Bridging advection and diffusion in the encounter dynamics of sedimenting marine snow

Sinking marine snow particles, composed primarily of organic matter, control the global export of photosynthetically fixed carbon from the ocean surface to depth. The fate of sedimenting particles is partly regulated by their encounters with suspended objects, which leads to mass accretion and potentially alters their buoyancy, and with bacteria that can colonise the particles and degrade them. Their collision rates are typically calculated using two types of models focusing either on direct (ballistic) interception with a finite interaction range, or advective-diffusive capture with zero interaction range. Yet, since many relevant marine encounter scenarios span across both regimes, quantifying such encounters remains challenging because the two models yield asymptotically different predictions at high Péclet numbers. We reconcile the two approaches by quantifying encounters in the general case using theoretical analysis and simulations. By solving the advection-diffusion equation in Stokes flow around a sphere to model mass transfer to a sinking particle by finite-sized objects, we determine a new formula for the Sherwood number as a function of the Péclet number and the ratio of particle sizes. Contrary to the common assumption, we find that diffusion still plays a significant role in generating encounters even at high Péclet numbers. We predict that at Péclet numbers as high as 10 6 the direct interception model underestimates the encounter rate by up to two orders of magnitude. This overlooked contribution of diffusion to encounters suggests that processes affecting the fate of marine snow may proceed at a rate much higher than previously thought.