I met an important scientist in my field in a scientific meeting last week. We agreed that I should write a project draft and send it to him, so we could set up a collaboration. Because I want to take as much advantage as possible from this opportunity (I am a PhD student), I want to be very careful with the project draft that I sent him. But this week I have been very busy with other work, and I have not been able to write the draft. My fear is that the interaction will 'cool off' as the days past. It's not been a week yet, and I am planning to write this in at most 2 more days. But in general experience, how long is it ok to wait before sending an email like this?
It will not cool off that quickly. Doing it right is more important than doing it soon. If you are a PhD student you must talk with your mentor/supervisor before establishing a collaboration or even sending this draft project. You don't know the political background.
This is about a professional relationship; so, as soon as possible you can finish your task, you should send him/her your email.