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Intuition about Stokes flow beween solid walls

  1. Dec 8, 2014 #1
    Hi there,

    I have a question about incompressible Stokes flow in a channel between solid walls (with no-slip boundary conditions at ##y = 0, L_y##). It is my intuition that, if the flow direction is ##x## (periodic), and the direction normal to the walls is ##y##, then there cannot be a net velocity in that direction, i.e. ##\langle v_y \rangle = 0##, as this somehow implies fluid must be passing through the walls? Is this correct and if so how should I go about showing this? I guess it might require some integration of the incompressibility condition but I've not got anywhere yet. Full equations:

    $$\eta\nabla^2 \textbf{v} - \nabla p = \textbf{f}, \qquad\nabla . \textbf{v}=0$$

    Please let me know if you require any additional information, and any replies greatly appreciated!
  2. jcsd
  3. Dec 13, 2014 #2
    Thanks for the post! This is an automated courtesy bump. Sorry you aren't generating responses at the moment. Do you have any further information, come to any new conclusions or is it possible to reword the post?
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