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.

Do Multiculturalism Policies Erode the Welfare State (Working Paper 33)

The past 30 years have witnessed a dramatic change in the way Western democracies deal with ethnic minorities. In the past, ethnic diversity was often seen as a threat to political stability, and minorities were subject to a range of policies intended to assimilate or marginalize them. Today, many Western democracies have adopted a more accommodating approach. This is reflected in the widespread adoption of multiculturalism policies for immigrant groups, the acceptance of territorial autonomy and language rights for national minorities, and the recognition of land claims and selfgovernment rights for indigenous peoples. We refer to these policies as “multiculturalism policies” or MCPs. The adoption of MCPs has been controversial, for two reasons. The first is a philosophical critique, which argues that MCPs are inherently inconsistent with basic liberal-democratic principles. Since the mid-1990s, however, this philosophical debate has been supplemented by a second argument: namely, that MCPs make it more difficult to sustain a robust Welfare State (hereafter WS). Critics worry that such policies erode the interpersonal trust, social solidarity and political coalitions that sustain a strongly redistributive WS. This paper reviews the reasons why critics believe that MCPs weaken political support for redistribution, and then examines empirically whether the adoption of MCPs has, in fact, been associated with erosion of the WS. This examination involves two steps: we develop a taxonomy of MCPs and classify Western democracies as “strong”, “modest” or “weak” in their level of MCPs. We then examine whether the strength of MCPs is associated with the erosion of the WS during the 1980s and 1990s. The evolution of the WS is measured through change in four indicators: social spending as a percentage of GDP; the redistributive impact of taxes and transfers; levels of child poverty; and the level of income inequality. We find no evidence of a consistent relationship between the adoption of MCPs and the erosion of the WS. Our analysis has limits, and we hope it stimulates further research. Nevertheless, the preliminary evidence presented here is clear: the case advanced by critics of MCPs is not supported. The growing ethnic diversity of Western societies has generated pressures for the construction of new and more inclusive forms of citizenship and national identity. The evidence in this paper suggests that debates over the appropriateness of multiculturalism policies as one response to this diversity should not be pre-empted by unsupported fears about their impact on the WS.