As encaustic medium does not deteriorate the brush and can always be remelted, brushes can be left uncleaned indefinitely. Generally, I don’t clean brushes. I wipe excess wax off on the side of the encaustic tins and then place them on the silicone mats to harden.
To clean brush handles, lay the brush on the griddle and once the handle is warm, wipe it clean with a paper towel..
No solvent is necessary for cleaning encaustic equipment. Should you wish to clean your brushes, you can put them in pot of molten encaustic medium. The colour will leach out of the brush into the medium. You can mix additional pigment into the medium and use it for painting.
Encaustic tools can be cleaned of wax and paint by leaving them on a hot surface and wiping them clean when the wax has melted.
Read more here about Cleaning Your Encaustic Studio
