Encounter rates between bacteria and small sinking particles

The ecological interaction between bacteria and sinking particles, such as bacterial degradation of marine snow particles, is regulated by their encounters. Current encounter models focus on the diffusive regime, valid for particles larger than the bacterial run length, yet the majority of marine snow particles are small, and the encounter process is then ballistic. Here, we analytically and numerically quantify the encounter rate between sinking particles and non-motile or motile micro-organisms in the ballistic regime, explicitly accounting for the hydrodynamic shear created by the particle and its coupling with micro-organism shape. We complement results with selected experiments on non-motile diatoms. 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 micro-organisms preferentially orient normally to the particle surface downstream of the particle (focusing) and tangentially to the surface upstream of the particle (screening). Non-motile elongated micro-organisms are screened from sinking particles because shear aligns them tangentially to the particle surface, which reduces the encounter rate by a factor proportional to the square of the micro-organism aspect ratio. For motile elongated micro-organisms, hydrodynamic focusing increases the encounter rate when particle sinking speed is similar to micro-organism swimming speed, whereas for very quickly sinking particles hydrodynamic screening can reduce the encounter rate below that of non-motile micro-organisms. For natural ocean conditions, we connect the ballistic and diffusive limits and compute the encounter rate as a function of shape, motility and particle characteristics. Our results indicate that shear should be taken into account to predict the interactions between bacteria and sinking particles responsible for the large carbon flux in the ocean's biological pump.