Abstract Innovation affects a nation’s sovereignty. In this paper, we look at Science and Technology indicators as proxies for Innovation using databases such as WIPO, INPI, Sucupira and Scival, and including patents registered, academic-corporate collaborations, patents citing Brazilian articles (Number of patents and documents) and technical production in Brazilian higher education institutions. We also look at two major previously state-owned companies (Embraer and Petrobras) to see their patenting and citation behaviour compared to other companies worldwide. Brazilian science is a citation basis for patenting in companies and universities worldwide, but Brazil does not use its own publications to support patent proposals. While USP is the major cited university, Unicamp has more patents. Academic-corporate collaboration exists between Brazilian and foreign universities, especially in the US and Europe. The Brazilian companies show low patenting behaviour, but Embraer has a higher impact than Petrobras. As a consequence of the dynamics of science and technology, we suggest that the analyses of the innovation processes could focus on the generation of startups and, in particular, academic spin-offs. nations nation s sovereignty paper WIPO INPI Scival registered academiccorporate corporate collaborations Number documents institutions stateowned state owned Petrobras worldwide proposals university Academiccorporate Academic Europe technology particular spinoffs. spinoffs spin offs. offs spin-offs

This paper proposes a numerical model to predict the growth of gaseous refrigerant bubbles in oil-refrigerant mixtures with high contents of oil subjected to isothermal depressurization. The model considers an Elementary Cell (EC) in which a spherical bubble is surrounded by a concentric and spherical liquid layer containing a finite amount of dissolved liquid refrigerant. The pressure reduction in the EC generates a concentration gradient at the bubble interface and the refrigerant is transported to the bubble by molecular diffusion. After a sufficiently long time, the concentration gradient in the liquid layer and the bubble internal pressure reach equilibrium and the bubble stops growing, having attained its stable radius. The equations of momentum and chemical species conservation for the liquid layer, and the material balance at the bubble interface are solved via a coupled finite difference procedure to determine the bubble internal pressure, the refrigerant radial concentration distribution and the bubble growth rate. Numerical results obtained for a mixture of ISO VG10 polyolester oil and refrigerant HFC-134a showed that the bubble growth dynamics depends on model parameters such as the initial bubble and liquid layer radii, the initial refrigerant concentration in the liquid layer, the initial pressure in the liquid phase, the decompression rate and the EC temperature. Despite its simplicity, the model demonstrated to be a potential tool for predicting bubble growth and foaming that may occur as a result of cavitation in oil-lubricated bearings and refrigerant degassing from the oil sump during compressor start-up.