HYDRODYNAMIC RESISTANCE OF THE ROW OF PARALLEL POLYDISPERSE FIBERS

The problem of the hydrodynamic resistance of the periodic row consist ing of parallel cylindrical fibers of various sizes arranged in the pl ane perpendicular to the flux is considered at low Reynolds numbers. F or the row with arbitrary fiber arrangement at the period, a system of equations was obtained that determines the resistance forces acting o n each fiber, provided that the distance between the nearest fibers is much larger than their radii. Based on this system of equations for t he row of equidistanced fibers, various characteristics of the distrib ution of local resistance forces were determined analytically and nume rically. The analytical expression for the dependence of the mean forc e on the fiber polydispersity was derived. It was revealed that the fi ber radii of the monodisperse row with the same resistance are less th an the arithmetic mean but larger than the geometric mean. Good agreem ent was found between the theory and the numerical calculations perfor med for the row with lognormal fiber radius distribution including cal culations carried out for high fiber polydispersity. A theory was deve loped for the rows containing defects, i.e., for monodisperse rows whe re there is one, two, or many long-distanced fibers with radii differe nt than those of main fibers.