For the case of a small drop of surfactant dropped onto the surface of water, Roché and coworkers performed quantitative experiments and developed a simple model that was in approximate agreement with the experiments. This described the expansion in the radius r of a patch of the surface covered in surfactant, due to an outward Marangoni flow at a speed u . They found that speed of expansion of the surfactant-covered patch of the water surface occurred at speed of approximately