In order to interpret the time dependence of the measured torque in a steady shear experiment on an aggregating dispersion, a microrheological model has been used in which two existing models are integrated. In this microrheological model, a theory for fractal aggregation in shear flow is combined with a theory for the sedimentation and resuspension of non-colloidal hard spheres. The former theory describes the viscosity as a function of shear rate, while the latter predicts the stress increase in a Couette device due to sedimentation. The connection between the two theories is made by identifying the aggregate parameters with the hard sphere parameters (size and volume fraction). The parameters of the aggregates as a function of shear stress are obtained by measuring a flow curve before sedimentation effects become significant and fitting this curve with the fractal aggregation theory. During the sedimentation, the aggregate size and volume fraction become a function of both time and position in the rheometer. Taking this into account, the predicted stress increase as a function of time is found to describe the experiments rather well. This result corroborates both of the existing theories.