Dynamics of finite-symmetry and general-shaped objects under shear and shear alignment of uniaxial objects at finite...

We prove that, for an object with a finitefold rotational symmetry (except for a twofold one) around an axis and mirror symmetries (such as a square rod or pentagonal slab, etc.), dynamics of the symmetry axis in low Reynolds number shear flow exactly follows the same form as that of a uniaxial object (e.g., a circular rod or symmetric ellipsoid) as the so-called Jeffery orbits. We use the formulation in which the dynamics of the rigid body follows first-order ordinary differential equations in time [Phys. Rev. E 84, 056309 (2011)]. Interaction between the object and the shear flow enters through a set of scalar coefficients, and the flow field does not need to be solved dynamically. Results of numerical simulations for general-shaped objects also are discussed. In the second part, Brownian dynamics of a uniaxial object is studied numerically. With D as the rotational diffusion constant, α as a parameter characterizing the aspect ratio, and γ as the shear rate, the object starts to align with the flow when the value of D/(γα) decreases near 1. At large α (the long object limit), the results suggest much lower flow alignment when D/(γα)>1.