Zargar Rojman, Najafi Ali, Miri Mirfaez
Institute for Advanced Studies in Basic Sciences (IASBS), P.O. Box 45195-1159, Zanjan 45195, Iran.
Phys Rev E Stat Nonlin Soft Matter Phys. 2009 Aug;80(2 Pt 2):026308. doi: 10.1103/PhysRevE.80.026308. Epub 2009 Aug 19.
We study the influence of a wall on the dynamics of a low-Reynolds-number three-sphere swimmer. A far swimmer whose arm makes an angle theta with the horizon experiences the wall presence as an angle-dependent quadrupole force proportional to (a/L)(2)(L/z)(2)cos theta, where a, L, and z are the radius of spheres, the arm length, and the swimmer distance to the wall, respectively. The wall-induced translational velocity of swimmer is perpendicular to the arms. A far swimmer prefers to orient its arms parallel to the plate. This state is stable. Remarkably, the parallel state is unstable when the swimmer is close to the wall. In this regime, the velocity of swimmer decreases as (z/L)(2). Numerical solution of the equations of motion for arbitrary initial z/L and theta reveals four different phases of locomotion.
我们研究了壁面对低雷诺数三球体游动者动力学的影响。一个远场游动者，其臂与水平面成θ角，会感受到壁面的存在，这表现为一种与角度有关的四极子力，该力与(a/L)²(L/z)²cosθ成正比，其中a、L和z分别是球体半径、臂长以及游动者到壁面的距离。壁面引起的游动者平移速度垂直于臂。一个远场游动者倾向于使其臂与平板平行。这种状态是稳定的。值得注意的是，当游动者靠近壁面时，平行状态是不稳定的。在这种情况下，游动者的速度随(z/L)²减小。针对任意初始z/L和θ的运动方程的数值解揭示了四种不同的运动阶段。
