Modeling of thermocapillary flow to purify single-walled carbon nanotubes

Single walled carbon nanotubes (SWNTs) are of significant interest in the electronic materials research community due to their excellent electrical properties. The mixture of synthesized SWNTs, however, significantly hampers device performance, particularly for potential applications in digital electronics. Recent purification techniques involve successful and complete removal of metallic SWNTs from horizontal arrays by using thermocapillary flows in thin film resists initiated by selective Joule heating. In this paper, an analytical model, as well as a fully coupled thermo-mechanical-fluid finite element model, is developed to study the physics of thermocapillary flow in this context. A simple scaling law for the film thickness profile is established in terms of the geometry (e.g., film thickness), material (e.g., thermal conductivity and viscosity) and loading parameters (e.g., power density). The results show that the normalized thickness profile only depends on three non-dimensional parameters in addition to the normalized position and normalized time. In particular, for the experimentally investigated system, the thickness profile only depends on a single non-dimensional parameter. These findings may serve as useful design guidelines for process optimization.