Bursts Characterize Coagulation of Rods in a Quiescent Fluid

Under favorable conditions, microscopic phytoplankton cells dwelling in the oceans can divide rapidly and reach high concentrations, forming blooms that span kilometers and last for weeks. When blooms collapse, dead cells settle and aggregate into "marine snow" particles, resulting in a large and climatically important vertical flux of carbon from the ocean surface to its depth, a process known as the "biological pump." To date, the formation of marine snow has been modeled as coagulation between spherical particles driven by gravitational settling and turbulent mixing, characterized by coagulation dynamics that converge onto time-independent concentrations of aggregates. However, many phytoplankton species are elongated and how their rodlike shape affects the aggregation process has remained unknown. Here, we study marine snow formation in a quiescent fluid assuming the constituent particles are elongated and form bundles upon encounter. We derive the collision kernel between dissimilar rods settling under gravity and discover that the most frequent collisions occur between the thinnest and thickest bundles, rather than between bundles of similar size. As a consequence, in the full coagulation model that combines exponential growth with settling, the thin-thick coupling can lead to statistically stationary states where the concentrations of aggregates of different size oscillate in time, exhibiting periodic bursts. The bursts are predicted to occur on the scale of a week and eventually lead to broadening of aggregate size spectra and may thus be highly relevant for plankton dynamics and the carbon cycle in the ocean.