Buoyancy-driven coalescence of spherical drops covered with incompressible surfactant at arbitrary Péclet number

Collision efficiencies are determined for two surfactant-covered spherical drops in the limits of nearly uniform surface coverage and bulk insolubility for Brownian and/or gravitational motion as a function of drop-size ratio, drop-to-medium viscosity ratio, and retardation parameter. For two equal-sized drops in Brownian motion in the limit of small viscosity ratio, the calculated collision efficiencies agree well with earlier results for bubbles. While the two-sphere relative mobility functions for motion parallel to the drops' line of centers tend to the same values in the limits of infinite viscosity ratio and infinite retardation parameter, the asymmetric mobility functions do not, because the coefficients for the rotational term in Lamb's singular solution are independent of the presence of surfactant. The complex dependence of the transverse mobility functions on the viscosity ratio and retardation parameter makes it possible for the gravitational collision efficiency to increase slightly with viscosity ratio at fixed size ratio and retardation parameter of O(10³) or larger. Typical hydrosols are also studied in gravitational motion at arbitrary Péclet number, showing the combined influence of Brownian and gravitational motion.