Two-dimensional simulations of flinstability at the interface of a three-layer, density-matched, viscosity-stratifi ed Poiseuille fl ow are performed using a front-tracking/fi nite difference method. This is an extension of the study for the stability of two-layer viscosity-stratifi ed fl ow of Cao et al., Int. J. Multiphase Flow, 30, 1485-1508 (2004). We present results for large-amplitude non-linear evolution of the interface for varying viscos- ity ratio m, Weber number We, and phase difference between the perturbations of the two interfaces. Strong non-linear behaviour is observed for relatively large initial perturbation amplitude. The higher viscosity fl uid is drawn out as a fi nger that penetrates into the lower viscosity layer. The fi nger originates at the crest of the perturbation at the interface. The simulated interface shape compares well with previously reported experiments. Increasing interfacial tension retards the growth rate of the interface as expected, whereas increasing the viscosity ratio enhances it. The sinuous instability appears to evolve faster than the varicose one. For certain fl ow parameters the high-viscosity fi nger displays a bulbous tip, which is also seen in our previously conducted experiments and two-layer results, although it is less pronounced. The low-viscosity intruding fi nger does not display this curious bulbous tip. Drop formation is precluded by the two-dimensional nature of the calculations.
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