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Encounter rates between bacteria and small sinking particles

Bacteria in aquatic environments often interact with particulate matter. A key example is bacterial degradation of marine snow responsible for carbon export from the upper ocean in the biological pump. The ecological interaction between bacteria and sinking particles is regulated by their encounter rate, which is therefore important to predict accurately in models of bacteria-particle interactions. Models available to date cover the diffusive encounter regime, valid for sinking particles larger than the typical run length of a bacterium. The majority of sinking particles, however, are small, and the encounter process is then ballistic rather than diffusive. In the ballistic regime, the shear generated by the particle's motion can be important in reorienting bacteria and thus determining the encounter rate, yet the effect of shear is not captured in current encounter rate models. Here, we combine analytical and numerical calculations to quantify the encounter rate between sinking particles and non-motile or motile microorganisms in the ballistic regime, explicitly accounting for the hydrodynamic shear created by the particle and its coupling with microorganism shape. We complement results with selected experiments on non-motile diatoms. We find that the shape-shear coupling has a considerable effect on the encounter rate and encounter location through the mechanisms of hydrodynamic focusing and screening, whereby elongated microorganisms preferentially orient normally to the particle surface downstream of the particle (focusing) and tangentially to the particle surface upstream of the particle (screening). We study these mechanisms as a function of the key dimensionless parameters: the ratio of particle sinking speed to microorganism swimming speed, the ratio of particle radius to microorganism length, and the microorganism's aspect ratio.