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.

经典的布朗运动表示由于与周围流体分子在热运动中的碰撞而导致的静态流体中小的被动颗粒的随机运动。不均匀流的存在显着改变了布朗运动的特征。理解和描述这种变化的本质至关重要，因为小型活性/被动颗粒在不均匀流体流动中的运动具有越来越实际的重要性。自然，这导致了近年来不同研究社区的不均匀流动中主动颗粒运动的兴趣大大增加。然而，迄今为止所做的研究尚未涵盖流体流量微妙对布朗运动对人造微/纳米机械设计甚至自然颗粒的设计的影响。在这种情况下，对不均匀流体流动对活动/被动布朗颗粒运动的影响有透彻的理解至关重要。为了朝这个方向迈出第一步 - 要研究剪切流中被动颗粒的布朗运动（具体而言，热波动的非模式生长的影响）是该项目的目的。流体动力稳定性群落揭示了1990年代非均匀/剪切流的非正常性质。非正常的本质如下：规范/光谱数学分析的运算符的相应特征模是非正交的，并且在研究剪切流动流动扰动的线性动力学的研究中被证明不是最佳的。在这种情况下，在这些流中线性过程的数学方法范式的变化，将重点从长期的不对称分析转变为短期行为的研究。结果，实现了对剪切流中线性现象的理解和描述的突破。发现线性现象是由于剪切流量非正态性引起的，导致扰动的非常特异性 - 代数/瞬态 - 生长。在层流剪切流中，流动非正常性显着影响流体分子的热运动，有时会改变静态液的波动背景 - 使其各向异性和增强。具体而言，形成的波动背景的速度场获得了规律性（空间相干性主要沿流向方向），并且其强度显着超过了波动数空间特定区域中流体分子的热速度。自然，这种新的 - 各向异性和增强的流体速度场的波动背景显着影响了布朗运动的性质和强度。我们的目标目的是通过重建langevin方程，这是由于剪切流量非正态修改的波动背景，揭示和研究了层平面剪切流中的布朗运动的新特征。