Slip flow past a gas–liquid interface with embedded solid particles

Abstract

We simulate shear flow past a stationary monolayer of spherical particles embedded in a flat gas–liquid interface. This problem is relevant to the understanding of the microhydrodynamics of particle-laden interfacial structures, including particle-laden drops, bubbles and foams. The combination of the free-shear condition at the gas–liquid interface and the no-slip condition at the particle surfaces gives rise to a velocity slip at the particle-laden interface. We study the characteristics of the flow near the monolayer, focusing on slip velocity, slip length and interfacial shear stress. Two microstructures are compared: a square array, and a reticulated array mimicking a percolating network of aggregated particles. We demonstrate that the scaling laws for the dependence of the slip length on solid area fraction developed for flow past superhydrophobic microstructured surfaces apply to the case of interfacial particles. The calculated slip lengths are in general smaller that those reported for microstructured superhydrophobic surfaces. This difference, which is due to the significant protrusion of the spherical particles in the liquid, can be accounted for in the case of the square array by an approximate argument. For a given area fraction, the reticulated array yields a larger slip length than the square array. We analyse the hydrodynamic forces acting on the particles, and the corresponding tangential stress exerted by the bulk ‘subphase’.