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

弯曲界面上的粒子：几何学、力学和自组装类固体粒子在软界面上的吸附在人造系统和生物世界中普遍存在。这些现象的多功能性范围从皮克林乳液滴被覆盖的致密胶体悬浮液，蛋白质驻留在细胞膜上。了解粒子和界面之间的相互作用以及粒子本身之间的相互作用力对于开发有效的自组装方法和控制载有粒子的乳液的稳定性是至关重要的。 各种物理机制被认为会影响这些相互作用，从表面张力和接触线钉扎到静电和范德华力。如果颗粒被吸附在弯曲的界面上，它们的力学也可能受到表面几何形状的显著影响。这种几何形状引起的影响尚未详细讨论，本建议的目的是开始对其进行系统研究。 专注于简单而非平凡的几何形状，我们提出了实验和理论研究，旨在照亮曲面上的粒子力学的普遍方面。智力Merit：（i）我们将研究的条件下，固体粒子的结合能曲面仅取决于当地的界面曲率附近的吸附粒子。(ii)我们将研究弯曲界面上几个粒子之间的几何诱导相互作用。我们将开发一组实验来测试曲率相关的相互作用。特别是，我们将探讨这种力量是否可以根据令人困惑的长期吸引力，往往存在于吸附粒子之间。(iii)我们将描述在非平衡表面流动下吸附颗粒的行为。我们将讨论流动的几何形状，允许几何诱导力和粘性应力与非平衡流之间的比较。(iv)我们将讨论与吸附粒子的稠密悬浮体的行为有关的基本问题。特别是，我们将探讨是否存在许多吸附颗粒可以影响弯曲界面的稳定性，以及吸附颗粒之间的相互作用的性质是什么在稠密suspension. Broad Impact：（i）拟议的研究将提供培训的研究生和一个或多个本科生在各种实验和分析方法，并有机会联合收割机在同一个项目中的两个角度。(ii)这两个PI的领导了一些教育项目，旨在为研究生和本科生在马萨诸塞州阿默斯特和其他地方。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，这将使他们对正在进行的软物质物理研究产生认识、兴奋和积极的接触。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)理解几何诱导力的基本原理将产生变革性的结果，可用于探索新的方法来定向组装的颗粒，并控制，颗粒稳定（皮克林）乳化。(iv)最后，该提案旨在探索最基本的几何形状引起的影响，重点是简单的（轴对称）接口和固体（球形）粒子。拟议研究的结果将激发一系列富有成效的研究，这些研究将解决以柔性粒子为特征的更复杂系统中几何诱导相互作用的表现（例如，蛋白质），其它类型的表面（例如，具有弯曲模量），以及复杂的表面几何形状和颗粒形状。

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.