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.

EFFECTS OF BUBBLE-FACILITATED VOC TRANSPORT FROM LNAPL SMEAR ZONES ON VAPOR INTRUSION

Light non-aqueous phase liquid (LNAPL) sources can pose a significant threat to indoor air through vapour intrusion (VI). Most conceptual and numerical models of VI assume that the transport of volatile organic compounds (VOCs) is a diffusion-limited process. Recently, alternate conditions have been identified that could lead to faster transport, including the presence of preferential pathways and methanogenic gas production. In this study, an additional mechanism that could lead to faster transport was investigated: bubble-facilitated VOC transport from LNAPL smear zones. A laboratory investigation was preformed using pentane in one-dimensional laboratory columns and two-dimensional visualization experiments. Results of the column experiments showed that average VOC mass fluxes in the bubble-facilitated columns were over two orders of magnitude greater than in the diffusion-limited columns. In addition, the flux signal was intermittent, consistent with expectations of bubble-facilitated transport as bubbles expand, mobilize and are released to the vadose zone at various times during the test. The results from the visualization experiments showed gas fingers growing and mobilizing over time, which supports the findings of the column experiments. In conclusion, these results demonstrate the potential for bubble-facilitated VOC transport to affect mass transfer in LNAPL smear zones, and lead to increased indoor air concentrations by VI.