(406c) Surfactant Effects On A Viscous Drop Injected Into A Viscous Medium In The Diffusion-Controlled Limit

The effects of a diffusion controlled surfactant on the evolution of a buoyant viscous drop injected into a viscous fluid are studied numerically for the case of finite bulk convection to resolve neck dynamics and detaching drop volumes. When the drop is formed, its interface initially expands. Surfactant adsorbs and depletes a region around the drop. When the drop is sufficiently elongated, a neck begins to form. The surface contracts rapidly above the neck, driving the surface concentration above its equilibrium value. Surfactant subsequently desorbs into the region adjacent to the interface that had previously been depleted of surfactant. This can create diffusion fluxes away from the neck that are larger than suggested by an a priori scaling of the governing equations. The rapid flux can remove surfactant effectively from the contracting neck, preventing the occurrence of strong local reductions in the surface tension. Through this mechanism, neck dynamics are altered only weakly for surface coverages x = Γ_eq/Γ_∞ less than or equal to 0.9. For surface coverages close enough to maximum packing (x = 0.92) and for diffusion fluxes that are sufficiently slow, surfactant accumulation can reduce the local surface tension sufficiently to prevent drops from detaching. For moderate surfactant coverages, drop volume V is bounded above by the surfactant-free value V_o and below by the volume of the drop with uniform surface tension at equilibrium with the surfactant solution V_∞. V decreases monotonically from V_o to V_∞ as diffusion rate to convection rate increases. For x = 0.92, however, non-monotic variations in V occur that are not bounded by these two limits. A phase diagram summarizing neck shapes and regimes where drops fail to detach is presented as a function of Ψ, which characterizes the rate of surfactant diffusion to the rate of surface contraction.