Encounter rates between motile bacteria and sinking particles

Many marine microbes rely on sinking particles of organic matter as their food source. Once attached to a particle, bacteria can solubilize its organic matter and convert it into biomass. This process hinders carbon from sinking to the deep ocean (a process known as the ‘biological pump’) and thus affects the magnitude of carbon flux in the ocean. Carbon consumption by bacteria is preceded by their encounter with sinking particles, whose quantification is needed to understand the biological pump. Here, we theoretically predict these encounter rates by combining the Stokes flow around the particle with Jeffrey's equation for a rod in flow. We show that elongated bacteria - unlike spherical particles often used in encounter rate estimates – break the fore-aft symmetry of the flow streamlines, with major consequences on encounter rates. Specifically, for small to intermediate sinking speeds, this symmetry-breaking implies that elongated swimmers are up to hundred times more likely to encounter the sinking particle than spherical bacteria with the same volume. We find that the mechanism for this encounter rate enhancement is the hydrodynamic focusing of elongated swimmers downstream of the sinking particle, which leads to their preferential attachment to the back of the particle.