In regards to week-long liquid diets, there is no advantage and may be disadvantageous depending on the liquid diet you choose.
If you were to choose something like Instant Breakfast which is mostly powdered skim milk or a complete nutritional supplement like Ensure, Sustacal or Meritene and you drank enough to get 100% of the RDA (usually 1800 calories or 6 cans), then the primary nutritional concern would be meeting fiber needs. But you may not lose weight at an 1800 calorie level so why would you drink only liquids?
Fruit contains mostly vitamin C, vitamin A, potassium, and fiber. Fruit is deficient in protein, essential fatty acids, many other vitamins, and minerals. Fruit would not be recommended as your sole food source. Even if you used a juicer with fresh fruits and vegetables, your diet would still be lacking in fiber.
Are you were interested in a vegetarian food style? You won’t necessarily lose weight tho due to the healthy oils in soy and other vegetable protein sources like nuts and legumes.
Frankly, I do not know of a good reference on just liquid diets other than a basic nutrition text written by an author with a degree in nutrition science.