Measurement of the Drag Coefficient of Spherical Particles Attached to Fluid Interfaces

Abstract

The drag coefficient, β, of spherical particles attached to a pure air-water interface is determined. The method is based on the measurement of the particle velocity V, under the action of a well-defined lateral capillary force F. The capillary force is created by controlled deformation of the water surface by means of a Teflon barrier whose vertical position can be precisely adjusted. The magnitude of the force is calculated by means of the theory of capillary interaction between a sphere and a vertical wall (Kralchevsky et al., J. Colloid Interface Sci. 167, 47, 1994). The drag coefficient is calculated from the ratio β = F/V at small Reynolds numbers. The dependence of the drag coefficient on the particle size and the three-phase contact angle is determined. For small spheres, which do not create substantial deformation of the fluid interface, β is always smaller than the Stokes coefficient, βs - 6 πηa (η is the water viscosity and a is the particle radius). For large spheres, however, β can be greater than βs. This higher hydrodynamic resistance can be explained by the presence of a curved meniscus around heavier particles. The measured values of β are compared with theoretical calculations and very good agreement is reached. It is demonstrated that the method is sensitive to the presence of adsorbed surfactants and that it can be used for the determination of the surface viscosity of adsorbed layers.