I am not an expert in rheology and might not be able to answer all your questions. I just want to bring your attention into two points.
1) when we estimate the viscosity of a mixture, we use mass fraction instead of volume fraction. Not sure if this is applicable in your case or not. This will not make huge difference as your densities are close.
2) strain rate will have different values at different locations. It is function of the velocity gradient, not just velocity. For the bulk fluid, it might be the same but near the walls and interfaces, if you have any, the values are different. Check the velocities at the wall, you might find an answer to your question.