In the left figure, equilibrium flow profiles of dusts are plotted for different ϵ. The solid red line curve shows the same for the Newtonian limit ( ). In the right figure, non-Newtonian viscosity is plotted against unperturbed velocity shear rate. For , shear thinning property exists until and then shear thickening begins. As ϵ increases, the property changes from shear thinning to shear thickening and for , shear thinning property almost ceases.
Growth rate of instability is plotted against wave number for different values of parameter ϵ in incompressible limit. The solid red line curve shows that for Newtonian limit. For , the growth rate is close to that of Newtonian limit.
In the left figure, two sets of curves are shown for two different Mach number (M) including and excluding dispersion term in Poisson's equation for . In each set of curves, dotted line represents the curve without dispersion effect and the solid line with dispersion term. In the right one, compressibility is introduced by increasing the Mach number and it indicates that the growth rate diminishes as compressibility strengthens in the medium for . Here, M = 0 curves show incompressible limit for comparison.
The left figure shows contour plot of growth rate in the plane of Mach number (M) and wave number for . In the right figure, surface plot of growth rate is drawn on the parametric space of ϵ and k for Mach no. M = 2.4.
Comparison of growth rates for different parameters M, k, and ϵ.
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