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Interfacial Instability of Thixotropic Fluids in Core-Annular Flow of Waxy Crude Oils: a Two-Dimensional Modelling
Author(s): Morteza Safarifard, Mohammad Pourjafar, Keyvan Sadeghy
Keywords: Core-Annular Flow, Waxy Crude Oil, Thixotropic Fluid, Interfacial Instability
Stability of core-annular flow of purely-viscous immiscible fluids is investigated in this work. It is assumed that the core fluid is thixotropic and obeys the Moore model as its constitutive equation while the fluid flowing through the annulus is assumed to be Newtonian. For ease of analysis, the core-annular flow is modelled using a two-dimensional, three-layered, planar configuration. Having found an analytical solution for the base-flow in all layers, a temporal, normal-mode, linear stability analysis is employed to investigate the role played by the rheological parameters of the core fluid on the critical Reynolds number and unstable modes. An eigenvalue problem is obtained this way which is solved numerically using the pseudo-spectral collocation method. It is found that the time constant introduced through the thixotropic behavior of the core fluid has a stabilizing effect on the interface. An increase in the viscosity-difference ratio of the core fluid is also predicted to have a stabilizing effect on the interface. An increase in the viscosity of the lubricating fluid (i.e., the Newtonian fluid in direct contact with the wall) is predicted to have a stabilizing or destabilizing effect on the interface depending on its value being smaller or larger than a threshold.