Two-phase viscous fingering of immiscible thixotropic fluids: A numerical study

• The shape of viscous fingers is controlled by the thixotropic time constant of the Moore fluid.
• For small values of the viscosity ratio, tip-splitting is suppressed for thixotropic fluids obeying the Moore model.
• The amplitude and wavenumber of the initial perturbation has a dramatic effect on the time-evolution of the viscous fingers.
• The slip of the displacing and/or the displaced fluid has a stabilizing effect on the viscous fingering phenomenon.

The effects of a fluid’s thixotropic behavior is investigated on the viscous fingering phenomenon in a rectangular Hele-Shaw cell assuming that the displacing fluid is Newtonian while the displaced fluid obeys the Moore model for thixotropic fluids. Lubrication theory is used to simplify the gap-averaged governing equations in which the interfacial tension is treated as a body force. It is shown that the shapes of the fingers are dramatically affected by the displaced fluid’s thixotropic behavior. For highly thixotropic fluids, a chaotic behavior, accompanied by a blowup at prolonged times, is predicted to occur for certain set of parameter values. The viscosity ratio of the Moore fluid is also predicted to influence the shapes of the fingers provided that the zero-shear viscosity of the displaced fluid is higher than the viscosity of the displacing fluid. It is shown that the amplitude and wavenumber of the initial perturbation plays a crucial role on its time evolution. Also, a partial slip of the displaced and/or the displacing fluid is predicted to have a stabilizing effect on the viscous fingering phenomenon.