Acid brush

The name 'acid brush' comes from plumbing, applying acid flux.

It can describe any small, disposable, inexpensive brush used to apply cleaner, glue, solvent, or anything else.

They may be held with something specific, like epoxy, to not fall apart with some specific chemicals.

In specific production applications you may want to get more specific, like a handle material that won't react, hairs that are static dissipative, but in the DIY sense you probably won't care.