Linear stability analysis of time-dependent fluids in plane Couette flow past a poroelastic layer

摘要

Linear stability of time-dependent fluids obeying the Quemada model is numerically investigated in plane Couette flow past a saturated poroelastic layer. Having assumed that the permeable layer is viscoelastic and obeys the Kelvin model, the base flow/deformation were obtained for the main channel and also in the poroelastic layer using mixture theory. The base state so obtained was then subjected to infinitesimally small, normal-mode perturbations in order to determine its vulnerability to poroelastic instability. An eigenvalue problem was obtained which was numerically solved using the iterative shooting scheme (ISS). The main objective of the work was to investigate the role played by the movement of the upper plate on the stability of the core fluid (i.e., the fluid flowing through the main channel). Of equal importance was to determine the influence of the rheological behavior of the core fluid on the growth rate of unstable mode(s). Numerical results were obtained mostly under creeping-flow conditions demonstrating that anti-thixotropy of the core fluid lowers the critical velocity of the moving plate whereas the viscosity-gap ratio (i.e., the viscosity of the core fluid divided by the viscosity of the interstitial fluid in the poroelastic layer) has a stabilizing effect on the core flow. By allowing permeability to be a function of porosity, the degree of nonlinearity of this relationship was found to have a stabilizing or destabilizing effect on the core flow depending on the layer's porosity.