Oscillating flow around a circular cylindrical post confined between two parallel flat plates

The three-dimensional oscillatory motion of a viscous fluid around a circular post confined between two plates is considered as a model for the flow of cerebrospinal fluid around the spinal-canal nerve roots. Besides the post aspect ratio λ, the problem depends on two dimensionless parameters, namely, the Womersley number $M$ (based on the post radius and the oscillation frequency) and the ratio ε of the stroke length to the cylinder radius, the latter assumed to be small herein. In the asymptotic limit ε«1, the leading-order motion is determined by a linear problem involving the balance of the local acceleration with the pressure and viscous forces. Convective acceleration introduces a small correction of order ε, including a steady-streaming component, numerically determined. Consideration is also given to the Stokes drift associated with the oscillating flow, comparable to the steady-streaming component, the sum of both determining the time-averaged Lagrangian velocity. Results reveal the formation of inner and outer streaming regions when $M$ is larger than a critical value which depends on λ. Consideration is given to limiting solutions arising for extreme values of λ and ε.