Vitoshkin Helena, Yu Hsiu-Yu, Eckmann David M, Ayyaswamy Portonovo S, Radhakrishnan Ravi
Department of Mechanical Engineering and Applied Mechanics, University of Pennsylvania, Philadelphia, PA, USA.
Department of Chemical and Biomolecular Engineering, University of Pennsylvania, Philadelphia, PA, USA.
Phys Rev Fluids. 2016;1. doi: 10.1103/PhysRevFluids.1.054104. Epub 2016 Sep 28.
We have carried out direct numerical simulations (DNS) of the fluctuating Navier-Stokes equation together with the particle equations governing the motion of a nanosized particle or nanoparticle (NP) in a cylindrical tube. The effects of the confining boundary, its curvature, particle size, and particle density variations have all been investigated. To reveal how the nature of the temporal correlations (hydrodynamic memory) in the inertial regime is altered by the full hydrodynamic interaction due to the confining boundaries, we have employed the Arbitrary Lagrangian-Eulerian (ALE) method to determine the dynamical relaxation of a spherical NP located at various positions in the medium over a wide span of time scales compared to the fluid viscous relaxation time = /, where is the spherical particle radius and is the kinematic viscosity. The results show that, as compared to the behavior of a particle in regions away from the confining boundary, the velocity autocorrelation function (VACF) for a particle in the lubrication layer initially decays exponentially with a Stokes drag enhanced by a factor that is proportional to the ratio of the particle radius to the gap thickness between the particle and the wall. Independent of the particle location, beyond time scales greater than /, the decay is always algebraic followed by a second exponential decay (attributed to the wall curvature) that is associated with a second time scale /, where is the vessel diameter.
我们对波动的纳维 - 斯托克斯方程以及控制纳米粒子或纳米颗粒（NP）在圆柱形管道中运动的粒子方程进行了直接数值模拟（DNS）。研究了限制边界、其曲率、粒子尺寸和粒子密度变化的影响。为了揭示由于限制边界导致的完全流体动力相互作用如何改变惯性区域中时间相关性（流体动力记忆）的性质，我们采用任意拉格朗日 - 欧拉（ALE）方法来确定位于介质中不同位置的球形NP在与流体粘性弛豫时间(\tau = \frac{\rho d^2}{18\mu})（其中(d)是球形粒子半径，(\mu)是运动粘度）相比的宽时间尺度上的动态弛豫。结果表明，与远离限制边界区域中粒子的行为相比，润滑层中粒子的速度自相关函数（VACF）最初呈指数衰减，斯托克斯阻力增强了一个与粒子半径与粒子和壁之间间隙厚度之比成正比的因子。与粒子位置无关，在大于(\tau)的时间尺度之后，衰减始终是代数形式，随后是与第二个时间尺度(\tau_{w}=\frac{d^3}{2\nu D})相关的第二个指数衰减（归因于壁曲率），其中(D)是血管直径。
