Mixer size depends on three factors:  quantity of material, difficult of material to mix, and mixing intensity.  For liquid mixing, quantity can be specified as volume, difficulty as viscosity, and intensity as fluid velocity.  If you want the same intensity with the same mixer, as viscosity increases, volume must decrease.
 
The effect of viscosity on either volume or speed depends on the impeller type and the impeller Reynolds number.  The volume and speed do not change with viscosity in the turbulent range, Reynolds number greater than 20,000.  The volume decreases or the speed increases in proportion to the Reynolds number for laminar conditions, Reynolds number less than 10.  The decreased volume or increased speed change as a gradual function of Reynolds number in the transition range, which is a rather complicated function.  It is possible to develop a relationship for either volume or speed for a specific set of conditions, but not a simple answer.