The ocean plays a crucial role in regulating Earth's climate being one of the principal reservoirs of CO2, the main cause of greenhouse effect. A fundamental process in the uptake of CO2 into the deep sea, where it can be stored million of years, is the sinking of particulate organic material. This problem can be addressed by considering biogenic particles transported in oceanic flow as passive particles with a constant settling velocity to account for the sinking dynamics. The validity of this approximation and the influence of different physical processes is generally not discussed in these analyses. Here we address this caveat by considering the theory of finite-size particles driven by fluid flows, which is based on the Maxey-Riley-Gatingol equation.