What content of water+radioisotope do you need in the sphere (v/w)? And how accurate dose the sphere has to be spheric?

You could try mixing light polymerizable resin with the water/radioisotope and cure it with light. Some water/radioisotope will be trapped in the resin. You can then shape your sphere.

Yoram

It's a very small amount of aqueous solution (

This is probably not what you are looking for but here are two ideas:

1. Casting your sphere from water soluble polymer and coat the sphere water repellent

2. Use something like DAS clay. I could not find information on what the chemistry is but I think it is at least somewhat water soluble until it dry.

Yoram

Thanks Yoram. I forgot to mention that we (ideally) don't want any dead-space on the outer surface of the sphere. From what I can tell, DAS clay is not waterproof after drying and requires a protective coat, although it is a good option if we do decide to allow for a thin outer layer of dead-space -- one I wouldn't have thought of. We'll keep looking and I'll update this if we find anything that fits our ideal requirements. 

One last crazy idea, thermoplastic starch?

http://cdn.intechopen.com/pdfs/34063/InTech-Thermoplastic_starch.pdf

We found a possible solution with liquid grouts. Specifically, we've tested the AV-100 developed by Avanti. You can control how long it takes to solidify through additives. The only negative is that it's tensile strength is pretty weak, which can make it fragile if you're not careful. There might be stronger grouts we could use, but Avanti donated some AV-100 for us to test.

See a demo here (note that AV-100 is not shown):

https://www.youtube.com/watch?v=JrLVtYPOdEI

Thanks! I looked at the Avanti webpage, very interesting product. BTW, their hydrophilic gels are more flexible, and they have hydrophobic gels - also activated by water.

Yoram