Seeped

Definition of SEEP
1: to flow or pass slowly through fine pores or small openings: ooze seeped in through a crack

2a : to enter or penetrate slowly seeped into the national consciousness — Tip O'Neill

b : to become diffused or spread seeped through his being — Agnes S. Turnbull

Think of a time when you've been sobbing hysterically. After the sobbing subsides, a slow, steady stream of tears continues. I'm trying to come up with a word to describe that stream. The tears don't flow or pour because the initial downpour has subsided. "Ooze" sounds to viscous. "Trickle" is a funny word, and I don't think it fits the situation.

Here's the sentence as it stands: "Tears seeped down Stella’s cheeks." I like seep because it has the liquidity and slowness I'm looking for, but it also carries the connotation of penetrating or moving through something. Perhaps the tears should seep out of the corner of her eyes. Except I'm trying to go for a short description here so I can move on to telling the story.

Perhaps more context is needed. This sentence comes near the start of a chapter. At the end of the chapter previous, the main character found out some complex and terrible news and after a fit of hysteria, calmed down a bit. I want to show that though she is calmly discussing the situation, it still affects her emotionally.

Here are my questions: Can tears "seep" down one's cheek? If not what is a better word? Or should they seep out of her eyes? Leave your suggestions in comments. Thanks!