Slender body theory for fluid-particle interactions at finite Reynolds numbers

We study the effects of finite fluid inertia on the translational and rotational dynamics of high aspect ratio fibers using slender body theory. We build on the weakly inertial slender body theory of Khayat and Cox (1989) (valid when the Reynolds number Re_D based on the fiber diameter is small) and extend the theory to Re_D = O(1). This is achieved by matching the quasi-two-dimensional solution to the full Navier-Stokes equation in the inner region (fiber diameter scale) to the three-dimensional solution of the linearized Navier-Stokes equation in the outer region (fiber length scale). The results for the orientation-dependent drag, lift, and torque for a broad range of values of fiber aspect ratios and Reynolds numbers are obtained and compared with complementary numerical simulation results. The finite-Re_D slender body theory is then used to explore the unsteady dynamics resulting from the coupled effects of translation and rotation of a freely sedimenting fiber. By incorporating the convection of the transient fiber-induced fluid momentum disturbance by the imposed flow in the fiber-attached reference frame, we obtain a more accurate description of fiber rotation than that given by the commonly invoked quasi-steady approximation.