Recently, I've been thinking about this but after figuring out later written forms of 四 (sì; four) in bronze scripts (see below chart from 小學堂 for reference) depict a nose breathing out air and was the original form of 呬 (sì; to rest; to breathe, to gasp) (according to 說文新證, 漢語多功能字庫, 文源, etc.), I've been wondering if 四 is used in 泗 (sì; mucous; nasal flow; sniffle; river in Shandong) as some sort of form component besides it's usage for sound.
I've did came across a few sources (and a question here) that claimed 四 also being the original form of 泗, but further digging into this, I couldn't determine whether or not 四 was being directly used as a picture of a nose in 泗 since not many sources talk about this and I thought it made sort of sense for 泗 to be a depiction of a nose (四) with mucus (氵) running out from the nose or just a simple phonosemantic character with 四 happening to also be a form component.
Just to clear things up here on my question, did 四 had another purpose in 泗 besides being used as a sound component? Was 四 even the original form of 泗? How can I be sure if this is actually true since I'm not entirely sure yet? I know I probably overthinking this but it probably either has to be a coincidence or it's true.
Would be much appreciated for answers on this question of mine! :)
Note: I am aware that 四 started off in the oracle bone script as a pictograph of four lines to represent four. I'm discussing about the more later interpretations of 四 when it changed it's shape.