This paper investigates the linear stability of viscoelastic liquid films flowing down an inclined porous substrate analytically and numerically. It focuses on the Stokes flow of viscoelastic films and uncovers two unstable modes triggered by elasticity. The elastic surface mode with a long wave number is solved analytically and numerically. Our results also indicate elasticity can trigger an elasto-porous mode at small incline angle and ratio of film thickness to substrate thickness. The Oldroyd-B model is used for the constitutive relation between the strain and polymer stress. The classical Beavers–Joseph condition is applied to describe the boundary conditions at the fluid-porous interface (Beavers and Joseph, 1967). This condition represents the linear relationship between velocity gradient of fluid layer and velocity difference between two layers, ${\partial }_{z}u=\frac{\alpha }{\sqrt{\kappa }}(u-u_m)$, where $\alpha$ is the Beavers–Joseph coefficient, representing slip flow at the interface; $\kappa$ is the permeability of the porous medium. Effects of porous medium properties, including permeability and depth ratio, as well as the impact of slip flow at the interface on the unstable modes are examined.

本文通过分析和数值研究了沿倾斜多孔基材流动的粘弹性液膜的线性稳定性。它重点关注粘弹性薄膜的斯托克斯流，并揭示了由弹性引发的两种不稳定模式。对长波数弹性表面模式进行了解析和数值求解。我们的结果还表明，弹性可以在小倾斜角度和薄膜厚度与基材厚度的比率下触发弹性多孔模式。Oldroyd-B 模型用于表示应变和聚合物应力之间的本构关系。经典的 Beavers-Joseph 条件用于描述流体-多孔界面的边界条件（Beavers 和 Joseph，1967）。该条件表示流体层的速度梯度与两层之间的速度差之间的线性关系，${\partial }_z你=\frac{\alpha }{\sqrt{\kappa }}（你-{你}_{米}）$， 在哪里$\alpha$是 Beavers-Joseph 系数，代表界面处的滑流；$\kappa$是多孔介质的渗透率。研究了多孔介质性质的影响，包括渗透率和深度比，以及界面滑流对不稳定模式的影响。