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

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SUMMARY

The discussion centers on the behavior of two immiscible fluids in a 2-D Poiseuille Flow, specifically addressing why these fluids cannot exhibit two maximum velocities. The analysis reveals that the maximum velocities of both fluids occur at the same height within the channel, indicating that the flow profile does not allow for dual maxima. This conclusion is derived from the mathematical representation of the velocity profiles, where the velocities of the two fluids are constrained to specific intervals.

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  • Understanding of fluid dynamics principles, particularly Poiseuille Flow.
  • Familiarity with immiscible fluids and their properties.
  • Basic knowledge of mathematical modeling in fluid mechanics.
  • Experience with analyzing velocity profiles in fluid systems.
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  • Study the mathematical derivation of velocity profiles in 2-D Poiseuille Flow.
  • Explore the properties and behaviors of immiscible fluids in various flow scenarios.
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Fluid dynamics researchers, mechanical engineers, and students studying multi-phase flow phenomena will benefit from this discussion.

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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