Fig. 1.

(A) The collision cross-section (blue broken line) between two rods is determined by their projections (blue and red rectangles) onto the plane perpendicular to their relative velocity $\mathrm{\Delta }{u}_{12}$. (B) The collision kernel ${\mathrm{\Gamma }}_{\text{rods}}$ for identical rods settling in a quiescent fluid (Eq. 3) as a function of the rod aspect ratio $A$ for a fixed rod volume (equivalent sphere radius $r=5\hspace{0.17em}\mathrm{\mu }\text{m}$) indicates an optimal aspect ratio of $A\approx 50$. (C and D) Comparison between ${\mathrm{\Gamma }}_{\text{rods}}$ and the collision kernels for (C) equal volume spheres colliding by differential settling due to size mismatch (Eq. 4) and (D) turbulence-induced encounters of identical spheres (Eq. 6). (C) The ratio of the encounter kernels $2{\mathrm{\Gamma }}_{\text{rods}}/{\mathrm{\Gamma }}_{\text{ds}}$ (Eq. 5) as a function of $A$ and the sphere size mismatch factor $f$ (how much larger half of the spheres are compared to the other half). (D) The ratio ${\mathrm{\Gamma }}_{\text{rods}}/{\mathrm{\Gamma }}_{\text{turb}}$ as a function of $A$ and the spherical particle radius $r$ (Eq. 7). Parameters are as follows: $ϵ=10^{-6}\hspace{0.17em}\text{W}\cdot {\text{kg}}^{-1}$, $\nu =10^{-6}\hspace{0.17em}{\text{m}}^2\cdot {\text{s}}^{-1}$, and $\mathrm{\Delta }\rho =100\hspace{0.17em}{\text{kg}\cdot \text{m}}^{-3}$.