We numerically calculate the drag on a sphere or a filament immersed in an incompressible viscous monolayer or membrane on one, or between two, viscous infinitely deep bulk phases. We show that contributions due to the Marangoni effect of the monolayer or membrane account for a significant part of the total drag. Effects of protrusion of objects into the three-dimensional fluids adjacent to the monolayer and membrane are investigated. Known analytical expressions in the limit of a very viscous membrane or monolayer are recovered by our numerics. A sphere in a membrane exhibits maximal drag when symmetrically immersed with the equator coinciding with the membrane plane. No discontinuity of the drag arises when the sphere is totally immersed into the subphase and detaches from the monolayer. Effects of protrusion are more important for objects moving in a membrane or monolayer of low surface viscosity. At large surface shear viscosity protrusions must be larger than the length defined by the ratio of surface to bulk viscosities to alter the drag on the object. Our calculations may be useful for the measurement of hydrodynamic radii of lipid rafts in membranes and for electrocapillary effects of spheres immersed in a surface
We present a quantitative theory and experiments for the expansion dynamics of domains in stratifying foam films. Foam films containing micelles, colloidal particles or polymer-surfactant complexes often form layered structures and thin in a stepwise fashion: circular domains of lower thickness are formed and expand following a R(t) proportional variant t1/2 law. In the present paper the film is modeled by an incompressible three-dimensional fluid with incompressible surfaces. The film tension difference between the film and domains results in the formation of a rim at the domain boundary and a gradient in film thickness and pressure in the surrounding film. The material transport due to this gradient lets the domains grow. We present experiments utilizing the thin balance method to qualitatively confirm the thinning mechanism and to determine material parameters including local film viscosity of a film composed of 4400 ppm acrylamide/acrylamidomethylpropanesulfonate-copolymer and 0.006 mmol/l dodecyltrimethylammonium bromide solution. We found a film viscosity of about 60 times the bulk viscosity, consistent with previous measurement in the same system but using another method.
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