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，采用小规模的活性颗粒的材料和设备的制造和设计取得了迅速的进展，以产生新颖的身体行为，例如自组织（例如，主动胶体悬架），或执行诸如货物运输（例如，目标药物输送）等特定任务。尽管很难设计合适的数值算法以及缺乏能够捕获主动推进的复杂多物理学的公共域代码，但尽管很难设计合适的数值算法，但在实验上取得了很多进展，但理论和计算建模滞后。在这项工作中，我们开发了新颖的计算方法，用于模拟悬挂在流体中的活性粒子，并在公共域代码IBAMR中实施开发的技术，因此可用于应用物理和工程研究人员。工作的一个特定区别是，由于该过程中涉及的少量分子，在处理小规模流动时必须持续包含随机的布朗运动。这种随机效应在典型的纳米和微荧光和微电机械设备的微型和纳米尺度的流动中很重要，新型材料（例如纳米流体）以及生物系统，例如脂质膜，棕色分子运动和纳米孔。因此，我们希望这项工作在科学和工程中具有广泛的应用，而不是以下特定的研究目标。该项目的科学组成部分将由教育和宣传组成部分补充，包括开发和丰富新的研究生课程，例如材料的粗粒子模型，其中包括统计力学上的培训，应用随机分析，流体动力学，体验动力学和性能计算的高度进行计算。例子包括溶剂中的胶体颗粒，聚合物链和大分子。我们旨在开发用于小雷诺数的流体结构耦合的新方法，这些方法始终包括热波动的影响。在小尺度上，浸没结构的运动是由热波动驱动的，从而导致布朗运动受水动力效应的强烈影响。我们计划开发将刚性体的浸入式拉格朗日融合的方法与有限体积液体求解器相对的方法。与基于Green功能的常用方法不同，我们依赖于显式流体波动的流体动力学公式，在这种情况下，我们在通常的粘应力张量中添加了随机应力张量。我们将通过从刚性移动的球形粒子集合中组成每个结构来处理复杂的刚性（例如，合成纳米棒）和半刚性（例如，短DNA片段）体。潜在的波动水动力制剂会自动确保正确的翻译和旋转布朗运动。该项目中开发的新方法将基于PI的先前工作，并启用浸入式结构的长期扩散（Brownian）动力学的模拟。特别是，我们将开发，实施和应用以下计算方法：（1）不使用时间分配，因此适用于稳定的stokes（粘性主导或低雷诺数）制度； （2）严格执行刚性限制； （3）即使在存在非平凡边界条件的情况下，也可以确保在过度阻尼的极限中的波动划分平衡。