It doesn't have to be a superfluid or silicon oil. Let's suppose a water droplets are falling to a hidrophobic (wd40 sprayed LOL) surface with double slits. It seems probable to me that scenario will happen that droplet will split on surface, pass through both slits (in some random ratio) and then recombine again into single drop completely before leaving the surface towards our water droplet detector. Surely recombining different ratios of water mass on departure will have different effects on final droplet momentum resulting in scattering and self interference patterns in our detector after sufficient number of droplets. Where am I wrong?