Trickle
/ˈtrɪkl/
verb
When a liquid or few items move slowly in a thin line or drop by drop.
Tears began to trickle down her cheeks.
Definition 1 of 4
Pro Tip 1/2Small Amount
Use 'trickle' to describe a meager flow, much less than a pour or stream. 
A trickle of olive oil enhanced the salad's flavor.
Pro Tip 2/2Continuous Motion
'Trickle' suggests a steady, continuous motion, not an abrupt one. 
Water trickled from the faucet, indicating a need for repair.