The effect of neighbors on the effective inertial collision efficiency of cylindrical collectors

We investigate the effect that an upstream cylinder has on the effective inertial collision efficiency of a downstream cylinder. We consider an initially uniform distribution of particles moving past a cylindrical fiber in a potential crossflow and numerically calculate the resulting particle distribution far downstream of the fiber using finite differences. We then investigate the effect that the downstream distribution of particles has on the effective inertial collision efficiency of a downstream test cylinder oriented parallel to the first. We show that the effective collision efficiency of the test cylinder depends on its relative offset in the transverse direction (normal to the flow) with respect to the upstream cylinder. For relatively small offsets there is complete shielding, and no particles collide with the test cylinder. As the offset increases, a growing effective collision efficiency is observed leading to a significant enhancement relative to the collision efficiency of an isolated cylinder for intermediate offsets and Stokes numbers close to unity. Importantly, we observe relative gains in effective collision efficiency above 100% for a range of Stokes numbers and offset values. For larger offsets and Stokes numbers, the effect of the upstream cylinder on the effective collision efficiency of the test cylinder decreases and eventually becomes negligible. Detailed results are provided for Stokes drag acting on the particles and we also show that a non-linear drag has a negligible effect on the observed trends for the conditions relevant to air filtration systems. These results suggest that the arrangement of fibers has a substantial effect on inertial particle impaction even when neighboring fibers do not alter the flow field around each individual collector. Moreover, periodic arrangements with specific orientations with respect of the flow could lead to a significant enhancement of the inertial collision of particles on an array of collectors, thus contributing towards a better filtration performance.