Phase separation in a binary liquid (e.g. oil and vinegar) is a phenomenon which can be described as a competition between a entropy mixing effects and demixing effects due to the internal energy (i.e. the attraction of molecules of the same liquid), provided that, for instance, the temperature is low enough. Liquid-liquid phase separation has recently become a sort of new paradigm in Cell Biology. Quoting from E. Dolgin: “Not only is phase separation intuitive, but it seems to be everywhere. Droplets of proteins and RNAs are turning up in bacteria, fungi, plants and animals. Phase separation at the wrong place or time could create clogs or aggregate of molecules linked to neuro degenerative diseases, and poorly formed droplets could contribute to cancers and might help explain the ageing process.” Well-known mathematical models for phase separation (e.g. in binary alloys) are given by the so-called Cahn-Hilliard equation or by the (conserved) Allen-Cahn equation. In the case of liquids, such equations must be suitably coupled with the Navier-Stokes equations for the averaged velocity of the binary mixture. This talk will be focused on Allen-Cahn-Navier-Stokes systems with some remarks on inviscid and pure transport cases.
This video was produced by the SITE Research Center at New York University, as part of their talk series.
