Modal stability and Squire’s theorem for an inhomogeneous viscoelastic suspension

We study the linear stability of Poiseuille flow a viscoelastic upper convected Maxwell fluid in which rheological parameters depend on concentration particles suspended (dense suspension with negligible diffusion). After determining basic and profile we consider temporal three dimensional perturbation form stream-wise span-wise wave. derive linearized perturbed equation prove validity Squire’s theorem, extending result Tlapa Bernstein (1970) theorem was proved for constant parameters. discuss relation between Weissenberg Reynolds numbers. finally 2D eigenvalue problem case coefficients non-constant low number. solve numerically by means spectral collocation method plot marginal curves discussing how depends rheology. • suspension. Rheology concentration. generalized Orr–Sommerfeld equation. curves.