Bubble Growth From First Principles

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.

Heat Transfer in an Airfoil Shaped Strut

Thesis (Ph.D, Mechanical and Materials Engineering) -- Queen's University, 2016-08-31 09:37:50.239

A Study of the Microwave Carbothermic Reduction of Chromite Ore

Microwave reduction testing using activated charcoal as a reducing agent was performed on a sample of Black Thor chromite ore from the Ring of Fire deposit in Northern Ontario. First, a thermodynamic model was constructed for the system. Activity coefficients for several species were found in the literature. The model predicted chromium grades of 61.60% and recoveries of 93.43% for a 15% carbon addition. Next, reduction testing on the chromite ore was performed. Tests were performed at increasing power levels and reduction times. Testing atmospheres used were air, argon, and vacuum. The reduced product had maximum grades of 72.89% and recoveries of 80.37%. These maximum values were obtained in the same test where an argon atmosphere was used, with a carbon addition of 15%, optimal power level of 1200 W (actual 1171 W), and a time of 400 seconds. During this test, 17.53% of the initial mass was lost as gas, a carbon grade of 1.95% was found for the sintered core product. Additional work is recommended to try and purify the sintered core product as well as reduce more of the initial sample. Changing reagent schemes or a two step reduction / separation process could be implemented.