NEAR-CONTACT MOTION OF SURFACTANT-COVERED SPHERICAL DROPS

A lubrication analysis is presented for the near-contact axisymmetric motion of spherical drops covered with an insoluble non-diffusing surf actant. Detailed results are presented for the surfactant distribution , the:interfacial velocity, a:nd the gap width between the drop surfac es. The effect of surfactant is characterized by a dimensionless force parameter: the external force normalized by Marangoni stresses. Criti cal values of the force parameter have been established for drop coale scence and separation. Surfactant-covered drops are stable to rapid co alescence for external forces less than 4 pi kTac(0), where c(0) is th e surfactant concentration at the edge of the near-contact region and a is the reduced drop radius. For subcritical forces, the behaviour of surfactant-covered drops is described by two time scales: a fast time scale characteristic of near-contact motion between drops with clean interfaces and a slow time scale associated with rigid particles. The surfactant distribution evolves on the short time scale until Marangon i stresses approximately balance the external force. Supercritical val ues of the external force cannot be balanced; coalescence and separati on occur on the fast time scale. The coalescence time normalized by th e result for drops with clean interfaces is independent of the viscosi ty ratio and initial gap width. Under subcritical force conditions, a universal long-time behaviour is attained on the slow time scale. At l ong times, the surfactant distribution scales with the near-contact re gion and the surface velocity is directed inward which impedes the dro p approach and accelerates their separation compared to rigid particle s. For drops pressed together with a sufficiently large subcritical fo rce, a shrinking surfactant-free clean spot forms. Surfactant-covered drops exhibit an elastic response to unsteady external forces because of energy stored in the surfactant distribution.