Why can't a channel flow with two immiscible fluids have two maximum velocities?

AI Thread Summary
In a 2-D Poiseuille flow involving two immiscible fluids of different densities, the analysis reveals that the maximum velocities for both fluids occur at the same height within the channel. This suggests that the flow cannot exhibit two distinct maximum velocities due to the nature of the flow profiles. The mathematical representation indicates that as one fluid's velocity reaches its peak, the other fluid's velocity is constrained by the same height parameters. Consequently, the system's dynamics dictate a single maximum velocity point for both fluids. Understanding this relationship clarifies why two maximums cannot exist in such a flow scenario.
member 428835
Hi PF!

I was recently looking at two immiscible fluids in a 2-D Poiseuille Flow with two immiscible fluids of different densities. Let the total distance of the channel be ##L+\epsilon L##, where the dividing line between the two flows is ##L##. I was thinking of the possible flow profiles and finally decided to solve the problem. When I did, I noticed the maximums of the two fluids' velocities always occurred at the same height (keep in mind I'm talking mathematically, as ##v_1 \in [0,L]## and ##v_2 \in [L,\epsilon L]##). The implication being the flow could never have two maximums.

Can someone explain why we cannot have two maximums?
 
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