Have tried to apply silica sol gel (prepared by acid catalyzed TEOS), however particles are formed on the surface instead of coating. The same sol gel forms a coating over metal substrates.
Dried clay (mud) raises a lot of possibilities. By dried, do you mean air dried? Drying at temperatures less than 300 C will not remove organic matter and less than 700-800 C will not produce many consolidating reactions. Any drying less than 700-800 C will leave you with particles with a lot of surface activity.
You may have an active flocculant in your clay or you may have rapid drying or absorbing reactions.
One technique that might work is to mist or lightly spray the solution and allow drying. It will require several coats. Once the surface is prepared you should be able to coat as intended.
Another technique is to pre-coat with a fluxing material or mix a binder into the clay before drying.
A lot depends or your drying and preparation conditions.