We consider the Galerkin nite element method for partial diiferential equations in two dimensions, where the nite-dimensional space used consists of piecewise (isoparametric) polynomials enriched with bubble functions. Writing L for the diierential operator, we show that for elliptic convection-diiusion problems, the component of the bubble enrichment that stabilizes the method is equivalent to...

Experiments were conducted in a 0.25 m diameter bubble column to investigate the effect of animal cell culture medium composition on oxygen transfer rate. Air is used as the dispersed phase. The gas superficial velocity is varied between 0.4 and 2 cm/s (aeration rate ranging between 0.05 and 0.25 vvm) and the bubble column is thus operated in the homogenous regime. Aqueous solutions the composi...

We perform a characterization of a recently reported microbubble injector in conditions relevant to microgravity. Injection of bubbles is based on the generation of a slug flow in a capillary T-junction, whose operation is robust to changes in the gravity level. We address questions regarding the performance under different working regimes. In particular, we focus on the regimes found within a ...

Identifying unambiguously the presence of a bubble in an asset price remains an unsolved problem in standard econometric and financial economic approaches. A large part of the problem is that the fundamental value of an asset is, in general, not directly observable and it is poorly constrained to calculate. Further, it is not possible to distinguish between an exponentially growing fundamental ...

Fast liquid jets, called micro-jets, are produced within cavitation bubbles experiencing an aspherical collapse. Here we review micro-jets of different origins, scales and appearances, and propose a unified framework to describe their dynamics by using an anisotropy parameter ζ > 0, representing a dimensionless measure of the liquid momentum at the collapse point (Kelvin impulse). This paramete...