Change in the nature and enhancement of Brownian motion in shear flows caused by the non-modal growth of thermal fluctuations

热波动非模态增长引起的剪切流布朗运动性质的变化和增强

• 批准号: 506557030
• 负责人: Dr.-Ing. Georg Khujadze
• 金额: --
• 依托单位: Lehrstuhl für Strömungsmechanik
• 依托单位国家: 德国
• 项目类别: Research Grants
• 财政年份: 2022
• 资助国家: 德国
• 起止时间: 2021-12-31 至 2023-12-31
• 项目状态: 已结题
• 来源: https://gepris.dfg.de/gepris/projekt/506557030?language=en
• 关键词: Change; nature; enhancement; Brownian; motion

Classical Brownian motion represents the random motion of small passive particles in a quiescent fluid due to collisions with the surrounding fluid molecules in thermal motion. The presence of an inhomogeneous flow significantly changes the character of Brownian motion. It is of fundamental importance to comprehend and describe the essence of this change since the motion of small active/passive particles in inhomogeneous fluid flows acquires more and more practical importance. This, naturally, led to a significant increase in interest to Brownian motion of active particles in inhomogeneous flows from the different research communities in recent years. Nevertheless, the research done to date does not cover the impact of fluid flow subtleties on Brownian motion on design of man-made micro/nanomachines and even of natural particles. In such cases, a thorough understanding of the influence of inhomogeneous fluid flow on the motion of active/passive Brownian particles is critical. To take the first step in this direction – to investigate the Brownian motion of passive particles in shear flows (specifically, the influence of non-modal growth of thermal fluctuations) is the aim of this project.The hydrodynamic stability community revealed the non-normal nature of inhomogeneous/shear flows in the 1990s. The essence of the non-normality is as follows: the corresponding eigenmodes of the operators of canonical/spectral mathematical analysis are non-orthogonal and turned out to be non-optimal in the study of the linear dynamics of perturbations in shear flows. This circumstance initiated the change of paradigm of the mathematical approach of linear processes in these flows, moving focus from the long-time asymptotic analysis to the study of short-time behavior. As a result, a breakthrough in the understanding and description of linear phenomena in shear flows was achieved. It was found that the linear phenomena induced due to the shear flow non-normality, lead to the very specific - algebraic/transient - growth of perturbations. In laminar shear flows, the flow non-normality significantly affects the thermal motion of fluid molecules and eventually modifies the fluctuation background of quiescent fluid -- makes it anisotropic and enhanced. Specifically, the velocity field of the formed fluctuation background acquires regularity (spatial coherence mostly in streamwise direction) and moreover, its strength significantly exceeds the thermal velocity of fluid molecules in specific area of wave number space. Naturally, this new - anisotropic and enhanced - fluctuating background of fluid velocity field significantly affects the nature and intensity of Brownian motion. Our targeted aim is to reveal and study the new character of Brownian motion of passive particles in laminar plane shear flow, by the reconstruction of Langevin equation due to the shear flow non-normality modified fluctuation background.

经典布朗运动代表静态流体中由于与周围流体分子在热运动中的碰撞而产生的随机运动。不均匀流动的存在显着改变了布朗运动的特征，理解和描述这一点至关重要。这种变化的本质是，由于非均匀流体流动中的小主动/被动颗粒的运动变得越来越具有实际重要性，这自然导致了不同研究对非均匀流动中的主动颗粒的布朗运动的兴趣显着增加。然而，迄今为止所做的研究并没有涵盖流体流动对布朗运动的微妙影响对人造微/纳米机器甚至自然粒子的影响。非均匀流体流动对主动/被动布朗粒子运动的影响至关重要，朝这个方向迈出第一步——研究剪切流中被动粒子的布朗运动（特别是热波动非模态增长的影响）。的目的水动力稳定性界在 20 世纪 90 年代揭示了非均匀/剪切流的非正态性。非正态性的本质如下：正则/谱数学分析的算子对应的本征模态是非正交的。在剪切流扰动的线性动力学研究中，这种情况被证明是非最佳的，这种情况引发了这些流中线性过程的数学方法范式的变化，将焦点从线性过程转移。长时渐近分析对短时行为的研究取得了突破，发现剪切流的非正态性引起了线性现象。 ，导致非常具体的 - 代数/瞬态 - 扰动增长 在层流剪切流中，流动非正态性显着影响流体分子的热运动，并最终改变静态流体的波动背景 - 使其各向异性和具体来说，所形成的波动背景的速度场具有规律性（空间相干性主要在流向），而且其强度显着超过波数空间特定区域中流体分子的热速度。流体速度场的增强脉动背景显着影响布朗运动的性质和强度，我们的目标是通过朗之万的重构来揭示和研究层流平面剪切流中被动粒子布朗运动的新特征。由于剪切流非正态修正波动背景而导致的方程。