Bubble size distributions in freely expanded polymer foams

Shafi, Muhammad Aamir; Joshi, Kishore; Flumerfelt, Raymond W.

doi:10.1016/s0009-2509(96)00433-2

Cited by 118 publications

(118 citation statements)

References 29 publications

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“…We then used the following equation to transfer the density into an expansion ratio. (The non-foaming material density for IP-004 is 0.8636 g/cm 3 . )…”

Section: Experimental Design To Correlate the Temperature Time Curve mentioning

confidence: 98%

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Designing Experimental Methods to Predict the Expansion Ratio of EVA Foam Material and Using Finite Element Simulation to Estimate the Shoe Expansion Shape

2012

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Correcting and quickly predicting the shrink mold shape in the sport shoe industry for direct injection-expanded foam molding manufacturing procedures are critical. Traditional methods rely on the engineer to guess the initial shrink mold shape when manufacturing the actual shrink mold and shoe sole product. The artificial experience is then used to compare the original large 3D model with the shoe sole product to modify the shrink mold, requiring numerous iterations to complete. In this study, we designed a series of rectangular specimens varying with z-thickness, and measured the density in the middle location of these specimens and transferred them into an expansion ratio. Furthermore, we performed a heat transfer simulation to determine the temperaturetime curve in these locations and correlated the expansion ratio with the curve. We then used the heat expansion finite element method to simulate the expansion behavior. Finally, we used the actual shoe sole to verify our algorithm; with the precision meeting the shoe sole requirement. Therefore, this algorithm can reduce the number of iterations.

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“…We then used the following equation to transfer the density into an expansion ratio. (The non-foaming material density for IP-004 is 0.8636 g/cm 3 . )…”

Section: Experimental Design To Correlate the Temperature Time Curve mentioning

confidence: 98%

“…3,4) Furthermore, the expansion ratio functions according to the thickness 5) or the temperature distribution.…”

Section: Introductionmentioning

confidence: 99%

Designing Experimental Methods to Predict the Expansion Ratio of EVA Foam Material and Using Finite Element Simulation to Estimate the Shoe Expansion Shape

2012

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“…[14][15][16][17] In this study, the bubble growth model was based on the Rosner and Epstein integration model. 14) They coupled the force balance equation of pressure difference between gas pressure and pressure of matrix and mass transfer of single bubble.…”

Section: Bubble Growthmentioning

confidence: 99%

A Simplified Bubble Nucleation, Growth and Coalescence Model for Coke Production Process

Taki

Hayashizaki

Fukada³

2014

ISIJ Int.

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Coke production process, which involves gas generation, cross-linking, gas foaming as well as solidification phenomena, is extremely complex and is difficult to model them without simplification. In this study, a simple phenomenological model was developed based on a gas foaming simulation model of polymer foaming, which enabled us to simulate the number density of bubbles and their distributed size. The model was extended to account their kinetics of bubble nucleation, growth and coalescence in nonisothermal chemical reactions of gas generation and cross-linking. The bubbles size and morphology obtained from the numerical simulation of two different coals agreed with the pictures of the experiment qualitatively. Five different coals were investigated to understand the relationship between the kinetic and final morphology of coke.

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“…Finally, note that this space-time approach makes it necessary to integrate over the time interval [t, t + t] the mixed formulation (9). Here, the velocity and the pressure fields are chosen constant over each time interval.…”

Section: A Mesh R-adaptation Techniquementioning

confidence: 99%

“…The mixed weak formulation (9) can easily be reformulated by substituting p g for p g i . The differential form of the ideal gas law p g | g i | g i | = constant can be expressed as…”

Section: J Bruchon and T Coupezmentioning

confidence: 99%

A numerical strategy for the direct 3D simulation of the expansion of bubbles into a molten polymer during a foaming process

Bruchon

Coupez

2007

Numerical Methods in Fluids

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International audienceIn the framework of the foam process modelling, this paper presents a numerical strategy for the direct 3D simulation of the expansion of gas bubbles into a molten polymer. This expansion is due to a gas overpressure. The polymer is assumed to be incompressible and to behave as a pseudo-plastic fluid. Each bubble is governed by a simple ideal gas law. The velocity and the pressure fields, defined in the liquid by a Stokes system, are subsequently extended to each bubble in a way of not perturbing the interface velocity. Hence, a global velocity-pressure-mixed system is solved over the whole computational domain, thanks to a discretization based on an unstructured first-order finite element. Since dealing with an Eulerian approach, an interface capturing method is used to follow the bubble evolution. For each bubble, a pure advection equation is solved by using a space-time discontinuous-Galerkin method, coupled with an r-adaptation technique. Finally, the numerical strategy is achieved by considering a global mesh expansion motion, which conserves the amount of liquid into the computational domain during the expansion. The expansion of one bubble is firstly considered, and the simulations are compared with an analytical model. The formation of a cellular structure is then investigated by considering the expansion of 64 bubbles in 2D and the expansion of 400 bubbles in 3D

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Bubble size distributions in freely expanded polymer foams

Cited by 118 publications

References 29 publications

Designing Experimental Methods to Predict the Expansion Ratio of EVA Foam Material and Using Finite Element Simulation to Estimate the Shoe Expansion Shape

Designing Experimental Methods to Predict the Expansion Ratio of EVA Foam Material and Using Finite Element Simulation to Estimate the Shoe Expansion Shape

A Simplified Bubble Nucleation, Growth and Coalescence Model for Coke Production Process

A numerical strategy for the direct 3D simulation of the expansion of bubbles into a molten polymer during a foaming process

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