The effective shear and dilatational viscosity of a particle-laden interface in the dilute limit

Abstract

The effective dilatational and shear viscosities of a particle-laden fluid interface are computed in the dilute limit under the assumption of an asymptotically vanishing viscosity ratio between both fluids. Spherical particles with a given contact angle of the fluid interface at the particle surface are considered. A planar fluid interface and a small Reynolds number are assumed. The theoretical analysis is based on a domain perturbation expansion in the deviation of the contact angle from $90^{\circ }$ up to the second order. The resulting effective dilatational viscosity shows a stronger dependence on the contact angle than the effective shear viscosity, and its magnitude is larger for all contact angles. As an application of the theory, the stability of a liquid cylinder decorated with particles is considered. The limits of validity of the theory and possible applications in terms of numerical simulations of particle-laden interfaces are discussed.

28 pages, 4 figures

References in corpus (4)

• Traces of surfactants can severely limit the drag reduction of superhydrophobic surfaces
• Drag and diffusion coefficients of a spherical particle attached to a fluid interface
• Driven particles at fluid interfaces acting as capillary dipoles
• Effective surface dilatational viscosity of highly concentrated particle-laden interfaces