VISCOELASTIC AND RHEOLOGICAL BEHAVIOR OF CONCENTRATED COLLOIDAL SUSPENSIONS

Molecular approaches are discussed to the density (phi), viscoelastic (omega), and theological (gamma) behavior of the viscosity eta(phi, omega, gamma) of concentrated colloidal suspensions with 0.3 < phi < 0.6, where phi is the volume fraction, omega the applied frequency, and gamma the shear rate. These theories are based on the calculation of the pair distribution function P-2(r; omega, gamma), where r is the relative position of a pair of colloidal particles. The linear viscoelastic behavior eta(phi, omega, gamma = 0) follows from an equation for P-2(r, omega, gamma) derived from the Smoluchowski equation for small phi, generalized to large phi by introducing the spatial ordering and (cage) diffusion typical for concentrated suspensions. The theological behavior eta(phi, omega = 0, gamma) follows from an equation for P-2(r; gamma) of a dense hard-sphere fluid derived from the Liouville equation. This leads to a hard-sphere viscosity eta(hs)(phi, gamma) which yields the colloidal one eta(phi, gamma) by the scaling relation eta(phi, gamma)/eta(0), = eta(hs)(phi, gamma)/eta(B), where eta(0) is the solvent viscosity, eta(B) is the dilute hard-sphere (Boltzmann) viscosity, and the gamma's are appropriately scaled. eta(phi, omega) and eta(phi, gamma) agree well with experiment. A unified theory for eta(phi, omega, gamma) is clearly needed and pursued.