why increasing viscosity is computational expensive?
 

I am modeling the solidification process of some molten droplets using the temperature dependent viscosity, in which the viscosity of the droplet increases as its temperature goes below the melting temperature and as a result the deformation of the droplet stops as it solidifies.

The problem is that by using a high viscosity (making the molten droplet to solid) the size of time step decreases dramatically. I am very interested to know the exact physical and/or numerical reason that why the computation time increases by increasing the viscosity of the droplet. It is good to mention that I have a two phase VOF problem, in which the molten droplets come down in air and impact a cold surface to solidify.