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.

Development of An Enhanced Oil Sands Fluid Tailings Generation Model

Bitumen extraction from surface-mined oil sands results in the production of large volumes of Fluid Fine Tailings (FFT). Through Directive 085, the Province of Alberta has signaled that oil sands operators must improve and accelerate the methods by which they deal with FFT production, storage and treatment. This thesis aims to develop an enhanced method to forecast FFT production based on specific ore characteristics. A mass relationship and mathematical model to modify the Forecasting Tailings Model (FTM) by using fines and clay boundaries, as the two main indicators in FFT accumulation, has been developed. The modified FTM has been applied on representative block model data from an operating oil sands mining venture. An attempt has been made to identify order-of-magnitude associated tailings treatment costs, and to improve financial performance by not processing materials that have ultimate ore processing and tailings storage and treatment costs in excess of the value of bitumen they produce. The results on the real case study show that there is a 53% reduction in total tailings accumulations over the mine life by selectively processing only lower tailings generating materials through eliminating 15% of total mined ore materials with higher potential of fluid fines inventory. This significant result will assess the impact of Directive 082 on mining project economic and environmental performance towards the sustainable development of mining projects.