A Refined Approach to Bubble Nucleation and Polymer Foaming Process: Dissolved Gas and Cluster Size Effects
✍ Scribed by James G. Lee; Raymond W. Flumerfelt
- Publisher
- Elsevier Science
- Year
- 1996
- Tongue
- English
- Weight
- 500 KB
- Volume
- 184
- Category
- Article
- ISSN
- 0021-9797
No coin nor oath required. For personal study only.
✦ Synopsis
the primary phase, g is the surface tension, m is the mass A refined approach to bubble nucleation is presented and apof a gas molecule, W crit is the critical work of formation for plied to polymer foaming process. The integral overall energy balthe cluster with radius R, k B is the Boltzmann constant, and ance and the integral Clausius-Duhem inequality are used to ana-T is the temperature. The work of formation W for a spherical lyze a bubble nucleation experiment. The computation of longcluster of radius R is given as (5-7) range intermolecular potential results in expressions for surface tension, work, and critical work for cluster formation, as functions of the Hamaker constant, molecular and/or repeat unit interaction
distance, molar fractions of each component, and cluster radius. The variation of surface tension with cluster size, temperature, and pressure is determined in terms of well-known macroscopic properties and compared with available experimental data. ᭧ 1996 Here g is the general surface tension (i.e., it may vary with Academic Press, Inc.
the cluster size), P (D) is pressure in the dispersed phase, and Key Words: bubble nucleation; polymer foaming; surface ten-P (C) is pressure in the continuous phase. In this classical sion; intermolecular potential; intermolecular force; cluster size representation, the critical cluster is the one at which the effect; dissolved gas effect.
work of formation is a maximum, i.e., W crit in Eq. [1].
With the increasing refinement of experimental techniques, the classical nucleation theory was found to be
2. HOMOGENEOUS BUBBLE NUCLEATION
Consider a container of fluid that is sealed with a piston Here E is a coefficient (generally of the order of one), N is the number of gas molecules dissolved per unit volume of which maintains a constant pressure. The container is submerged in an isothermal bath. Initially, we have a continuous phase occupying the entire region in the system at tempera-1 To whom correspondence should be addressed. Present address: ture T 0 and pressure P (C) (Fig. 1). The temperature T(t)