Unless the drums leak or you are anticipating a leak air works well. However, if you are of the opinion at some point the drum(s) will begin leaking you should use some form of styrofoam.

If your drums are plastic, and in good shape, I would fill them with foam, it's quite expensive sometimes. If you are using the drum with the ring tops where the lids come off,, you may need floatation foam in them. If using the bung hole top type, I'd clean the threads up good on the hole caps and apply some teflon pipie sealer in paste form on the plug threads , then some teflon tape on top of the pasted threads, and one last coating of the paste. tighten the cap plugs use good and tight and it will stay watertight. This is the method I use.
Also, if using the bung hole capped drums, when you attach the drum into place on the framework, make sure the larger bung hole(capped) is located up top, keeping the larger hole out of water as much as possible. The smaller hole seems to stay more watertight over long periods of time..

Of course, if you have knotheads out for target pratice or envious of your setup during season,,,, foam filled drums will stay afloat when the jerks shoot the drums..........

Because its public i didnt want ro go out one morning and find my blind sunk. Last season some idiot shot up my buddies barrels. The barrels are a thick plastic that were used to transport chemicals

I've built several floating duck blinds. The barrels are the worst way to go. You need to use styrofoam blocks, the type pipeline construction use. There was a company in Rayne that was giving them away. Wilco Construction I think the name was.

If you insist on using these chemical barrels(which might end up leaking) make darn sure you clean them of any residue. Personally I wouldn't use them ............