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Looking for a non-parabolic circular flow

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Old   November 12, 2021, 09:04
Default Looking for a non-parabolic circular flow
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Hi guys and gals,

I am currently working on a (at least for me) hard homework. Without going to much into detail:
Working with Stokes flow, I am trying to implement a superposition-solution for a very specific microfluidic problem. For that, I need a velocity-field in polar-coordinates with, that is not parabolic.

My first try was to work my way through the Navier-Stokes-equations, implementing the following properties:
- flow is incompressible
- very low Reynolds number
- flow is fully developed
- flow is stationary
- non-rotational
- no angle-dependent flow changes

So, I ended up with a Hagen-Poiseuille (HP) flow. That is, however, not really what I need, since is not linear in relation with the radius.
In 2-D I could implement a Couette-flow without a problem. Could that maybe be a solution for a circular flow itself?
Maybe I need to combine HP with Couette or something?

To sum up:
I am looking for a velocity-field w(r,phi) that has a linear dependence on r.
Oh man I am lost on that. Maybe I am just overthinking.

Thank you sooo much. I would really appreciate the help.
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Old   November 13, 2021, 01:50
Default Itīs done
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I have found a solution. Turns out, I was actually just overthinking stuff.
Simply writing down the question helped a lot, though.

So cheers and have a nice weekend.
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couette flow, creeping flow, hagen poiseuille, stokes flow

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