Scaling of the enhancement.  How much can you expect?

Finally, it is tempting to try to scale the enhancement.  It looks almost linear in M.  If we divide out M, we find that for large M, there is no M variation.  

[Graphics:../Images/lubricatedflow_gr_126.gif]
[Graphics:../Images/lubricatedflow_gr_127.gif]
Plots of the scaled enhancment
[Graphics:../Images/lubricatedflow_gr_128.gif]

[Graphics:../Images/lubricatedflow_gr_129.gif]

[Graphics:../Images/lubricatedflow_gr_130.gif]

[Graphics:../Images/lubricatedflow_gr_131.gif]

[Graphics:../Images/lubricatedflow_gr_132.gif]

[Graphics:../Images/lubricatedflow_gr_133.gif]

[Graphics:../Images/lubricatedflow_gr_134.gif]

[Graphics:../Images/lubricatedflow_gr_135.gif]

[Graphics:../Images/lubricatedflow_gr_136.gif]

Back to conclusions

[Graphics:../Images/lubricatedflow_gr_137.gif]

[Graphics:../Images/lubricatedflow_gr_138.gif]

We see that the scaling is correct and that the maximum enhancement is about 50% of the viscosity ratio.  Now you know enough to tell if this process for transporting oil will be worthwhile!  


Converted by Mathematica      December 22, 1999