Linear stability of the thixotropic boundary-layer flow over a flat plate

Abstract

Linear temporal stability of an ideal thixotropic fluid obeying the Moore model in a flat plate boundary-layer flow is investigated in the present work. The Moore model captures the thixotropic and shear-thinning behaviors; both are controlled by the fluid time scale. Besides being shear-thinning and thixotropic, the Moore model can approximate the bi-viscous Bingham model. This means that the Moore fluid mimics the viscoplastic behavior, too, which is controlled by the inverse of the fluid time scale. This study’s main purpose is to investigate the effect of thixotropy on boundary-layer flow stability. However, it is found that without emphasizing the Moore fluid shear-thinning and viscoplastic behaviors, the interpretation of stability results is impossible. Following the Blasius solution, the generalized Blasius equation is derived and solved numerically. Basic solution results show that the Deborah number (the dimensionless fluid time scale) and viscosity-gap ratio reduce the basic flow’s drag force and boundary-layer thickness. Linear stability analysis is used to investigate the flow stability, infinitesimally-small normal-mode perturbations are introduced to the basic flow, and the generalized Orr–Sommerfeld equation is derived, which is solved using the spectral method. Based on the stability results, the thixotropy destabilizes the flow when the Deborah number is large enough. For small values of Deborah number, the shear-thinning and viscoplastic behaviors, which are known to have a stabilizing effect, are dominant and stabilize the flow. As the Deborah number becomes larger, the thixotropy overcomes the stabilizing effect of the shear-thinning and viscoplasticity and destabilizes the flow.