What are these deposits that ants (?) leave on my bathroom sink?

Recently, piles of little brown flakes have started appearing on my bathroom sink I have sometimes seen an ant, occasionally two, never more than two, crawling around my sink so I assume they are depositing them. I wash the flakes away, but they return.

They are left in only one small area. The flat part of the sink next to the tap, and the groove where the sink joins the wall. Most of them on only the right-hand side of the sink. A very few are in the middle, and none on the left.

What are these flakes, and why have the ants decided on that specific location to deposit them?

Is it wood? They could be chewing up the wood in the walls.

Carpenter ant frass: What does it look like? (envirocarepestcontrol.net)

Why have they picked that specific place for their leavings?

Is this a serious problem?