validated for two different PU systems applied in four batches with chemical and physical blowing agents. The results demonstrate the efficacy and reliability of the developed model in the simulation of different PU foam properties such as apparent density and temperature evolutions.

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“…1 3 87 Page 2 of 11 be used to derive models which characterize the droplet size and distribution macroscopically (Ferkl et al 2016).…”

Section: Introductionmentioning

confidence: 99%

Head-on collision of Newtonian drops in a viscoelastic medium

Mitrias

Hulsen

Anderson

2019

Microfluid Nanofluid

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Depending on the application, one needs to either stabilize or destabilize the interfacial properties of an emulsion. An aspect of the dynamics that governs the stability of emulsions in general is the drainage time of the film that is formed when two drops collide. In this work, we study the effect that viscoelasticity of the matrix fluid has on this drainage time of two Newtonian drops that perform a head-on collision under an applied macroscopic extensional rate. For the modeling of the viscoelastic matrix material, the Giesekus model is chosen. A cylindrical coordinate system is applied with imposed axisymmetry and the resulting equations are solved using fully resolved numerical simulations employing a finite element discretization. Our results show that viscoelasticity reduces the drainage time, which is a combined effect of three different stages.

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Multi-scale modelling of expanding polyurethane foams: Coupling macro- and bubble-scales

Cited by 33 publications

References 19 publications

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

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

Bridging the gap across scales: Coupling CFD and MD/GCMC in polyurethane foam simulation

Head-on collision of Newtonian drops in a viscoelastic medium

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