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We investigate the flow of viscous interfaces carrying an insoluble surface active material, using numerical methods to shed light on the complex interplay between Marangoni stresses, compressibility, and surface shear and dilatational viscosities. We find quantitative relations between the drag on a particle and interfacial properties as they are required in microrheology, i.e., going beyond the asymptotic limits. To this end, we move a spherical particle probe at constant tangential velocity, symmetrically immersed at either the incompressible or compressible interface, in the presence and absence of surfactants, for a wide range of system parameters. A full three-dimensional finite element calculation is used to reveal the intimate coupling between the bulk and interfacial flows and the subtle effects of the different physical effects on the mixed-type velocity field that affects the drag coefficient, both in the bulk and at the interface. For an inviscid interface, the directed motion of the particle leads to a gradient in the concentration of the surface active species, which in turn drives a Marangoni flow in the opposite direction, giving rise to a force exerted on the particle. We show that the drag coefficient at incompressible interfaces is independent of the origin of the incompressibility (dilatational viscosity, Marangoni effects or a combination of both) and that its higher value can not only be related to the Marangoni effects, as suggested earlier. In confined flows, we show how the interface shear viscosity suppresses the vortex at the interface, generates a uniform flow, and consequently increases the interface compressibility and the Marangoni force on the particle. We mention available experimental data and provide analytical approximations for the drag coefficient that can be used to extract surface viscosities.

We compare dynamical nonequilibrium molecular dynamics and continuum simulations of the dynamics of relaxation of a fluid system characterized by a non-uniform density profile. Results match quite well as long as the lengthscale of density nonuniformities are greater than the molecular scale (~10 times the molecular size). In presence of molecular scale features some of the continuum fields (e.g., density and momentum) are in good agreement with atomistic counterparts, but are smoother. On the contrary, other fields, such as the temperature field, present very large difference with respect to reference (atomistic) ones. This is due to the limited accuracy of some of the empirical relations used in continuum models, the equation of state of the fluid in the present example.

Abstract