I have a long microchannel where flows some water. The reynolds number is much smaller than one. Within the structure of this microchannel there is a big defect. It looks like a bump of size approximately 20 micrometer and the microchannel's width and height are 100 micrometer.
My question is the following: On what length scale will the defect modify the Poiseuille-like structure of the flow field?
I think it's possible to show by a scaling argument that the defect's effect will be "damped' very very fast, and that the Poiseuille-like flow shape will be recover after a few micrometers past the defect.