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

我们研究了粘弹性上部对流麦克斯韦流体的泊肃叶流的线性稳定性，其中流变参数取决于悬浮在流体中的颗粒的浓度（稠密的悬浮液，扩散可忽略不计）。在确定基本流量和基本浓度分布之后，我们考虑以水流和展向波形式的时间三维扰动。我们推导了线性化摄动方程，并证明了Squire定理的有效性，扩展了Tlapa和Bernstein（1970）的结果，在该结果中，定理被证明具有恒定的流变参数。我们讨论了魏森伯格数和雷诺数之间的关系。最后，我们研究了常数系数和低Weissenberg数的非常数系数情况下的二维特征值问题。