Collaborative Research: Fluctuating Hydrodynamics of Suspensions of Rigid Bodies

合作研究：刚体悬架的脉动流体动力学

• 批准号: 1418706
• 负责人: Aleksandar Donev
• 金额: $ 25.22万
• 依托单位: New York University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2014
• 资助国家: 美国
• 起止时间: 2014-07-01 至 2017-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1418706&HistoricalAwards=false
• 关键词: Collaborative; Research; Fluctuating; Hydrodynamics; Suspensions

Over the last decade there has been rapid progress in the manufacturing and design of materials and devices that employ small-scale active particles to produce novel physical behaviours such as self-organizing flows (e.g., active colloidal suspensions), or to perform specific tasks such as cargo transport (e.g., targeted drug delivery). While much progress has been made experimentally, theoretical and computational modelling lags behind, due to the difficulty in designing suitable numerical algorithms and the lack of public-domain codes capable of capturing the complex multi-physics of active propulsion. In this work we develop novel computational methods for simulating active-particles suspended in fluid, and implement the developed techniques in the public-domain code IBAMR, therefore making them available to applied researchers in physics and engineering. A specific distinguishing aspect of the work is the consistent inclusion of the random Brownian motion necessarily present when dealing with small-scale flows due to the small numbers of molecules involved in the process. Such stochastic effects are important in flows at micro and nano scales typical of nano- and micro-fluidic and microelectromechanical devices, novel materials such as nanofluids, and biological systems such as lipid membranes, Brownian molecular motors, and nanopores. We therefore expect the work to have a broad range of applications in science and engineering, beyond the specific research goals detailed below. The scientific component of this project will be supplemented by an educational and outreach component, including the development and enrichment of new graduate courses, such as Coarse Grained Modeling of Materials, which will include training in statistical mechanics, applied stochastic analysis, fluid dynamics, and high-performance computing.This collaborative project focuses on computational methods for problems involving Brownian rigid and semi-rigid structures immersed in a fluid. Examples include colloidal particles, polymer chains, and macromolecules in a solvent. We aim to develop novel methods for fluid-structure coupling at small Reynolds numbers that consistently include the effects of thermal fluctuations. At small scales, the motion of immersed structures is driven by thermal fluctuations, giving rise to Brownian motion strongly affected by hydrodynamic effects. We plan to develop methods that couple an immersed-boundary Lagrangian representation of rigid bodies to a fluctuating finite-volume fluid solver. Unlike commonly-used methods based on Green's functions, we rely on an explicit-fluid fluctuating hydrodynamics formulation in which we add a stochastic stress tensor to the usual viscous stress tensor. We will handle complex rigid (e.g., synthetic nanorods) and semi-rigid (e.g., short DNA segments) bodies by composing each structure from a collection of spherical particles constrained to move (semi)rigidly. The underlying fluctuating hydrodynamics formulation automatically ensures the correct translational and rotational Brownian motion. The novel methods developed in this project will build upon prior work by the PIs and enable simulations of the long-time diffusive (Brownian) dynamics of the immersed structures. In particular, we will develop, implement, and apply computational methods that: (1) do not employ time splitting and are thus suitable for the steady Stokes (viscous-dominated or low Reynolds number) regime; (2) strictly enforce the rigidity constraint; and, (3) ensure fluctuation-dissipation balance in the overdamped limit even in the presence of nontrivial boundary conditions.

在过去的十年中，在采用小尺度活性颗粒来产生诸如自组织流动（例如，活性胶态悬浮液），或执行特定任务如货物运输（例如，靶向药物递送）。虽然在实验上取得了很大进展，但由于难以设计合适的数值算法，以及缺乏能够捕捉主动推进的复杂多物理场的公共领域代码，理论和计算建模滞后。在这项工作中，我们开发了新的计算方法来模拟悬浮在流体中的活性粒子，并在公共领域代码IBAMR中实现所开发的技术，从而使它们可用于物理和工程应用研究人员。一个具体的区别方面的工作是一致的列入随机布朗运动时，必然存在的处理小规模的流动，由于参与的过程中的分子数量少。这种随机效应在纳米和微流体和微机电装置、诸如纳米流体的新型材料和诸如脂质膜、布朗分子马达和纳米孔的生物系统的典型的微米和纳米尺度的流动中是重要的。因此，我们希望这项工作在科学和工程领域有广泛的应用，超越下面详细介绍的具体研究目标。该项目的科学部分将辅之以教育和外联部分，包括开发和充实新的研究生课程，如材料的粗粒建模，其中将包括统计力学、应用随机分析、流体动力学、和高性能计算。这个合作项目的重点是计算方法的问题，涉及布朗刚性和半-浸入液体中的刚性结构。实例包括溶剂中的胶体颗粒、聚合物链和大分子。我们的目标是开发新的方法，在小雷诺数的流体结构耦合，始终包括热波动的影响。在小尺度下，浸没结构的运动是由热涨落驱动的，从而产生强烈受流体动力效应影响的布朗运动。我们计划开发的方法，耦合浸入边界拉格朗日表示的刚体波动有限体积流体求解器。不同于常用的方法的基础上绿色的功能，我们依赖于一个显式流体波动的流体动力学制剂中，我们添加了一个随机应力张量通常的粘性应力张量。我们将处理复杂的刚性（例如，合成纳米棒）和半刚性（例如，短的DNA片段）体，通过由被限制为（半）刚性移动的球形颗粒的集合组成每个结构。基本的波动流体动力学公式自动确保正确的平移和旋转布朗运动。在这个项目中开发的新方法将建立在PI之前的工作基础上，并能够模拟浸没结构的长时间扩散（布朗）动力学。特别是，我们将开发，实施和应用计算方法：（1）不采用时间分裂，因此适用于稳定的斯托克斯（粘性主导或低雷诺数）制度;（2）严格执行刚性约束;（3）确保波动耗散平衡过阻尼限制，即使在存在非平凡的边界条件。