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

Abstract

This work is motivated by the interest in determining the effect of the micro-anatomy of the spinal subarachnoid space (SSAS) on the cerebrospinal fluid flow. To that aim, we model the nerve roots in the SSAS by circular posts of radius a, confined between two parallel plates separated by a distance 2h and subjected to an oscillatory flow of angular frequency ω. First, we analyze the asymptotic limit of small values of the dimensionless stroke length of the oscillatory flow, for a harmonic waveform, varying the aspect ratio of the post λ=h/a and the Womersley number Wo=(a2ω/ν)1/2. For low values of Wo, the time-averaged steady flow exhibits symmetric recirculating vortices attached to the wall of the post whose size decreases as Wo increases. However, for values of Wo larger than a critical one, Woc(λ), which depends on λ, a second, outer vortex is also formed. The dependence of Woc(λ) has been quantified in the range 0.5<λ<∞, showing a decrease in Woc with λ. The analysis has been corroborated experimentally for λ = 2, and varying Wo, the stroke length as well as the wave form of the oscillating flow. Imposing an anharmonic oscillating flow shows that the fort-and-aft symmetry of the steady flow is broken, with the formation of two vortices of different size when Wo<Woc and only one outer vortex in the systolic direction when Wo>Woc. Finally, the study is experimentally extended considering an array of equally spaced posts, separated a semi-distance d=2a aligned with the flow. Qualitatively, the steady flow patterns induced for ℓ=d/a=2 are similar to those for ℓ→∞, although the presence of the nearby posts confines the recirculating vortices and delays the flow transition, increasing Woc(λ).