Flow fields in soap films: Relating viscosity and film thickness

We follow the diffusive motion of colloidal particles in soap films with varying $h/d$, where $h$ is the thickness of the film and $d$ is the diameter of the particles. The hydrodynamics of these films are determined by looking at the correlated motion of pairs of particles as a function of separation $R$. The Trapeznikov approximation [A. A. Trapeznikov, Proceedings of the 2nd International Congress on Surface Activity (Butterworths, London, 1957), p. 242] is used to model soap films as an effective two-dimensional (2D) fluid in contact with bulk air phases. The flow fields determined from correlated particle motions show excellent agreement with what is expected for the theory of 2D fluids for all our films where $0.6\ensuremath{\le}h/d\ensuremath{\le}14.3$, with the 2D shear viscosity matching that predicted by Trapeznikov. However, the parameters of these flow fields change markedly for thick films $(h/d>7\ifmmode\pm\else\textpm\fi{}3)$. Our results indicate that three-dimensional effects become important for these thicker films, despite the flow fields still having a 2D character.