Bhattacharya Sukalyan
Department of Mechanical Engineering, Texas Tech University, Lubbock, TX 79409, USA.
J Chem Phys. 2008 Feb 21;128(7):074709. doi: 10.1063/1.2830713.
In this article, we analyze the collective motion of a two-dimensional periodic array of spheres in a slit-pore confined by two parallel planar walls. We determine the friction coefficient of the spheres when all particles move with the same velocity along a particular direction and cooperate with each other in their motion. In order to solve this many-body problem, we use Stokesian dynamics algorithm and resolve multiparticle hydrodynamic interactions in wall-bounded geometry. Apart from particle-particle interactions, we also recognize that the aforementioned collective motion of all particles creates a cumulative effect on the fluid medium. This effect is manifested as either a net induced flow for a periodic pressure field or an additional pressure gradient for quiescent fluid. In our analysis, we focus on both periodic pressure and no-flow conditions. For both cases, the hydrodynamic friction on the translating particles is calculated using our multiparticle Stokesian dynamics simulation. The simulation for the no-flow condition is relatively straightforward-we only need to compute the multiparticle hydrodynamic interactions in quiescent fluid. However, for the periodic pressure condition, the net induced flow dragged by the particles has to be evaluated also. We express this net induced flow in terms of an additional pressure-driven velocity field. We present the hydrodynamic friction as a function of the dimensions of the two-dimensional periodic lattice. For closely packed arrays, the results show a considerable reduction in friction coefficients that usually increase with interparticle distance. Hence, our work renders the theoretical justification for other recent findings that indicate the importance of interparticle mutual cooperation.
在本文中，我们分析了由两个平行平面壁限定的狭缝孔隙中二维周期性球体阵列的集体运动。当所有粒子沿特定方向以相同速度运动并在其运动中相互协作时，我们确定了球体的摩擦系数。为了解决这个多体问题，我们使用斯托克斯动力学算法，并解决壁面边界几何中的多粒子流体动力学相互作用。除了粒子间相互作用外，我们还认识到所有粒子的上述集体运动对流体介质产生了累积效应。这种效应表现为周期性压力场的净感应流或静态流体的附加压力梯度。在我们的分析中，我们关注周期性压力和无流条件。对于这两种情况，使用我们的多粒子斯托克斯动力学模拟来计算平移粒子上的流体动力学摩擦。无流条件的模拟相对简单——我们只需要计算静态流体中的多粒子流体动力学相互作用。然而，对于周期性压力条件，还必须评估粒子拖动的净感应流。我们用附加的压力驱动速度场来表示这种净感应流。我们将流体动力学摩擦表示为二维周期性晶格尺寸的函数。对于紧密排列的阵列，结果表明摩擦系数显著降低，而摩擦系数通常会随着粒子间距离的增加而增大。因此，我们的工作为其他近期表明粒子间相互协作重要性的研究结果提供了理论依据。
