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, mu(s), of such monolayers collapses onto a single curve: mu(s)/mu(so) = [1 - (A/A(c))](-1) , in which mu(so) is the viscosity of the liquid phase, A is the area fraction of the solid phase measured by fluorescence microscopy, and A(c) 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.