Interfacial Instability of Thixotropic Fluids in Triple-Layered Channel Flow

Abstract

Interfacial stability of purely-viscous fluids is numerically investigated in channel flow. It is assumed that the main fluid (i.e., the fluid flowing through the center of the channel) is thixotropic and obeys the Moore model as its constitutive equation while the fluids flowing above and below this central (core) layer are assumed to be the same Newtonian fluids with the same thickness. Having found an analytical solution for the base-flow in all three layers, a temporal, normal-mode, linear stability analysis is employed to investigate the vulnerability of the base flow to small perturbations. An eigenvalue problem is obtained this way which is solved numerically using the pseudo-spectral collocation method. The main objective of the work is to explore the role played by the time-constant introduced through the core fluid’s thixotropic behavior on the critical Reynolds number. It is found that the thixotropic behavior of the core fluid has a stabilizing effect on the interface. An increase in the viscosity of the upper/lower Newtonian fluids is predicted to have a stabilizing or destabilizing effect on the interface depending on the parameter values of the Moore model (e.g., the ratio of the zero-shear viscosity to infinite-shear viscosity in this fluid model).

Keywords

• core-annular flow; interfacial instability; thixotropy; spectral method; moore model.