I start my PhD in Electrical Engineering this October. I have met with both my two academic supervisors, and my industrial supervisor - and I treated all like a formal job interview. That means dress fairly smart!
All three meetings were fairly rigorous. During the meetings, we discussed my ideas for the project at length. Then they probed into how serious I was about research, and finally my two academic supervisors set me on-the-spot mathematical problems to solve in front of them.
Preparation is key, the more you do, the better equipped you are for the interview!
Good luck!