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Cyan: drag-corrected terminal speed at the surface temperature. Dashed grey: pure Stokes law (valid only at Reynolds number below about 1). Large fluffy aggregates are held back by the nonlinear drag.
The science
Aggregates. Marine snow is made of tiny primary particles (here 10 micrometres) glued into fractal flakes. A flake of diameter d and fractal dimension Df contains a solid volume fraction φ = (d/d0)Df - 3, so it is almost all water. Its excess density over seawater is Δρ = φ (ρs - ρw); minerals (opal, CaCO3, dust) raise ρs ("ballast").
Sinking speed. Weight minus buoyancy balances drag: Δρ g (π/6) d3 = CD (π/8) ρw d2 w2 with CD = (24/Re)(1 + 0.15 Re0.687), Re = ρw w d / μ. At Re << 1 this reduces to Stokes' law w = Δρ g d2/(18 μ). Cold deep water is more viscous, so aggregates slow down with depth.
Bacteria. Attached bacteria respire the carbon: dm/dt = -k m with k(T) = k0 Q10(T - 10)/10. For one size class the mass left at depth z is exp(- ∫ k/w dz).
The Martin curve. Observed sediment-trap fluxes follow F(z) = F100 (z/100)-b with b near 0.86 (Martin et al. 1987). No single size gives a power law; it emerges from summing many sizes with different speeds: slow flakes are eaten in the upper ocean, fast ones survive. Here the surface carbon flux per size is q(d) ∝ d1 - α + Df (number spectrum slope α), and b is fitted between 100 and 1000 m. Warmer water makes bacteria faster, so b rises and less carbon reaches the deep sea (Marsay et al. 2015 report this trend).
Sediment trap. The moving particles in the 3D column are drawn in proportion to the carbon they carry, each with the same weight, so the share of carbon that reaches the trap is simply the average of the surviving mass of the agents that cross its depth.
Honest simplifications. Flakes are treated as solid spheres with a mean density (real aggregates are porous and fluid flows partly through them, which speeds them up); no aggregation or fragmentation on the way down (it changes b), no zooplankton feeding or fecal pellets, no horizontal currents, one bacterial rate for all sizes; particle numbers shown are drawn for clarity. Parameter values are illustrative and not calibrated to a particular ocean site. Educational use only.