Collective dynamics of particles at fluid interfaces

This proposal is concerned with an analytical and numerical investigation of the dynamics of particles confined to a fluid interface. Specifically, our proposal considers surface--trapped particles on a drop in an applied flow field and seeks to determine the flow-driven particle organization. These are mathematically challenging multiphase problems with application to the study of emulsions and the development of new novel materials with designed properties. The primary focus will be on investigating the dynamics of particle-laden drops at medium to low surface coverage in applied flow fields. Recent experiments have shown that the particles assemble into intriguing patterns that can be dynamically controlled by applied external fields, but understanding of these novel phenomena is lacking and requires a better understanding of the particle-drop dynamics. To fill this void we propose to develop mathematical models, analytical solutions, and accurate and efficient computational solutions of the dynamics of many particles on a moving drop interface. This is a complex free boundary problem that presents several challenges: the dynamics of the three-phase contact line, the curvature and deformability of the interface, and the many-body hydrodynamic interactions mediated by the fluids embedding the interface. We propose a multifaceted approach where analytical solutions using asymptotic methods will be sought for the dynamics of a single particle, a novel numerical approach using chimera grids and level set methods to determine the full-range dynamics of the particle-fluid system, and a point-particle method that efficiently simulates the collective dynamics of large number of particles. Intellectual merit: An interdisciplinary and multifaceted approach is proposed to investigate this novel complex free boundary problem involving three phases: the drop, the host fluid, and the particles. The novel mathematical challenges are many and includes analytical solutions o