Prediction of cellular structure in free expansion of viscoelastic media

Abstract

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.

Tunable Microcellular Morphologies from Poly(ferrocenylsilane) Ceramic Precursors Foamed in Supercritical CO2

“…A narrower cell size distribution is likely to be expected when homogeneous nucleation rates are increased by lowering surface tension or bubble growth rates, for instance. [49] In pressure-quench foaming such as that employed here, an increase in CO 2 pressure exacerbates the thermodynamic instability generated upon rapid depressurization, thereby increasing the number of stable nucleation sites formed and, thus, the final pore cell density.…”

Modeling Foam Growth in Thermoplastics

“…3). [12,13,23] The functional form is defined by setting the initial and final cell radius and the expansion time interval. Subsequently, for each arbitrarily selected time segment, the extension rate can be calculated for which the transient biaxial extensional viscosity can be obtained from the Lodge model.…”

Dynamics of gas bubble growth in oil-refrigerant mixtures under isothermal depressurization

“…For dispersed systems such as two-phase bubbly and foam flows, non-equilibrium models generally also take into account nucleation and growth of individual gas bubbles in the liquid phase. These models have been widely employed to describe the growth of bubble clusters and foam growth in polymers and viscoelastic fluids (Amon and Denson, 1984;Arefmanesh and Advani, 1991;Arefmanesh et al, 1992;Joshi et al, 1998) and in magmatic melts (Proussevitch et al, 1993;Proussevitch and Sahagian, 1996). ABCM In spite of the significant number of papers in related fields, the physical mechanisms that govern bubble growth in oilrefrigerant mixtures have never been studied from their first principles.…”