If you think a food processor can solve all your mixing problems, think again. This is only partially true, and in the case of emulsions, even the most renowned kitchens tend to use their trusty old whisk.
The reason is simple: this utensil can incorporate a large quantity of air into the mixture, expanding it and making it lighter and more pleasant in texture. The only thing to be aware of is that you need to make a constant, rotating movement, trying to keep the bowl tilted, and to keep immersing the whisk in at the same spot. It is the mixture that should gently sink towards the whisk, blend together and fill with air. Alternatively, electric whisks work well too.
And if you are in a real hurry – or have to prepare vast quantities of emulsion – you can of course still opt for a food processor. With just one rule: do not use it at top speed, and never (ever, ever) use the blade.