Collective dynamics of particles at fluid interfaces

Project: Research project

Project Details


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 of single particle dynamics on interfaces, careful consideration of contact-lines on multiple particles, detailed numerical methods for solving the motion of multiple fully resolved particles on a moving fluid interface, and a computationally efficient point-particle algorithm for a very large numbers of particles that incorporates the analytical and fully resolved computational results. Benchmark experiments to complement the mathematical research are proposed to justify and validate the mathematical models and to ensure that the research has impact both in and beyond the applied mathematics community.

Broader impact: The potentially transformative nature of this proposal lies in the emergent collective dynamics of the surface-trapped particles that could inspire new research directions and applications related to colloidal self-assembly and the design of novel active materials. 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 proposed research is interdisciplinary which will be very beneficial for the education and development of the students associated with the project. We will be involved in the successful outreach programs at NU to translate the relevance and significance of our work to attract students from underrepresented groups in STEM. The research findings will be presented at professional meetings to enhance understanding among the community of applied mathematicians, physicists and engineers.
Effective start/end date7/1/176/30/20


  • National Science Foundation (DMS-1716114)

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