Settling of highly porous and impermeable particles in linear stratification: implications for marine aggregates

Abstract

The settling velocity of porous particles in linear stratification is affected by the diffusive exchange between interstitial and ambient water. The extent to which buoyancy and interstitial mass adaptation alters the settling velocity depends on the ratio of the diffusive and viscous time scales. We conducted schlieren experiments and lattice Boltzmann simulations for highly porous (95 %) but impermeable spheres settling in linear stratification. For a parameter range that resembles marine porous particles, ‘marine aggregates’, i.e. low Reynolds numbers ( $0.05\leq \textit {Re}\leq 10$ ), intermediate Froude numbers ( $0.1\leq \textit {Fr}\leq 100$ ) and Schmidt number of salt ( $\textit {Sc}=700$ ), we observe delayed mass adaptation of the interstitial fluid due to lower-density fluid being dragged by a particle that forms a density boundary layer around the particle. The boundary layer buffers the diffusive exchange of stratifying agent with the ambient fluid, leading to an enhanced density contrast of the interstitial pore fluid. Stratification-related drag enhancement by means of additional buoyancy of dragging lighter fluid and buoyancy-induced vorticity resembles earlier findings for solid spheres. However, the exchange between density boundary layer and pore fluid substantially increases stratification drag for small $\textit {Fr}$ . To estimate the effect of stratification on marine aggregates settling in the ocean, we derived scaling laws and show that small particles ( $\leq$ 0.5 mm) experience enhanced drag which increases retention times by 10 % while larger porous particle (>0.5 mm) settling is dominated by delayed mass adaptation that diminishes settling velocity by 10 % up to almost 100 %. The derived relationships facilitate the integration of stratification-dependent settling velocities into biogeochemical models.