In this paper, we consider the dynamics of a helicoidal object, which can be either a passive particle or an active swimmer, with an arbitrary shape in a linear background flow at low Reynolds number, and derive a generalized version of the Jeffery equations for the angular dynamics of the object, including a new constant from the chirality of the object as well as the Bretherton constant. The new constant appears from the inhomogeneous chirality distribution along the axis of the helicoidal symmetry, whereas the overall chirality of the object contributes to the drift velocity. Further investigations are made for an object in a simple shear flow, and it is found that the chirality effects generate non-closed trajectories of the director vector which will be stably directed parallel or anti-parallel to the background vorticity vector depending on the sign of the chirality. A bacterial swimmer is considered as an example of a helicoidal object, and we calculate the values of the constants in the generalized Jeffery equations for a typical morphology of Escherichia coli. Our results provide useful expressions for the studies of microparticles and biological fluids, and emphasize the significance of the symmetry of an object on its motion at low Reynolds number.

中文翻译：

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低雷诺数流动中的螺旋粒子和游泳者

在本文中，我们考虑螺旋物体的动力学，它可以是被动粒子或主动游泳者，在低雷诺数的线性背景流中具有任意形状，并推导出杰弗里方程的广义版本物体的角动力学，包括来自物体手性的新常数以及布雷瑟顿常数。新常数来自沿螺旋对称轴的非均匀手性分布，而物体的整体手性对漂移速度有贡献。对简单剪切流中的物体进行了进一步研究，并且发现手性效应产生导向向量的非闭合轨迹，其将根据手性的符号稳定地平行或反平行于背景涡度向量。细菌游泳者被认为是螺旋形物体的一个例子，我们计算了典型大肠杆菌形态的广义 Jeffery 方程中的常数值。我们的结果为微粒和生物流体的研究提供了有用的表达，并强调了物体的对称性对其在低雷诺数下运动的重要性。