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.

Healthcare and the Common Good: Restructuring the Economy of Medical Knowledge through Communitarian Political Theory

The pharmaceutical industry wields disproportionate power and control within the medical economy of knowledge where the desire for profit considerably outweighs health for its own sake. Utilizing the theoretical tools of political philosophy, this project restructures the economy of medical knowledge in order to lessen the oligarchical control possessed by the pharmaceutical industry. Ultimately, this project argues that an economy of medical knowledge structured around communitarian political theory lessens the current power dynamic without taking an anti-capitalist stance. Arising from the core commitments of communitarian-liberalism, the production, distribution, and consumption of medical knowledge all become guided processes seeking to realize the common good of quality healthcare. This project also considers two other theoretical approaches: liberalism and egalitarianism. A Medical knowledge economy structured around liberal political theory is ultimately rejected as it empowers the oligarchical status quo. Egalitarian political theory is able to significantly reduce the power imbalance problem but simultaneously renders inconsequential medical knowledge; therefore, it is also rejected.