Biochar in a pack sprayer to warm mulched soil?

Generally, soil is slow to warm up in the spring, especially a clay soil under mulch. So, at the time of year when there is the most water available in my high plains desert climate, the cool soil temps are slowing things down. I like the idea of using biochar to heat things up, and I was wondering if I could make the practice easier and more uniform somehow. I though that if I mixed up some Fish oil (a sticker/ spreader) with finely crushed biochar, I could apply a darkening coating to the mulch/ soil surface, which would stick instead of washing away. I could make it more multifunctional by using pulsing agents (stuff to get the sleepy soil life into high gear in the spring. The Holistic Orchard has a lot of stuff on this.) This should have a really synergistic effect on the soil life.

The possible problems I can see would be:

The sprayer clogging up. I could smash the charcoal up really fine to avoid this. Do you know of which, if any, sprayer models would cope with this?

Permanent black stains on anything the spray touches. So, I wouldn't wear any clothes I cared about, and would stay away from anything valuable.

Is there anything else I am forgetting about?

I don't think you are going to be too happy trying to spray it. I even have trouble clogging up those end-of-the-hose sprayers, and they have far bigger orifices. Sprayers are meant for liquids, or maybe two immiscible liquids that don't form mayonnaise in the spray bottle. You get any sort of precipitation, suspended solids, micelle formation, and those spray nozzles are going to clog up.

That doesn't mean there aren't ways to apply solid powdery materials in a liquid suspension. Just use a watering can with good size holes in it. If a store-bought watering can keeps clogging up, ream out the holes with a 2 or 3 mm drill bit. I like using a gallon milk jug that I have drilled a bunch of 3 mm holes in (plus a couple of air holes back on the handle to equalize pressure).

Biochar doesn't really give you "permanent" black stains on stuff. It's not paint that bonds to the surface it is applied to. Charcoal is inert material and can be removed with abrasive scrubbing materials or water pressure. When I come inside after applying biochar solutions, and my forearms are black above where the gloves end, it just takes a little soap and water to clean up. Far less scrubbing required than after working on the car engine.