A theory is developed for the hydrodynamic interactions of surfactant-covered
spherical drops in creeping flows. The surfactant is insoluble, and flow-induced
changes of surfactant concentration are small, i.e. the film of adsorbed surfactant is
incompressible.
For a single surfactant-covered drop in an arbitrary incident flow, the Stokes
equations are solved using a decomposition of the flow into surface-solenoidal
and surface-irrotational components on concentric spherical surfaces. The surface-solenoidal component is unaffected by surfactant; the surface-irrotational component
satisfies a slip-stick boundary condition with slip proportional to the surfactant
diffusivity. Pair hydrodynamic interactions of surfactant-covered bubbles are computed
from the one-particle solution using a multiple-scattering expansion. Two terms in a
lubrication expansion 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 motion. An asymptotic
analysis is presented for weak surfactant diffusion and weak van der Waals attraction.
In the absence of surfactant diffusion, collision efficiencies for surfactant-covered
bubbles are higher than for rigid spheres in straining flow and lower in shear flow. In
shear flow, the collision efficiency vanishes for surfactant diffusivities below a critical
value if van der Waals attraction is absent.