Bubble Growth From First Principals

We consider the simplest relevant problem in the foaming of molten plastics, the growth of a single bubble in a sea of highly viscous Newtonian fluid, and without interference from other bubbles. This simplest problem has defied accurate solution from first principles. Despite plenty of research on foaming, classical approaches from first principles have neglected the temperature rise in the surrounding fluid, and we find that this oversimplification greatly accelerates bubble growth prediction. We use a transport phenomena approach to analyze the growth of a solitary bubble, expanding under its own pressure. We consider a bubble of ideal gas growing without the accelerating contribution from mass transfer into the bubble. We explore the roles of viscous forces, fluid inertia, and viscous dissipation. We find that bubble growth depends upon the nucleus radius and nucleus pressure. We begin with a detailed examination of the classical approaches (thermodynamics without viscous heating). Our failure to fit experimental data with these classical approaches, sets up the second part of our paper, a novel exploration of the essential decelerating role of viscous heating. We explore both isothermal and adiabatic bubble expansion, and also the decelerating role of surface tension. The adiabatic analysis accounts for the slight deceleration due to the cooling of the expanding gas, which depends on gas polyatomicity. We also explore the pressure profile, and the components of the extra stress tensor, in the fluid surrounding the growing bubble. These stresses can eventually be frozen into foamed plastics. We find that our new theory compares well with measured bubble behavior.

Cape Breton Provides Pointers for the Adjustment Programs Required by the Decline of the Old Economy (Working Paper 14)

The Cape Breton Development Corporation need not, should not, be dying in the way it is. “Devco” has been widely represented as a failure dragged out too long. In fact it had for a time considerable success in a role too difficult to be often attempted. The main failure was in the political will to stick to its purpose. This commentary is in three parts. The first, major section discusses the purpose of Devco and the policies that served the purpose quite well but were maintained for little more than a decade. It suggests that the benefits would have been greater if Devco had been started earlier in the period of postwar prosperity. The second section comments on the enfeeblement of Devco in the 1980s. The removal of its development function also weakened, and has eventually led to the abandonment of, Devco’s social purpose in the operation of coal mining. Third, a short epilogue pointing out that, while the Cape Breton case is extreme, there will be increasing need to moderate the socially disruptive consequences of accelerating economic change. There are lessons from the Devco experience: the longer remedial action is delayed, the more difficult and expensive it becomes, and the more necessary for its effectiveness is a steady political will.