Several experiments have attempted to test Martin's hypothesis that addition of soluble iron to iron-limited ocean regions will lead to an increase in carbon sequestration via phytoplankton growth and sedimentation. However, artificially iron-induced blooms do not always trigger increases in vertical carbon export. Here we show that to trigger export, a patch must be larger than a threshold size. Phytoplankton sink en masse only after reaching a critical concentration for aggregation, and concentration is dependent on the competitive balance between growth and horizontal turbulent diffusion, which in turn varies with patch length scale. We summarize this balance using a non-dimensional parameter, Q, and use a simple 2D model solving a growth-diffusion-export equation to show that export flux occurs from a fertilized patch when Q < 1, and that flux is maximized at a value of Q below this critical point. A simple nutrient limitation model generates predictions of particle export from patch fertilization experiments.