BROWNIAN-MOTION AT LIQUID-GAS INTERFACES .5. EFFECT OF INSOLUBLE SURFACTANTS NONSTATIONARY DIFFUSION

The nonstationary dynamic of a sphere floating at the Liquid-gas inter face in the presence of insoluble surfactants is studied. Taking into account the difference between the diffusion (D-s) and viscous (v) coe fficients (D-s/v less than or equal to 10(-3)), a diffusion-limited mo del for the process is assumed. The additional drag force, Delta F(t), caused by the surfactant gradients on the moving sphere (Marangoni ef fect) is analyzed. The numerical result shows two successive periods: an initial stage (Delta F approximate to 0), followed by an active rea ction of the system, with a well-expressed log-increasing resistance f orce, Delta F(t) similar to ln t. The problem with the unlimited force is discussed from the viewpoint of the Stokes paradox. The analogy wi th the dynamic behavior of the same system in steady state, is pointed out, where the resistance force proves to be proportional to Reynolds number Delta F(t) similar to ln Re.