My apologies for the confusion, A particle can include any small piece of matter. It's a very sweeping term that applies to any of the basic forms of mater and energy. I said a while ago it was charged particles of silver, that's what a silver ion is. This is what a colloid is, courtesy of Merriam-Webster:
a : a substance that consists of particles dispersed throughout another substance which are too small for resolution with an ordinary light microscope but are incapable of passing through a semipermeable membrane
Silver ions, suspended in water, are colloidal silver. It's not a vague term. "Silver ions disinfecting water through mechanical agitation.", is agitating colloidal silver. I'd assume low-dosage, but colloidal silver still. Colloidal silver is produced by ionizing silver molecules and suspending them in water. In order to get it back into suspension, you shake (a.k.a. "agitate") it. So you're essentially agitating colloidal silver, if I read you description literally. So where do the silver ions go after you are done sanitizing the water? Do you remove them?
Yes, I do know what insoluble means. That does not mean that silver ions cannot remain in suspension for quite some time. They will eventually settle out, "eventually" being the active term here.
Still though, you have not given a reason why this is in any way better than the current method of chlorination. If you just want to change it for the sake of changing it, then there's really no point to this discussion. If you want to change it for some compelling reason, like safety or cost, I'm all ears. Otherwise, this is just pointless.