Uma B, Ayyaswamy P S, Radhakrishnan R, Eckmann D M
Department of Anesthesiology and Critical Care, University of Pennsylvania, Philadelphia, PA 19104 ; Department of Mechanical Engineering and Applied Mechanics, University of Pennsylvania, Philadelphia, PA 19104.
Int J Micronano Scale Transp. 2012 Jun 1;3(1-2):13-20. doi: 10.1260/1759-3093.3.1-2.13.
The Brownian motion of a nanoparticle in an incompressible Newtonian fluid (quiescent or fully developed Poiseuille flow) has been investigated with an arbitrary Lagrangian-Eulerian based finite element method. Results for the motion in a compressible fluid medium are estimated. Thermal fluctuations from the fluid are implemented using a fluctuating hydrodynamics approach. The instantaneous flow around the particle and the particle motion are fully resolved. Carriers of two different sizes with three different densities have been investigated (nearly neutrally buoyant). The numerical results show that (a) the calculated temperature of the nearly neutrally buoyant Brownian particle in a quiescent fluid satisfies the equipartition theorem; (b) the translational and rotational decay of the velocity autocorrelation functions result in algebraic tails, over long time; (c) the translational and rotational mean square displacements of the particle obeys Stokes-Einstein and Stokes-Einstein-Debye relations, respectively. Larger the particle, longer the time taken to attain this limit; and (d) the parallel and perpendicular diffusivities of the particle closer to the wall are consistent with the analytical results, where available.
利用基于任意拉格朗日 - 欧拉法的有限元方法，研究了纳米颗粒在不可压缩牛顿流体（静止或充分发展的泊肃叶流）中的布朗运动。估算了在可压缩流体介质中运动的结果。使用波动流体动力学方法考虑了来自流体的热涨落。颗粒周围的瞬时流动和颗粒运动都得到了充分解析。研究了具有三种不同密度的两种不同尺寸的载体（近中性浮力）。数值结果表明：（a）在静止流体中近中性浮力布朗颗粒的计算温度满足能量均分定理；（b）速度自相关函数的平动和转动衰减在长时间内导致代数尾；（c）颗粒的平动和转动均方位移分别服从斯托克斯 - 爱因斯坦关系和斯托克斯 - 爱因斯坦 - 德拜关系。颗粒越大，达到此极限所需的时间越长；（d）靠近壁面的颗粒的平行和垂直扩散系数与现有解析结果一致。
