Why nugget ice works here
Nugget ice is made from compressed flakes, so it has lots of surface area. That surface area pulls heat out of lemonade quickly, which is great when you want an instantly cold drink without waiting for the pitcher to chill.
Because nugget ice is porous, it also melts faster than a solid cube. That is why the lemonade is mixed slightly strong at first. As the ice melts, the drink lands in the sweet spot instead of tasting thin.
