Particles on Curved Liquid Interfaces: Geometry, Mechanics, and Self-Assembly

弯曲界面上的粒子：几何、力学和自组装类固体粒子在软界面上的吸附在人工系统和生物世界中普遍存在。这些现象的多功能性从被稠密的胶体悬浮液覆盖的Pickering乳液滴，到存在于细胞膜上的蛋白质。了解颗粒与界面之间的相互作用以及颗粒之间的相互作用力，对于开发有效的自组装方法和控制颗粒乳液的稳定性是至关重要的。各种物理机制被认为影响这些相互作用，从表面张力和接触线钉扎到静电学和范德华力。如果颗粒被吸附在弯曲的界面上，其力学性能也可能受到表面几何形状的显著影响。这种几何效应尚未被详细讨论，本提案的目的是开始对它们进行系统的研究。以简单但非平凡的几何为中心，我们提出了实验和理论研究，旨在阐明曲面上粒子力学的普遍方面。智力上的优点：(I)我们将研究固体粒子与曲面的结合能仅取决于被吸附粒子附近的局部界面曲率的条件。(Ii)我们将研究曲面上几个粒子之间的几何诱导相互作用。我们将开发一系列实验来测试曲率相关的相互作用。特别是，我们将探索这种力是否可以成为吸附颗粒之间经常存在的令人费解的长程引力的基础。(Iii)我们将描述被吸附颗粒在非平衡表面流动下的行为。我们将讨论允许在几何诱导力和与非平衡流动相关的粘性应力之间进行比较的流动几何。(Iv)我们将解决与吸附颗粒的稠密悬浮行为相关的基本问题。特别是，我们将探索许多吸附颗粒的存在是否会影响弯曲界面的稳定性，以及稠密悬浮液中吸附颗粒之间相互作用的性质。广泛影响：(I)拟议的研究将为研究生和一名或多名本科生提供各种实验和分析方法的培训，并有机会将这两种观点结合到同一项目中。(Ii)两个PI正在领导一系列教育项目，面向马萨诸塞州阿默斯特大学和其他地方的研究生和本科生。该提案的一个新组成部分是为地区高中学生和教师制定外展计划，这将使人们意识到、兴奋并积极接触正在进行的软物质物理研究。将强调来自低收入和代表性不足社区的学生和教师的参与。(Iii)了解几何诱导力的基本原理将产生变革性的结果，可用于探索粒子定向组装和可控的粒子稳定(Pickering)乳化的新方法。(Iv)最后，该提案寻求通过关注简单(轴对称)界面和固体(球形)粒子来探索最基本的几何诱导效应。拟议的研究结果将促进一系列卓有成效的研究，这些研究将解决更复杂系统中几何诱导相互作用的表现，这些系统以柔性粒子(例如蛋白质)、其他类型的表面(例如弯曲模数)以及复杂的表面几何和粒子形状为特征。

This Particles on Curved Interfaces: Geometry, Mechanics, and Self AssemblyThe adsorption of solid like particles on soft interfaces is ubiquitous in man-made systems as well as in the biological world. The versatility of these phenomena range from Pickering emulsions drops that are covered by a dense colloidal suspension, to proteins that reside on cellular membranes. Understanding the interactions between particles and interfaces and the mutual forces between particles themselves is crucial for developing effective self assembly methods and for controlling the stability of particle laden emulsions. A variety of physical mechanisms are believed to affect these interactions, from surface tension and contact line pinning to electrostatics and van-der-Waals forces. If particles are adsorbed on a curved interface, their mechanics may also be significantly influenced by the surface geometry. Such geometry induced effects have not been addressed in detail, and the purpose of this proposal is to commence their systematic study. Focusing on simple yet nontrivial geometries, we propose experimental and theoretical studies aimed at illuminating universal aspects of the mechanics of particles on curved surfaces.Intellectual Merit:(i) We will study the conditions under which the binding energy of solid particles to curved surfaces depends only on the local interfacial curvatures near the adsorbed particle.(ii) We will study the geometry induced interactions among a few particles on a curved interface. We will develop a set of experiments to test the curvature dependent interactions. In particular, we will explore whether such forces can underlie the puzzling long range attraction that often exists between adsorbed particles.(iii) We will characterize the behavior of adsorbed particles under nonequilibrium surface flows. We will address flow geometries that allow comparison between geometryinduced forces and the viscous stresses associated with nonequilibrium flow.(iv) We will address basic problems related to the behavior of a dense suspension of adsorbed particles. In particular, we will explore whether the presence of many adsorbed particles can affect the stability of curved interfaces, and what is the nature of interactions between adsorbed particles in dense suspension.Broad Impact:(i) The proposed research will provide training for a graduate student and one or more undergraduate students in a variety of experimental and analytic methods, and the opportunity to combine both perspectives within the same project.(ii) Both PI's are leading a number of educational projects, intended for graduate and undergraduate students in UMass Amherst and elsewhere. A new component of the proposal is the development of outreach programs for regional high school students and teachers, which will impart awareness, excitement, and active exposure to ongoing research in soft matter physics. An emphasis will be given to participation of students and teachers from low income and underrepresented communities.(iii) Understanding the basic principles underlying geometry induced forces will yield transformative results, that could be used to exploring new approaches to directed assembly of particles, and to controlled, particle stabilized (Pickering) emulsification.(iv) Finally, the proposal seeks to explore the most basic geometry induced effects by focusing on simple (axially symmetric) interfaces and solid (spherical) particles. The results of the proposed studies will spur a fruitful line of research that will address the manifestations of geometry induced interactions in more complicated systems, characterized by flexible particles (e.g., proteins), other types of surfaces (e.g., with bending modulus), and complicated surface geometries and particle shapes.