Shear flow driven instability in an incompressible dusty plasma with a density dependent viscosity

The influence of viscosity gradient (via density) in an incompressible dusty plasma is analyzed. It is shown that for a well known dusty plasma model, the density dependence of viscosity leads to shear driven instability in a weakly coupled dusty plasma. The inhomogeneous viscous force coupled with density inhomogeneity in presence of velocity shear is responsible for this instability. For any finite value of shear flow parameter the viscous gradient force surpasses the viscous dissipation leading to instability.