Hydrodynamic interactions and collision efficiencies of spherical drops covered with an incompressible surfactant film

A theory is developed for the hydrodynamic interactions of surfactant-cover ed spherical drops in creeping flows. The surfactant is insoluble, and flow -induced changes of surfactant concentration are small, i.e. the film of ad sorbed surfactant is incompressible. For a single surfactant-covered drop in an arbitrary incident flow, the Sto kes equations are solved using a decomposition of the flow into surface-sol enoidal and surface-irrotational components on concentric spherical surface s. The surface-solenoidal component is unaffected by surfactant; the surfac e-irrotational component satisfies a slip-stick boundary condition with sli p proportional to the surfactant diffusivity. Pair hydrodynamic interaction s of surfactant-covered bubbles are computed from the one-particle solution using a multiple-scattering expansion. Two terms in a lubrication expansio n are derived for axisymmetric near-contact motion. The pair mobility functions are used to compute collision efficiencies for equal-size surfactant-covered bubbles in linear flows and in Brownian motio n. An asymptotic analysis is presented for weak surfactant diffusion and we ak van der Waals attraction. In the absence of surfactant diffusion, collis ion efficiencies for surfactant-covered bubbles are higher than for rigid s pheres in straining flow and lower in shear flow. In shear flow, the collis ion efficiency vanishes for surfactant diffusivities below a critical value if van der Waals attraction is absent.