A study of the dynamics of foam growth: Analysis of the growth of closely spaced spherical bubbles

Abstract

A mathematical analysis of bubble growth in an expanding foam is presented. The analysis is based on a cell model whereby the foam is divided into spherical microscopic unit cells of equal and constant mass, each consisting of a liquid envelope (or shell) and a concentric spherical gas bubble. Expansion occurs by diffusion of a dissolved gas from the supersaturated envelope into the bubble. This cell model is capable of describing important qualitative features of a real system of numerous bubbles growing in close proximity to one another, and is intended as the building block of a global analysis of macroscopic foam expansion. The coupled algebraic and differential equations governing the growth of a cell are derived and solved numerically. Five dimensionless parameters are identified for the case of constant temperature and pressure outside the cell, and their effects are demonstrated through computer simulations of the system. Of these parameters, surface tension and initial radius prove to be of relatively little importance in the practical cases considered. The other parameters are the thermodynamic driving force, the cell mass (inversely proportional to the number density of bubbles), and the ratio of characteristic times for mass and momentum transport.

Three-dimensional Modeling Of Intumescent Behavior In Fires

“…[14] A more realistic calculation of bubble growth must include viscous resistance to bubble expansion, reaction chemistry, and response of local physical parameters and chemistry to the temperature. An approach that includes variations in the concentration of dissolved gas in the liquid with radius and time is described by Street et al [15] and Amon and Denson [16]. These models consider a solitary bubble expanding in a spherical cell containing a specific amount of liquid.…”

Relating vesicle shapes in pyroclasts to eruption styles

“…Although somewhat larger than the size of a critical bubble nucleus, this choice of initial bubble radius does not significantly affect the model results. The bubble growth model is based on established formulations (e.g., Amon and Denson 1984;Arefmanesh and Advani 1991;Proussevitch et al 1993) and H 2 O is the sole volatile phase considered, with a solubility based on Dixon (1997) and Liu et al (2005) for basaltic and silicic eruptions, respectively. The model couples Eq.…”

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

“…The neglect of inertia and the assumption of Newtonian behavior is imposed because the fluids are very viscous and the initial bubble growth rates are very small. Nevertheless, Amon and Denson [13] studied heat transfer analysis in polymer-gas systems in great detail. They found from reliable empirical correlations that the effective thermal conductivity of gas-filled polymeric bubble system changes by no more than a few percentage points over the whole range of foam densities.…”

“…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.…”