Viscosity of Two-Dimensional Suspensions

Over a range of conditions, lipid and surfactant monolayers exhibit coexistence of discrete solid domains in a continuous liquid. The surface shear viscosity, μs, of such monolayers collapses onto a single curve: μs/μso = [1-(A/Ac)]-1, in which μso is the viscosity of the liquid phase, A is the area fraction of the solid phase measured by fluorescence microscopy, and Ac is a critical solid phase fraction. This scaling relationship is directly analogous to that of three-dimensional dispersion of spheres in a solvent with long-range repulsive interactions, with area fraction replacing volume fraction.