(721c) Capturing the Phase Interface Using the Gradient Theory in the Mixing of Hydrocarbons and Supercritical Water
Handling the emerged partial, non-closed phase interface in the mixture of hydrocarbons and supercritical water in 3-D is mathematically and numerically challenging, yet fascinating. The non-closed surface is usually cut off by the domain boundary in most cases. For example, we can have a hemisphere on a flat solid surface. The solid surface cut the sphere into a half, and the hemisphere is a non-closed surface cut off by the domain boundary, which is the solid surface. However, in the mixture of hydrocarbons and supercritical water, the non-closed surface can be random holes on an originally closed surface, for example, a sphere. Such holes are also not at all similar to the holes on the membrane of a live biological cell. The membrane with many holes is still a closed surface, while it is just that the dimension of its thickness is significantly small. The holes on the non-closed surface in the mixture of hydrocarbons and supercritical water are the regions, where the sharp phase interface physically and gradually grows into one-phase. It is a multi-scale coupled thermodynamics and transport phenomena, ranging from the molecular scale into the macro-scale.
In this talk, we present preliminary results of a novel multi-scale method coupling the Gradient Theory, thermodynamics, and transport models to capture the diminished and/or emerged multi-dimensional phase interface in the mixture of hydrocarbons and supercritical water. We propose to use novel methods to overcome the meta-stable phase behavior regions, where the non-ideal diffusional driving force does not cause the phase separation, while it should result in a phase separation based on the global minimization of the Gibbs energy. Results of our new method is compared with our former 1-D sharp interface method. Good agreement has been observed. The capability of capturing the partial, non-closed 3-D phase interface is demonstrated.