An improved analytic solution for analysis of particle trajectories in fibrous, two-dimensional filters

The Kuwabara solution for creeping fluid flow through periodic arrangement of cylinders is widely used in analytic and numerical studies of fibrous filters. Numerical solutions have shown that the Kuwabara solution has systematic errors, and when used for the particle trajectories in filters it results in some error in the predicted filter efficiency. The numerical solutions, although accurate, preclude further analytic treatments, and are not as compact and convenient to use as the Kuwabara solution. By reexamining the outer boundary conditions of the Kuwabara solution, a correction term to the Kuwabara solution has been derived to obtain an extended solution that is more accurate and improves prediction of the filter efficiency. By comparison with the numerical solutions, it is shown that the Kuwabara solution is the high porosity asymptote, and that the extended solution has an improved porosity dependence. A rectification is explained that can make particle collection less efficient for periodic, in‐line arrangements of fibers with particle diffusion or body force. This rectification also results in the alignment of particles with inertia (i.e., high Stokes number particles)