trickle
To move or come slowly in a thin, small flow.
Trickle means to flow in a thin, slow stream, drop by drop or in a small, steady flow. When you turn a faucet just barely on, water trickles out instead of gushing. After a rainstorm, water might trickle down a windowpane, finding its way slowly from top to bottom. Maple syrup trickles down a stack of pancakes, moving lazily instead of pouring quickly.
The word captures that specific slowness and smallness of the flow. A river doesn't trickle; it flows or rushes. But a tiny creek in the woods might trickle over rocks, making a gentle sound as it goes.
As a noun, a trickle is a small, slow flow. You might see a trickle of water running down a wall or feel a trickle of sweat on your forehead.
People also use trickle to describe anything that comes slowly in small amounts. Information might trickle in to a newsroom as reporters gather facts bit by bit. Students might trickle into the classroom one or two at a time before the bell rings, rather than arriving all at once. When donations trickle in for a fundraiser, they arrive gradually, a few dollars here and there, instead of in one big rush. The word always suggests that slow, steady, small-scale movement, whether it's water, people, or anything else.