Modeling of Periodical Shearing Flow in a Fibrous Space*

In this paper, a theoretical model is developed to describe the fluid flow in a thin fibrous gap between two parallel plates, in response to an oscillating shearing impact imposed on one of the boundaries. The fluid velocity field is determined by an effective medium approach, while the fiber deformation is solved by treating each fiber as a soft string. It has been found that the shearing behavior is mainly influenced by the oscillation frequency, fiber stiffness, and porous resistance. The key dimensionless parameters governing the process are the Womersley number, Brinkman number, and Bingham number. The fluid velocity, fiber displacement, shear stress, and porous resistance have been examined through parametric studies. The theory is applied to estimate the interaction between the arachnoid trabecula and the cerebral spinal fluid flow in the subarachnoid space, as the head is exposed to shaking impacts. The results indicate that the shear stress could penetrate through the porous gap and reach the brain matter, and the shear stress acting on the brain surface (Pia Mater) could be even higher than that on the inner surface of the skull (Dura Mater). For the first time, the transmission of the shearing impact from the skull to the soft brain matter is quantitatively determined.