Watch the paper towel very carefully and you'll easily notice it soaking up colored water. It'll take a bit, but eventually the colored water will soak all the way through the towel and start coloring the clear water. In our experiment the blue did MUCH better than the red. The next day we woke up to this:
You can't really see it in the picture, but the blue water soaked up through the red water' jar's paper towel and turned it a very light shade of blue. My daughters thought this was pretty cool, especially the next morning when the clear water was now blue!