论文标题
剪切流中布朗颗粒扩散的广义理论
A generalized theory of Brownian particle diffusion in shear flows
论文作者
论文摘要
这项研究提出了一种通用理论，用于剪切流中布朗颗粒的扩散。通过使用随机而不是经典的微积分来求解Langevin方程，我们提出了一种新的数学公式，该公式在所有时间尺度上都可以在任何二维平行剪切流中解析粒子MSD，该公式由多项式速度曲线描述。我们表明，在长期尺度上，粒子MSD中的多项式时间顺序为n+2，其中n是速度分布的横向坐标的多项式顺序。我们概括了在所有时间尺度上都在任何多项式剪切流中解析粒子扩散的理论，包括粒子松弛时间尺度的顺序，这在当前理论中尚未解决。然后研究粒子在所有时间尺度上的扩散，以了解COUETTE和PLANE-POISEUILE流动的情况，以及双曲线切线流的多项式扩展，同时忽略边界效应。我们观察到沿粒子扩散的三个主要阶段沿着粒子MSD由于不同主导的物理机制而明显不同的时间表。因此，可以实现用于剪切流中扩散过程的较高时间和空间分辨率，这表明是布朗颗粒扩散的更准确的分析方法。
This study presents a generalized theory for the diffusion of Brownian particles in shear flows. By solving the Langevin equations using stochastic instead of classical calculus, we propose a new mathematical formulation that resolves the particle MSD at all time scales for any two-dimensional parallel shear flow described by a polynomial velocity profile. We show that at long-time scales, the polynomial order of time in the particle MSD is n+2, where n is the polynomial order of the transverse coordinate of the velocity profile. We generalize the theory to resolve particle diffusion in any polynomial shear flow at all time scales, including the order of particle relaxation time scale, which is unresolved in current theories. Particle diffusion at all time scales is then studied for the cases of Couette and plane-Poiseuille flows and a polynomial expansion of a hyperbolic tangent flow while neglecting the boundary effects. We observe three main stages of particle diffusion along the timeline for which the particle MSD is distinctly different due to different dominated physical mechanisms. Thus, higher temporal and spatial resolution for diffusion processes in shear flows may be realized, suggesting a more accurate analytical approach for the diffusion of Brownian particles.
