Enhanced diffusivity and skewness of a diffusing tracer in the presence of an oscillating wall
Enhanced diffusivity and skewness of a diffusing tracer in the presence of an oscillating wall
复制标题
在存在振荡壁的情况下增强扩散示踪剂的扩散率和偏度
DOI：
10.1007/s40687-021-00257-4
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发表时间：
2021
影响因子：
1.2
通讯作者：
Woodie, Hunter
中科院分区：
文献类型：
--
作者：
Ding, Lingyun;Hunt, Robert;McLaughlin, Richard M.;Woodie, Hunter
我们发展了一个理论，增强扩散和倾斜度的纵向分布的扩散示踪平流的周期性随时间变化的剪切流在直通道。虽然适用于任何类型的溶质和流体流动，我们限制我们的理论的例子，以示踪剂平流的流动是由一个周期性振荡壁在牛顿流体两个无限平行板之间，以及在一个无限长的管道流动引起的。这些壁面运动产生了著名的斯托克斯层剪切解，它是Navier-Stokes方程的精确解。有了这些，我们首先计算的第二阿里斯时刻的所有时间和其长期限制的有效扩散率的几何参数，频率，粘度和扩散率的函数。使用一个新的形式主义的基础上的亥姆霍兹算子，我们建立了一个新的单一的系列公式的方差有效的所有时间。我们表明，粘性占主导地位的限制结果在线性剪切层的有效扩散率有界的上限，其中示踪剂扩散率，A是振幅的振荡，和L是差距的厚度。另外，对于有限的粘度，我们表明，增强扩散是无界的，在高频极限发散。无量纲化和物理参数来解释这些显着的差异。的高频率的行为，以及低粘度极限的渐近计算。我们提出了一个研究的有效扩散率表面作为一个函数的无量纲参数，它显示了如何最大可以存在各种参数扫描。在水中进行物理实验，使用粒子跟踪测速仪定量测量流体流动。使用荧光素染料作为被动示踪剂，我们的文件，该理论是定量准确的。具体地，图像分析建议使用对噪声具有鲁棒性的半峰全宽统计量来测量分布方差。此外，我们表明，标量偏度为零的线性剪切流在任何时候，而非线性斯托克斯层，精确的分析表明，偏度符号可以通过相位的振荡壁控制。此外，对于单频壁模，我们建立了长时间的偏度衰减速度比稳态剪切标量偏度衰减速度快。这些结果证实了使用蒙特-卡罗模拟。
We develop a theory of enhanced diffusivity and skewness of the longitudinal distribution of a diffusing tracer advected by a periodic time-varying shear flow in a straight channel. Although applicable to any type of solute and fluid flow, we restrict the examples of our theory to the tracer advected by flows which are induced by a periodically oscillating wall in a Newtonian fluid between two infinite parallel plates as well as flow in an infinitely long duct. These wall motions produce the well-known Stokes layer shear solutions which are exact solutions of the Navier–Stokes equations. With these, we first calculate the second Aris moment for all time and its long-time limiting effective diffusivity as a function of the geometrical parameters, frequency, viscosity, and diffusivity. Using a new formalism based upon the Helmholtz operator, we establish a new single series formula for the variance valid for all time. We show that the viscous dominated limit results in a linear shear layer for which the effective diffusivity is bounded with upper bound, whereis the tracer diffusivity,Ais the amplitude of oscillation, andLis the gap thickness. Alternatively, for finite viscosities, we show that the enhanced diffusion is unbounded, diverging in the high-frequency limit. Non-dimensionalization and physical arguments are given to explain these striking differences. Asymptotics for the high-frequency behavior as well as the low viscosity limit are computed. We present a study of the effective diffusivity surface as a function of the non-dimensional parameters which shows how a maximum can exists for various parameter sweeps. Physical experiments are performed in water using particle tracking velocimetry to quantitatively measure the fluid flow. Using fluorescein dye as the passive tracer, we document that the theory is quantitatively accurate. Specifically, image analysis suggests that the distribution variance be measured using the full width at half maximum statistic which is robust to noise. Further, we show that the scalar skewness is zero for linear shear flows at all times, whereas for the nonlinear Stokes layer, exact analysis shows that the skewness sign can be controlled through the phase of the oscillating wall. Further, for single-frequency wall modes, we establish that the long-time skewness decays at the faster rate ofas compared with steady shear scalar skewness which decays at rate. These results are confirmed using Monte-Carlo simulations.
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