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: ${\mu }_s/{\mu }_{\mathrm{so}}=[1-(A/A_c){]}^{-1\mathrm{}}$, in which ${\mu }_{\mathrm{so}}$ 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.