Collective Dynamics of Particles at Fluid Interfaces

本项目关注的是一个跨学科和多方面的研究动力学的颗粒限制在一个流体界面。具体来说，我们的建议考虑了应用流场中液滴表面捕获的颗粒，并试图确定流动驱动的颗粒组织。这些都是数学上具有挑战性的多相问题，应用于乳液的研究和具有设计性能的新材料的开发。具体的例子包括通过电场可调节有效粘度的乳液，胶体光子晶体的制造，或软机器人中的“数字胶体”的制造。主要的重点将是在应用流场中，在中到低表面覆盖下，研究颗粒负载液滴的动力学。pi将开发数学模型，解析解，以及移动液滴界面上许多粒子动力学的准确和有效的计算解。这是一个复杂的自由边界问题，提出了几个挑战：三相接触线的动力学，界面的曲率和可变形性，以及由嵌入界面的流体介导的多体水动力相互作用。pi计划开发一种多方面的方法，其中将使用渐近方法寻求单个粒子动力学的解析解，一种新的数值方法，使用嵌合体网格和水平集方法来确定粒子-流体系统的全范围动力学，以及一种有效模拟大量粒子集体动力学的点粒子方法。

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.