Add the chopped fruit, celery, and lime zest to a freezer-safe bowl for 1-2 hours before you want to enjoy your smoothies, so that they'll be nice and cold.
Add the cooled fruit mixture to your blender or food processor along with the frozen pineapple. Blend until smooth. Add the arugula in two batches, continuing to blend until the arugula is well incorporated. Serve immediately.