Publish in OALib Journal
APC: Only $99
This paper is to extend the Poincar’e Lemma for differential forms in a bounded, convex domain  in Rn to a more general domain that, we call, is deformable to every point in itself. Then we extend the homotopy operator T in  to the domain defromed to every point of itself.
The investigation of surface tension is a very important task for gas hydrate studying. Surfactants can effectively reduce the surface tension, improve the gas storage capability of hydrate and increase the formation rate, shorten the induction time. The objective of this study were to obtain a better understanding of the role of surface tension on hydrate formation and build gas hydrate models involve surfactant. In this study it was highlighted that the surface tension of Intechem-01 + SDS composite surfactants in natural gas hydrate promotion system and the change rules at different temperatures, concentration and proportion. According to the results of experiment, the surface tension of composite surfactants decreased with the increase of Intechem-01. The best cooperating effect was observed in proportion (Intechem-01 content) of 0.6 - 0.7, where the surface tension was the lowest. In this proportion range, the composite surfactants showed the same effect to pure fluorine carbon surfactant. The study shown the surface tension of composite surfactants decreased with the rise of temperature, and they were in a linear relationship within a certain range. Surface tension of composite surfactants decreased with the increase of surfactant concentration, however, it was no longer decreased above critical micelle concentration (CMC). The fitting equation of surface tension with various factors has been obtained.