John, don't quote me and I am sure one of our professional chemists will hopefully correct me but Id think that everything left after drying is the 'solid' part of Total Dissolved Solids. Otherwise I think it'd be classified as VOC Volatile Organic Coumpound (may evaporate) or otherwise.
Heres the thing, do you give it a good stirring and test it or let it set for half an hour, an hour or 12 hours for some of the suspended solids to settle to the bottom ie the mud? How does this affect your TDS then? What are we going to use as a control?
Aaron