Linear stability of a viscoelastic fluid obeying the Walters’ B model is analytically and numerically investigated in the entrance region of a plane channel formed between two parallel plates. The plates are compliant and obey the two degree-of-freedom von Karman solid model. Having obtained the base-flow velocity profiles using the boundary-layer theory, their vulnerability to infinitesimally small varicose disturbances is investigated using the temporal, normal-mode, linear stability analysis. The results obtained show that a fluid’s elasticity has a stabilizing effect on the developing velocity profiles. The distance at which the flow becomes unstable shifts further downstream (i.e., towards the fully-developed section) of the channel when the Deborah number is increased. An increase in the flexural rigidity of the plates is shown to have a stabilizing effect on the short waves (i.e., the flutter modes) whereas an increase in its mass can dramatically destabilize such modes. The flow becomes more stable when the stiffness of the soft matter restraining the vertical movement of the plates is increased with the effect being more significant on the long waves (i.e., flow-induced modes). Boosting the dissipating effect of this material is predicted to have a stabilizing effect on the short waves.

中文翻译：

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粘弹性流体在通过顺应通道流动时的水弹性不稳定性

在两个平行板之间形成的平面通道的入口区域，通过解析和数值研究了服从Walters B模型的粘弹性流体的线性稳定性。平板是顺应性的，并遵守两个自由度的von Karman实体模型。已经使用边界层理论获得了基流速度分布图，使用时间，正常模式，线性稳定性分析研究了它们对于无限微小的静脉曲张干扰的脆弱性。所得结果表明，流体的弹性对显影速度分布具有稳定作用。流体变得不稳定的距离进一步向下游移动（即，则当Deborah编号增加时，向该通道的完全展开部分）。板的抗弯刚度的增加显示出对短波具有稳定作用（即，颤振模式），而其质量的增加则可以极大地破坏这种模式的稳定性。当软质材料的刚度限制板的垂直运动时，流动变得更稳定，这对长波影响更大（即流动引起的模态）。预计增强这种材料的消散作用对短波具有稳定作用。