Viscous Flow Through Polydisperse Row of Parallel Fibers: Account for the Slip Effect

A general theory of the flow through the flat periodic row of parallel polydisperse fibers randomly arranged at the fiber period is elaborated. An approximate solution of the problem with account for the slip effect at low Reynolds numbers is obtained for normal incident flow. The system of equations for determining local drag forces acting on each fiber in a row, as well as the system of equations for determining local buoyancy forces, are derived. It was demonstrated that, in the approximation obtained, the buoyancy forces are equal to zero, provided that bilateral symmetry is present in the fiber arrangement. The behavior of local forces as a function of row parameters is considered using bimodal row as an example. The form of flow function is established for the velocity field near the arbitrary fiber.