Uma B, Radhakrishnan R, Eckmann D M, Ayyaswamy P S
Department of Anesthesiology and Critical Care, University of Pennsylvania, Philadelphia, PA 19104.
J Heat Transfer. 2013 Jan 1;135(1):0110111-9. doi: 10.1115/1.4007668.
A hybrid scheme based on Markovian fluctuating hydrodynamics of the fluid and a non-Markovian Langevin dynamics with the Ornstein-Uhlenbeck noise perturbing the translational and rotational equations of motion of a nanoparticle is employed to study the thermal motion of a nearly neutrally buoyant nanoparticle in an incompressible Newtonian fluid medium. A direct numerical simulation adopting an arbitrary Lagrangian-Eulerian based finite element method is employed in simulating the thermal motion of the particle suspended in the fluid contained in a cylindrical vessel. The instantaneous flow around the particle and the particle motion are fully resolved. 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; and (d) the parallel and perpendicular diffusivities of the particle closer to the wall are consistent with the analytical results, where available. The study has important implications for designing nanocarriers for targeted drug delivery.
采用一种基于流体的马尔可夫涨落流体动力学和非马尔可夫朗之万动力学的混合方案，其中奥恩斯坦 - 乌伦贝克噪声扰动纳米颗粒的平移和旋转运动方程，以研究几乎中性浮力的纳米颗粒在不可压缩牛顿流体介质中的热运动。采用基于任意拉格朗日 - 欧拉的有限元方法进行直接数值模拟，以模拟悬浮在圆柱形容器内流体中的颗粒的热运动。颗粒周围的瞬时流动和颗粒运动都得到了充分解析。数值结果表明：（a）在静止流体中计算得到的几乎中性浮力布朗颗粒的温度满足能量均分定理；（b）速度自相关函数的平移和旋转衰减在长时间内导致代数尾部；（c）颗粒的平移和旋转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；（d）靠近壁面的颗粒的平行和垂直扩散系数与现有的解析结果一致。该研究对于设计用于靶向药物递送的纳米载体具有重要意义。
