Dynamics of an open elastic rod with intrinsic curvature and twist in a viscous fluid

A twisted elastic rod with intrinsic curvature is considered. We investigate the dynamics of the rod in a viscous incompressible fluid. This fluid is governed by the Navier–Stokes equations and the fluid-rod interaction problem is solved by the generalized immersed boundary method combined with the Kirchhoff rod theory. We classify the equilibrium configurations of an open elastic rod as they depend on the rod’s intrinsic characteristics and fluid properties. We assume that the intrinsic curvature and twist are distributed uniformly along the rod. In the case of zero intrinsic curvature i.e., the stress-free state of the rod is straight , we find a critical value of twist, below which the straight state of the rod is stable. When the twist is above this critical value, however, the rod buckles locally and produces a loop or a plectoneme or a combination of both. When the constant intrinsic curvature is nonzero, we also find a critical value of twist that distinguishes a buckled rod from a stable helix. We also find that fluid viscosity plays an important role in determining equilibrium configuration in this paper. © 2010 American Institute of Physics. doi:10.1063/1.3326075