On the collision of rods in a quiescent fluid

Abstract

Rods settling under gravity in a quiescent fluid can overcome the bottleneck associated with aggregation of equal-size spheres because they collide by virtue of their orientation-dependent settling velocity. We find the corresponding collision kernel Γrods=lβ1ΔρVrodg/(16Aμ), where l, A, and Vrod are the rods’ length, aspect ratio (length divided by width), and volume, respectively, Δρ is the density difference between rods and fluid, μ is the fluid’s dynamic viscosity, g is the gravitational acceleration, and β1(A) is a geometrical parameter. We apply this formula to marine snow formation following a phytoplankton bloom. Over a broad range of aspect ratios, the formula predicts a similar or higher encounter rate between rods as compared to the encounter rate between (equal volume) spheres aggregating either by differential settling or due to turbulence. Since many phytoplankton species are elongated, these results suggest that collisions induced by the orientation-dependent settling velocity can contribute significantly to marine snow formation, and that marine snow composed of elongated phytoplankton cells can form at high rates also in the absence of turbulence.