Collective Dynamics of Particles at Fluid Interfaces

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This project is concerned with an interdisciplinary and multifaceted 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. Specific examples include emulsions with effective viscosity tunable by an electric field, the fabrication of colloidal photonic crystals, or the fabrication of "digital colloids" in soft robotics. The primary focus will be on investigating the dynamics of particle-laden drops at medium to low surface coverage in applied flow fields. The PIs will 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. The PIs plan to develop 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 numbers of particles.