HAnd-animate some msks or shape layer paths.
Make two black circles on a white background on top of one another.
Animate them moving apart.
Add an adjustment layer on top.
Apply a strong blur to the adjustment layer.
Apply Levels and crush them to make the blur look sharp again.
You could try using different tools under the distortion menu on two copies of your shape. Liquify comes to mind. There are literally hundreds of ways to do this. It just depends on what you want the design to look like.