Farzin Majid, Ronasi Kiyandokht, Najafi Ali
Department of Physics, Zanjan University, Zanjan 313, Iran.
Phys Rev E Stat Nonlin Soft Matter Phys. 2012 Jun;85(6 Pt 1):061914. doi: 10.1103/PhysRevE.85.061914. Epub 2012 Jun 19.
We investigate hydrodynamic interactions between two three-sphere swimmers analytically and numerically. Hydrodynamic forces exerted on the swimmers as well as the translational and angular velocities of them are obtained in the far field regime. We demonstrate that the active term of the translational velocity is along the intrinsic direction of swimming (n) and has no component along the direction of relative positions of swimmers (r[over ̂]) as reported in previous papers. Using numerical simulations we investigate the long-time swimming paths of swimmers in two general situations of swimming in the same and opposite directions. The former reveals four swimming states for symmetric swimmers-attractive, repulsive, parallel, and oscillatory-and only three swimming states for asymmetric swimmers-attractive, repulsive, and contracting-oscillatory, confirming that the expanding-oscillatory state reported in previous papers is not stable. The latter shows that there are rotative bound states in hydrodynamic scattering of the swimmers.
我们通过解析和数值方法研究了两个三球体游动者之间的流体动力学相互作用。在远场区域中，获得了作用在游动者上的流体动力以及它们的平动和角速度。我们证明，平动速度的有源项沿游动的固有方向（n），并且如先前论文所报道的那样，在游动者相对位置的方向（r̂）上没有分量。通过数值模拟，我们研究了游动者在同向和反向游动这两种一般情况下的长时间游动路径。前者揭示了对称游动者的四种游动状态——吸引、排斥、平行和振荡，而非对称游动者只有三种游动状态——吸引、排斥和收缩 - 振荡，这证实了先前论文中报道的膨胀 - 振荡状态是不稳定的。后者表明，在游动者的流体动力学散射中存在旋转束缚态。
