So if I understand correctly, the only difference here is the diameter of the tank.
With a larger tank, there is going to be more surface area clinging to the material, and resisting movement. To get the vortex, you need to overcome the resistance, and get all the material moving fast enough to whirlpool.
So, it probably is not a linear relationship between diameter and mixer dimeter; but you need to get the material moving, and I would suspect a larger diameter spiral is needed, and perhaps a bit more speed.
If not a larger diameter spiral, more spiral surface is needed.
Think about a glass of water; Put in your finger and stir, you make a vortex. Now get a larger glass, and you either have to stir faster or you have to use two fingers. Now use a swimming pool, and your fingers are no longer large enough, you have to put in people and have them run around in a circle. The closer to the edge of the tank you are the better chance you have.
Charlie