An adsorption-desorption-controlled surfactant on a deforming droplet

The effects of a sorption-controlled, monolayer-forming surfactant on a dro p deforming in an extensional how are studied numerically. Scaling argument s are presented for drops of 1 cm and 1 pm, indicating the applicability of these results. For all simulations, when mass transfer is slow compared to surface convection, the insoluble limit is recovered; when mass transfer i s rapid, the drop behavior is the same as that for a surfactant-free drop. Fora surfactant which forms a monolayer, there is an upper bound to the sur face concentration, Gamma(infinity). The surface tension reduction diverges as the surface concentration Gamma approaches this limit, strongly alterin g the hydrodynamics, The drop deformation is:studied relative to a surfactant-free drop in terms of the capillary number, Ca, the ratio of characteristic viscous stresses to surface tension. In the insoluble limit, for Gamma much less than Gamma( infinity), droplets deform more than in the absence of surfactants at a giv en Ca and break-up at lower Ca. When stable drop shapes are attained, stagn ant caps form at the drop tips. Finite surfactant mass transfer rates elimi nate these caps and diminish the deformation. For Gamma approaching Gamma(infinity) in the insoluble limit, interfaces ar e strongly stressed for perturbative surface concentration gradients; Gamma remains nearly uniform throughout the deformation process. Deformations ar e reduced at a given Ca. When stable drop shapes are attained, the surface is completely stagnated. Marangoni stresses force the surface velocity to z ero to keep Gamma below its upper bound. For soluble surfactants, as mass t ransfer rates increase, the magnitude of these stresses diminishes; Deforma tions change nonmonotonically with mass transfer rates and are not bounded by the limiting clean interface and insoluble limits. The drop contribution to the volume averaged stress tensor Sigma is also ca lculated. The axial component Sigma(zz) increases with the drop length; the radial component Sigma(rr) increases with the drop breadth. Since the defo rmation is strongly influenced by the surfactant concentration and the mass transfer rates, so too is Sigma. (C) 1998 Academic Press.