Hole Closure in Langmuir Fluid Monolayers

Amphipathic molecules are basically long chains, one end of which likes water (is hydrophilic) and the other end abhors it (is hydrophobic). These molecules tend to sit vertically in a fluid and adhere to each other. This attraction of adjacent molecules causes the molecules to condense into regions, referred to as polymer Langmuir layer domains, which are a single molecule thick and behave like a two dimensional fluid. This attraction also manifests itself as a line tension, analogous to surface tension in a fluid droplet, which causes the regions to become circular as they attempt to minimize the length of their perimeter. Often the layer will form holes, gaps in the liquid monolayer which contain a much smaller density of molecules. In the presence of humidity, the holes are observed to close up, pulled together by the line tension as well as condensation of the hole molecules at the boundary. Previous researchers have computed the fluid velocity for the process when the hole is assumed to be a vacuum. I, however, propose to replace this model with a gas, adding condensation of gas from the hole into the liquid domain of the monolayer to the line tension force. The hope is to obtain a mathematical model that better corresponds to the physical problem than current models do