As nouns the difference between trickle and drench
is that
trickle is a very thin river while
drench is a draught administered to an animal or
drench can be (obsolete|uk) a military vassal, mentioned in the domesday book.
As verbs the difference between trickle and drench
is that
trickle is to pour a liquid in a very thin stream, or so that drops fall continuously while
drench is to soak, to make very wet.