Drop deformation in a planar elongational flow: impact of surfactant dynamics

Drops in extensional flow undergo a deformation, which is primarily fixed by a balance between their surface tension and the viscous stress. This deformation, predicted and measured by Taylor on millimetric drops, is expected to be affected by the presence of surfactants but has never been measured systematically. We provide a controlled experiment allowing us to measure this deformation as a function of the drop size and of the shear stress for different surfactants at varying concentrations. Our observation is that the deformation predicted by Taylor is recovered at zero and high surfactant concentration, whereas it is smaller at concentrations close to the critical micellar concentration. This is in contradiction to the existing analytical models. We develop a new analytical model, taking into account the surfactant dynamics. The model predicts a transition between a deformation similar to that of a pure liquid and a smaller one. We show that the transition is driven by a parameter K_L, which compares adsorption and desorption dynamics. Finally, the concentration C*, at which we observe this transition in the extensional flow is in good agreement with the one predicted by independent measurements of K_L.