Collaborative Research: Fluctuating Hydrodynamics of Suspensions of Rigid Bodies

在过去十年中，材料和设备的制造和设计取得了快速进展，这些材料和设备使用小规模的活性颗粒来产生新的物理行为，如自组织流动(例如，活性胶体悬浮液)，或执行特定任务，如货物运输(例如，靶向药物输送)。虽然在实验上已经取得了很大的进展，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的公共领域代码，理论和计算模型滞后。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，并在公共领域程序IBAMR中实现了所开发的技术，从而使其可供物理和工程应用研究人员使用。这项工作的一个特别的区别方面是一致地包含了随机布朗运动，由于过程中涉及的分子数量很少，所以在处理小规模流动时必须存在随机布朗运动。这种随机效应在微米和纳米尺度的流动中非常重要，典型的流动包括纳米和微流体和微型机电设备、新型材料(如纳米流体)和生物系统(如脂膜、布朗分子马达和纳米孔)。因此，我们预计这项工作将在科学和工程中有广泛的应用，而不仅仅是下面详述的具体研究目标。该项目的科学部分将由教育和推广部分补充，包括开发和丰富新的研究生课程，如材料粗粒建模，其中将包括统计力学、应用随机分析、流体力学和高性能计算方面的培训。这个合作项目侧重于涉及浸入流体中的布朗刚性和半刚性结构问题的计算方法。例子包括胶体颗粒、聚合物链和溶剂中的大分子。我们的目标是开发新的方法，在小雷诺数下进行流固耦合，始终包括热涨落的影响。在小尺度上，浸没结构的运动是由热涨落驱动的，从而产生了受流体动力效应强烈影响的布朗运动。我们计划开发一种方法，将刚体的浸没边界拉格朗日表示与波动的有限体积流体解算器耦合。与常用的基于格林函数的方法不同，我们依赖于显式流体涨落流体动力学公式，在该公式中，我们在通常的粘性应力张量上添加一个随机应力张量。我们将处理复杂的刚性(例如，合成纳米棒)和半刚性(例如，短DNA片段)身体，方法是由一组被约束为(半)刚性移动的球形粒子组成每个结构。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。该项目开发的新方法将建立在PI先前工作的基础上，并能够模拟浸没结构的长期扩散(布朗)动力学。特别是，我们将开发、实施和应用以下计算方法：(1)不使用时间分裂，因此适用于定常Stokes(粘性主导或低雷诺数)区域；(2)严格执行刚性约束；以及(3)即使在非平凡边界条件存在的情况下，也确保过阻尼极限中的涨落-耗散平衡。

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.