On the effect of trabeculae on steady streaming in the subarachnoid space
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The pulsating motion of the cerebrospinal fluid in the subarachnoid space (SAS) surrounding the brain and the spinal cord is known to be affected by the presence of trabeculae. Effects of trabeculae on steady streaming are addressed in this paper using as a model problem that of oscillatory flow in a slender channel subject to a harmonic longitudinal pressure difference. The presence of trabeculae is described using a homogenized model accounting for the disparity of length scales present in the problem, resulting in a resistance term linearly proportional to the flow velocity. The asymptotic analysis for small stroke lenghts provides a closed-form solution for the steady--streaming motion. The analysis reveals significant differences between the secondary flow developed in the presence of trabeculae and that of unobstructed flow, with the former exhibiting much smaller velocities, especially for the moderately large values of the Womersley number characterizing flow in the SAS.