The original work plan was composed of four Work Packages (WP). The first one dealt with the global management of the project and also included an intense learning and training phase. The remaining three WPs were more technical and of increasing complexity. In agreement with the work plan, I spent the first 6 months or so gaining new scientific knowledge, mostly on Phase-Field (PF) methods, and getting trained in numerical simulations based on finite elements (WP1). Afterwards, I began addressing the tasks of WP2, which focuses on the behavior of a single particle trapped at a fluid interface. The case of an isotropic/isotropic (referred to as Iso-Iso hereafter) interface (no LC here) was tackled first in order to validate our approach. We achieved very good agreement with literature data for both static (absence of prescribed external flows) and dynamic (computation of drag forces) situations. Switching to an Iso-LC interface made things a lot more challenging for we had to deal with one of the core issues of the project, i.e. the so-called elastocapillary coupling. We considered the simplest of all LC phases, i.e. the nematic (N) phase. Building on existing theoretical models, we coupled the PF method, which describes the dynamics of a fluid interface (surface tension), to a tensor-based theory able to account for the partial ordering of the N phase (elastic properties) along with the possible formation of topological defects. We faced numerous issues and it took us a lot more time than we originally thought to troubleshoot and validate our methodology on benchmark examples. With our validated model, we were able to explore both the static (floating particle configurations) and dynamic (computation of drag forces) behaviors of a particle trapped at an Iso-N interface. Our results show that the interplay of elastic distortions, surface tension and boundary conditions (anchoring of LC), together with the two-way coupling between the flow and the nematic fields, govern the response of such systems. WP2 can be considered finished despite a few ongoing, but soon ending, side-studies.
Extending the previous studies to the case of curved Iso-Iso and Iso-N interfaces was the matter of WP3. Unfortunately, only embryonic explorations could be performed at such interfaces, mainly because of a lack of time.
Finally, the first task of the last work package (WP4) could be partially addressed. This WP focuses on collective phenomena involving two or more particles straddling an Iso-N interface. As in WP2, we first successfully benchmarked our model for an Iso-Iso interface with two particles undergoing an attractive capillary interaction. We then extended our calculations to an Iso-N interface and obtained preliminary results highlighting the possibility of having attractive capillary interactions competing with repulsive elastic interactions. However, this promising investigation could not be pursued further due to a lack of time.
The results collected so far allowed us to publish several papers, as described in the next section.
