Magnetic particle imaging (MPI) is a relatively new tomographic imaging technique using static and oscillating magnetic fields to image the spatial distribution of magnetic nanoparticles. The latter being the contrast MPI has been initially designed for. However, recently it has been shown that MPI can be extended to a multi-contrast method that allows one to simultaneously image the signals of different MPI tracer materials. Additionally, it has been shown that changes in the particles environment, e.g. the viscosity have an impact on the MPI signal and can potentially be used for functional imaging. The purpose of the present work is twofold. First, we generalize the MPI imaging equation to describe different multi-contrast settings in a unified framework. This allows for a more precise interpretation and discussion of results obtained by single- and multi-contrast reconstruction. Second, we propose and validate a method that allows one to determine the viscosity of a small sample from a dual-contrast reconstruction. To this end, we exploit a calibration curve mapping the sample viscosity onto the relative signal weights within the channels of the dual-contrast reconstruction. The latter allows us to experimentally determine the viscosity of the particle environment in the range of 1-51.8 mPa s with a relative methodological error of less than 6%.