Felderhof B U
Institut für Theoretische Physik A, Rheinisch Westfälische Technische Hochschule Aachen, Templergraben 55, 52056 Aachen, Germany.
J Chem Phys. 2005 Nov 8;123(18):184903. doi: 10.1063/1.2084948.
Brownian motion of a particle situated near a wall bounding the fluid in which it is immersed is affected by the wall. Specifically, it is assumed that a viscous compressible fluid fills a half space bounded by a plane wall, and that the fluid flow satisfies stick boundary conditions at the wall. The fluctuation-dissipation theorem shows that the velocity autocorrelation function of the Brownian particle can be calculated from the frequency-dependent admittance valid locally. The admittance can be found from the linearized Navier-Stokes equations. The t(-3/2) long-time tail of the velocity relaxation function, valid in bulk fluid, is obliterated by the wall and replaced by a t(-5/2) long-time tail of positive amplitude for motions parallel to the wall and by a t(-5/2) long-time tail of negative amplitude for motions perpendicular to the wall. In both cases the amplitude of the t(-5/2) long-time tail turns out to be independent of fluid compressibility and bulk viscosity.
浸没在流体中的粒子，若位于界定该流体的壁面附近，其布朗运动会受到壁面的影响。具体而言，假设粘性可压缩流体充满由平面壁界定的半空间，且流体流动在壁面处满足无滑移边界条件。涨落耗散定理表明，布朗粒子的速度自相关函数可根据局部有效的频率相关导纳来计算。该导纳可由线性化的纳维 - 斯托克斯方程求得。在体流体中有效的速度弛豫函数的(t^{-\frac{3}{2}})长时间尾部，会被壁面消除，并被平行于壁面运动时具有正振幅的(t^{-\frac{5}{2}})长时间尾部以及垂直于壁面运动时具有负振幅的(t^{-\frac{5}{2}})长时间尾部所取代。在这两种情况下，(t^{-\frac{5}{2}})长时间尾部的振幅均与流体的可压缩性和体粘度无关。
