Direct calculation of anisotropic surface stresses during deformation of a particle-covered drop

The modification of the surface tension and the surface shear elasticity by particles in particle-covered drops can be attributed to a particle-induced surface stress. This stress represents at the macroscopic, continuum level the microscopic effect of lateral particle-particle interactions. Understanding the link between the isotropic and anisotropic components of the surface stress and the particle microstructure, and how these components change when structured interfaces deform, is a crucial problem in the field of particle-laden interfaces. In this paper, we analyse static and transient three-dimensional simulations of a pendant drop whose surface is covered by colloidal particles displaying purely repulsive particle-particle interactions. We compute the isotropic and anisotropic surface stress from the inter-particle forces using a version of the Kirkwood-Irving formula suitable for interfacial suspensions; we validate the approach by comparing against surface tension values obtained using Fordham's method (Proc. R. Soc. London, Ser. A, 1948, 194). In the parameter range simulated, the combination of parameters for which the drop does not pinch off (stable drop) gives rise to a homogeneous and isotropic surface stress; we argue that in the absence of attractive interactions the drop becomes unstable before anisotropic effects can manifest themselves. For unstable drops, stress non-uniformity and anisotropy are significant when the drop deformation and the solid area fraction are sufficiently large. Our results have implications for the dynamic deformation of structured interfaces with geometrically complex and time dependent morphologies.