The work presents an analytical study of the effective viscosity of a mono-dispersion of liquid aerosol droplets in a gas medium based on a steady-state low-Reynolds number hydrodynamics. The Kundsen and Reynolds numbers are assumed to be small, and thus fluid flows inside and outside the fluid particle can be described using a continuum model with a hydrodynamic slip at the drop-gas interface, while the flow fields are governed by the Stokes equations. Three types of cell models are employed to solve the problem, namely the Simha, Happel and Kuwabara cell models. Regarding the limitations of this study, the analytical expression of apparent viscosity as functions of the particle volume fraction in a closed form agree with the literature. The bulk viscosity is significantly influenced by the surface properties of the droplet-gas interface and by the internal-to-external viscosity ratio of the droplet. Generally, the influence of the concentration effect of the particles on the apparent viscosity increases with the volume fraction of the dispersed liquid drops.