Effects of soluble and insoluble surfactants on the motion of drops

Abstract

The fluid dynamics of moving drops in the presence of a soluble surfactant and an insoluble impurity is examined in detail. The main purpose of this analysis is to establish a fairly general theory that agrees with experimental measurements. Particular attention is paid to situations involving a stagnant cap which arise when low-solubility surfactants are present. Earlier theories on stagnant caps have not satisfactorily explained the experimental results and a two-impurity model is therefore proposed. The analysis is carried out semi-analytically using a matched asymptotic analysis of the Proudman-Pearson type for weakly inertial flows. The results seem to be in good agreement with the available data at a Péclet number of about 700 for the soluble surfactant. In particular the predicted flow field within the drop is found to be consistent with the experimental measurements of Horton. The concentration profiles graphically exhibit the physical phenomena involved in the mass transport. Another new result is the analytical expression for the drag force corrected up to O(Re) for the case involving only the insoluble surfactant.