Effects of non-linear interfacial mechanics on the transient response of a drop to an external flow field

The time-dependent response of a drop suspended in an axisymmetric extensional flow is studied. The dynamics of such multiphase systems is of interest in areas that include the petroleum, pharmaceutical, biomedical and food industries. The focus is on the role that a surfactant monolayer on the drop interface plays during the deformation and retraction processes. The steady-state characteristics and the bulk flow are analyzed for validation. The transient processes are simulated using an axisymmetric boundary integral method. At each time step the shape of the drop is determined based on the velocity of points at the interface and surfactant is redistributed accordingly.; The response time taus of drop deformation in an extensional flow was seen to depend monotonically on the initial surfactant coverage X on the interface. That is, higher X leads to increasing values of taus. In this sense, it was seen that Marangoni stresses developing on the interface due to surface tension gradients act to slow the response time of the drop.; Retraction of the drop when the external flow ceases is caused by an imbalance between the traction along the drop's interface and the shear stresses. Neglecting the initial stages, the retraction process can be closely approximated by an exponential decay. It was shown that the retraction time tau r depends non-monotonically on X. Small amounts of surfactant slow down the retraction process compared to that of the clean drop for X ≤ 0:5. Further increasing the surfactant concentration accelerates the retraction process and as X → 1, the value of taur approaches that of the clean drop. These dynamics emerge from the competition between the convective flux that creates the surfactant gradients and the large Marangoni stresses that develop to oppose them during the extension process. At low to intermediate surfactant concentrations, large surfactant gradients developed during the deformation process persist until equilibrium is reached because diffusion time is much longer than the retraction rate. At higher initial surfactant concentrations, lower surfactant gradients develop during deformation and these quickly vanish during the initial stages of retraction leading to a nearly uniform surface tension distribution along the interface.