Critical viscoelastic behavior of colloids

The linear and nonlinear frequency-dependent viscoelastic response of a sus pension of spherical colloids in the vicinity of the gas-liquid critical po int is analyzed in the mean-field region. Explicit expressions for the shea r rate and frequency dependence of the static structure factor are derived, starting from the N-particle Smoluchowski equation, which is the fundament al equation of motion for the probability density function of the position coordinates of the spherical colloids. Microscopic expressions for the anom alous parts of the linear and nonlinear response functions are derived, whi ch are then expressed as wave-vector integrals weighted with the static str ucture factor. These integrals are evaluated in part numerically, leading t o explicit results for the viscoelastic response functions. The critical en hancement of both the linear and nonlinear viscoelastic response functions is found to be far more pronounced than for molecular systems as a result o f long-ranged hydrodynamic interactions between the colloidal particles. Vi scoelastic response functions are found to diverge with the same exponent a s the correlation length of the quiescent, unsheared suspension. The freque ncy spectrum of the Linear response functions is found to be extremely broa d, while nonlinearity affects only the low-frequency behavior of the lowest -order response functions. The lowest-order response functions attain their linear response values at higher frequencies even far into the nonlinear r egime. Nonlinear effects are thus absent at higher frequencies. For these h igher frequencies the lowest-order response functions are found to vary wit h the frequency omega as omega(-1/4) close to the critical point and cross over to a omega(-1/2) dependence further away from the critical point. In a ddition to the viscoelastic response of an otherwise quiescent suspension, the viscoelastic response of a stationary sheared suspension is discussed. The response of such a stationary sheared system to a superimposed oscillat ory shear flow probes the dynamics of the partially distorted microstructur e by the stationary shear flow. The frequency spectrum of the linear viscoe lastic response functions is found to be strongly affected by the microstru cture distortion due to the stationary shear flow. [S1063-651X(98)15512-5].