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

Sinking marine snow particles, composed primarily of organic mattet, play a critical role in transporting photosynthetically fixed carbon from the ocean surface to the sea bed. Their downward flux is influenced by interactions with suspended micron-sized objects, which can alter particle mass and buoyancy, and with bacteria capable of colonizing and degrading them. Collision rates between sinking particles and smaller entities are typically estimated using two contrasting models: one based on direct (ballistic) interception with finite interaction range, and another on advective-diffusive transport assuming zero interaction range. However, the appropriate conditions for applying each model remain unclear, particularly since many marine interactions fall between these two regimes. This ambiguity complicates encounter rate predictions, especially at high Péclet numbers where the models diverge significantly.

Here, we bridge these two approaches through a combination of theoretical analysis and numerical simulations. By solving the advection-diffusion equation in Stokes flow around a sinking sphere, we model mass transfer from small, finite-sized objects to larger particles and derive a new expression for the Sherwood number. This formulation captures the dependence on both the Péclet number and the size ratio between small and large particles. Surprisingly, we find that diffusion remains a significant contributor to encounter rates even at very high Péclet numbers (up to 10⁶), where the direct interception model can underestimate encounter frequencies by as much as two orders of magnitude. Our findings reveal that diffusion-driven encounters may substantially accelerate key processes such as bacterial colonization, plankton attachment, and gel accretion, ultimately affecting the biological carbon pump more than previously recognized.