An asymptotic analysis of cavity flow induced by a flexible membrane in an oscillatory channel flow: case study of syringomyelia
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In an effort to shed light into the role of pulsatile motion in the development of syringomyelia, asymptotic methods are employed to analyze departures from harmonic Womersley flow in a two dimensional channel separated by an elastic membrane from a slender fluid-filled cavity. Closed-form expressions are derived for the mean Lagrangian motion induced in the channel and in the cavity, given by the sum of steady-streaming and Stokes drift velocities, as well as for the induced pressure difference.