  The Kelvin-Helmholtz (KH) instability is studied in a non-Newtonian dusty
plasma with an experimentally verified model [Phys. Rev. Lett. {\bf 98}, 145003
(2007)] of shear flow rate dependent viscosity. The shear flow profile used
here is a parabolic type bounded flow. Both the shear thinning and shear
thickening properties are investigated in compressible as well as
incompressible limits using a linear stability analysis. Like the stabilizing
effect of compressibility on the KH instability, the non-Newtonian effect in
shear thickening regime could also suppress the instability but on the
contrary, shear thinning property enhances it. A detailed study is reported on
the role of non-Newtonian effect on KH instability with conventional dust fluid
equations using standard eigenvalue analysis.
