An inertial slender-body theory to characterize particle-fluid interactions at finite Reynolds numbers

We present a fully inertial slender-body theory to study the effects of moderate to large fluid inertia on

high aspect ratio translating particles. This is obtained by matching a solution of the full Navier-Stokes

equation in the inner region (on the scale of the particle diameter) to an outer solution that consists of a

superposition of a solution of the Oseen’s linearized Navier-Stokes equation driven by a line of forces and a

potential flow solution driven by a distribution of sources and source dipoles. The theory is validated by

comparing the orientation-dependent force and torque on a steadily translating slender particle to

the results obtained by a finite-difference Navier-Stokes solution. The drag and lift forces result from the

distribution of Oseen force singularities. These Oseenlets also predominately govern the torque at small Reynolds

numbers and large aspect ratios. However, the potential flow singularities play a crucial role in yielding

a torque that grows at large Reynolds numbers and finite aspect ratios. We demonstrate the accuracy of

our theory for Re_D up to 10, where Re_D is the Reynolds number based on the particle diameter.