Flow induced by an oscillating sphere in probing complex viscosity of polymer solutions

A theoretical investigation is presented for a linear viscoelastic flow induced by an oscillatory colloidal particle in nonadsorbing polymer solutions. At small-amplitude oscillations, the polymer distribution is assumed to be at equilibrium and forms a depletion zone around the particle based on the mean-field approximation. The goal of the theoretical approach is to predict the apparent complex viscosity sensed by the particle and compare this with the actual viscosity of the bulk fluid. Due to the local inhomogeneity, substantial deviation between the apparent and true viscosity in the bulk needs to be corrected quantitatively. The resulting apparent complex viscosity or friction coefficient in the Fourier domain will help to interpret active and passive microrheological measurements of colloid-polymer mixtures that take polymer depletion into account.