Combine 2 cups (500 mL) water with 2 cups (500 mL) of the grape juice, sugar and food colouring in a large saucepan. Bring to a boil before slowly whisking in the tapioca, cooking for one minute. Remove from the heat and let cool to room temperature, stirring often.
Meanwhile, stir the remaining grape juice and lemonade concentrate together in a large pitcher, cover and keep chilled. Once cooled, add the tapioca mixture to the pitcher, stirring to separate the tapioca. Cover and refrigerate until ready to serve.
Just before serving, stir up tapioca mixture while adding the sparkling water. Garnish with ice, slices of lime and serve with a thick straw.