Let's say you spill 10ml of water on the kitchen counter. It forms a small puddle that would evaporate after a while (assuming room temperature and sane humidity). Would spreading a large, dry towel over the puddle cause the water to evaporate quicker? What I mean is a towel that's much larger than the diameter of the puddle. Say 4x as large.
On the one hand, the water by itself comes into direct contact with the air which causes it to evaporate. On the other hand, assuming the towel absorbs the water almost entirely, it increases the wet surface area significantly, but also "locks" away some of the water in the fabric where it has less contact with air.