We recently had similar issue - tiny -super tiny- black ants on countertops/sink. Just a few now&then.
Neighbor told us they were "Sweet Grease Ants". Publix - sells a bottle - Protexall Ant-Kill, like $4, 2 fl oz. small white plastic bottle with red cap. Squirt a couple drops of the blue liquid where they come - they will slurp it up and take it back to colony where they...you know. We had tried those plastic traplike things but did not work at all.
We don't have them in the D/W - but they probably come from under cabinets etc. I'd say it's safe to put some drops in the D/W too - when it runs, it should take away all the ant-kill.
Simple, easy, cheap - hopeful-solution to your problem. The bottle should last OUR lifetime.
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I have CDO. It's like OCD but all the letters are in alphabetical order - AS THEY SHOULD BE. 
"Yesterday Belongs to History, Tomorrow Belongs to God, Today Belongs to Me"
Last edited by DeanFL; 12-11-2015 at 03:12 PM.
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