| We investigate the flow of viscous interfaces carrying 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 the either 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 analytic approximations for the drag coefficient that can be used to extract surface viscosities.
for LaTeX users @article{MPourali2021-33,
author = {M. Pourali and M. Kr\"oger and J. Vermant and P. D. Andersson and N. O. Jaensson},
title = {Drag on a spherical particle at the air-liquid interface: Interplay between compressibility, Marangoni flow, and surface viscosities},
journal = {Phys. Fluids},
volume = {33},
pages = {062103},
year = {2021}
}
\bibitem{MPourali2021-33} M. Pourali, M. Kr\"oger, J. Vermant, P.D. Andersson, N.O. Jaensson,
Drag on a spherical particle at the air-liquid interface: Interplay between compressibility, Marangoni flow, and surface viscosities,
Phys. Fluids {\bf 33} (2021) 062103.MPourali2021-33
M. Pourali, M. Kr\"oger, J. Vermant, P.D. Andersson, N.O. Jaensson
Drag on a spherical particle at the air-liquid interface: Interplay between compressibility, Marangoni flow, and surface viscosities
Phys. Fluids,33,2021,062103 |
mk@mat.ethz.ch
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