External Slip Flows
In this section, a simulation of slip-flow past a circular cylinder
is presented as a prototype of an external flow around a micro-probe.
The slip velocity is proportional to
tangential stress, (tau_s), which is plotted in figure below
for the case of Re=10. From this plot it is evident that separation
occurs at an angle approximately 147 degrees from the front stagnation point.
For comparison of tangential stress variations, we also plot the
tangential stresses corresponding to the continuum case, Kn=0. As expected, a reduction in skin friction is obtained
especially in the front part of the cylinder where the flow accelerates.
Shear stress distribution around the cylinder
For incompressible flows over flat
no-slip surfaces the viscous normal stress components, (tau_n), are identically
zero; however, in slip surfaces the viscous normal stresses
achieve finite values and increase substantially proportional to
the Knudsen number. This effect is demonstrated in the figure below
where we plot the viscous normal stress distribution around the cylinder periphery. In this case the viscous normal stresses for Kn=0
are
non-zero due to the curvilinear boundary; however, they are considerably smaller compared to the slip-flow
even for this relatively
small value of Knudsen number (Kn=0.015).
Levels of the pressure distribution
are also reduced compared to
the no-slip case.
The reduction in the pressure
levels is counter-balanced by the increase in the viscous normal stresses; therefore, the total normal stresses (i.e. combined pressure
and viscous normal stresses) do not vanish as
the rarefaction effects increase.
Viscous normal stress distribution around the cylinder
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