Prediction of cellular structure in free expansion polymer foam processing

Abstract

A model is presented for free expansion polymer foam processing that includes simultaneous nucleation and bubble growth. The nucleation model includes dissolved gas, small critical cluster size, elastic, and non‐ideal solution effects. An influence volume approach, which couples nucleation and bubble growth, is used to account for the limited supply of dissolved gas. 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.

Theoretical and experimental study of foaming process with chain extended recycled PET

“…However, the sample treated with 0.50% of PMDA appears as the best accomplishment between the two parameters. Since the polymer matrix was produced by a chain extension process, we considered the viscosity changing with the chain extender content using a polynomial fittings curve to interpolate the experimental data of η 0 vs. %PMDA [11] using Equation (1): Viscosity is related to temperature by an Arrhenius expression [23] and its variation with thermal profile is given by Equation (2): (2) where E a is an activation energy for viscous flow (94 000 J/mol [23]), η 0 and η 0T r are the zero shear viscosity corresponding to T and T r , respectively. The effectiveness of the foaming process is strongly dependent on the viscosity of the polymer matrix and, consequently, on concentration of the chain extender.…”

“…To achieve the latter, we must perturb one or more of these variables from the equilibrium state. The bubble growth is a strong function of the value of the initial radius, arbitrary choice of it can lead to considerable error [11].…”

“…In order to calculate the initial conditions for bubble growth, the approach used follows from Shafi et al [11]. Following this procedure, we get the initial conditions for bubble growth (see Equations (26) and (27)):…”

“…Therefore, researchers have attempted to optimize the foaming processes in order to produce high quality final products. One of the most used methods for the optimization of the manufacturing process, as well as final product quality is numerical modeling: a large number of mathematical models for bubble growth were presented in the literature [11][12][13][14][15][16][17][18][19][20][21]. Some models have been written for bubble growth assumed to be governed by mass transfer alone, while others assumed momentum transfer alone.…”

“…The goal of this work is twofold: -starting from preliminary results obtained in a previous work [7], the first goal of this work is to improve the process of extrusion foaming by chemical blowing agent (CBA) in order to produce high density foams from PET industrial scraps with a very low viscosity; -the second goal of this work is to develop a simple and useful tool which can help the companies in choosing foaming conditions without performing complicated laboratory tests. With this aim, according to literature indications [11,14,16], the growth of a spherical bubble in a polymeric liquid has been theoretically studied by taking into account both mass transfer phenomenon and viscous forces effect. Moreover, with the aim of predicting the morphology of the final foam, a non isothermal model was developed.…”