Coalescence of drops with tangentially mobile interfaces: Hydrodynamic effects of surfactant and ambient flow

A theoretical and computational study is presented for the axisymmetric near-contact motion of drops in the presence of adsorbed insoluble surfactant and ambient flow. Small deformation conditions are assumed.;The near-contact dynamics of drops with surfactant-covered interfaces is characterized by an elasticity paramater, and two distinct behaviors are predicted. For surfactant elasticities larger than a critical value, film thinning is monotonic in time, whereas for subcritical elasticity, surfactant redistribution leads to a period of film thickening. These qualitative features are predicted for the near-contact motion between drops and the near-contact motion of a drop toward a rigid wall.;Film drainage for drops with surfactant-covered interfaces occurs on two distinct time scales. Initially, the system evolves on the time scale characteristic of drops with clean interfaces, which is controlled by the drop-phase viscosity. During the initial evolution, surfactant is passively convected out of the near-field region. Marangoni stresses are unimportant locally; they affect the evolution only through the resulting Marangoni force that they generate.;At long times, Marangoni stresses become dominant and the system evolves on the time scale characteristic of rigid particles. The long-time evolution depends only on the surfactant elasticity, whereas the drop-phase viscosity and the initial conditions have a negligible influence. The surfactant distribution and film thickness profile evolve quasistatically.;An intermediate-time regime occurs for subcritical values of the elasticity parameter. In this regime, the length scales for the surfactant and film thickness profiles are well separated and the short- and long-time approximations co-exist. In the near-field region, the film profile evolves according to the short-time approximation, on the clean-drop time scale. In a far-field region scaling with the drop radius, the surfactant profile forms a front that retracts on the rigid-particle time scale. Film thickening occurs as the surfactant front retracts into the near-field.;A new thin-film formulation for the near-contact motion of drops in the presence of ambient flow is presented. The influence of ambient flow conditions on film drainage is characterized by a single flow-strength parameter, S. According to the analysis presented, film drainage is qualitatively affected by ambient flow conditions at long times. Two distinct behaviors occur, depending on the direction of the drop-scale tangential stresses generated by the ambient flow. For drop-scale stresses that are radially inward in the near-contact region (S < 0), film drainage is arrested; film drainage is accelerated for drop-scale stresses that are radially outward in the near-contact region (S > 0).;For sufficiently negative values of the flow-strength parameter, a stationary film profile is attained. A critical magnitude of the flow-strength parameter is found, below which the film profile exhibits sustained temporal oscillations that grow in amplitude and period with distance from the critical point. The near-contact motion of a drop towards a rigid wall exhibits the same features. For positive values of the flow-strength parameter, film drainage occurs exponentially between drops at long times. An analytical solution is presented for the accelerated near-contact motion of a drop towards a rigid wall.;Qualitative agreement is found between the evolution predicted by our thin-film simulations and exact results obtained from finite-deformation boundary integral simulations. Approximate simulations of offset drop collisions in straining flow and in buoyancy-driven motion are presented.