Longitudinal permeability of spatially periodic rectangular arrays of circular cylinders II. An arbitrary distribution of cylinders inside the unit cell
We study the longitudinal permeability of unidirectional disjoint circular cylinders, when a Newtonian fluid is flowing at low Reynolds number along these cylinders; the longitudinal velocity satisfies the Poisson equation. The cylinders are arranged according to a doubly periodic structure. The number of cylinders in each rectangle can be arbitrary as well as their positions and radii. The method of functional equations yields analytical formulae for permeability in terms of these quantities. These formulae are written also in continuous form to study the flow for large numbers of cylinders. Special attention is paid to the case of the square unit cell, equal radii and lognormal distribution of radii.