Abstract
In this study, the effect of anisotropy of porous media on Saffman–Taylor instability (viscous fingering instability) of viscoelastic fluids is investigated for the first time. The Oldroyd-B model is used as the constitutive equation of viscoelastic phase. In linear stability analysis, the quasi-steady state approximation and six order shooting method are used to predict the growth rate of the disturbance in the flow field. In addition, the spectral method based on Hartley transforms and fourth-order Adams–Bashforth technique is used to numerically simulate this instability and the results include concentration contours, transversely averaged concentration profiles, mixing length and sweep efficiency. The results show that the flow becomes more stable by increasing the Deborah number, i.e., elasticity property of displacing viscoelastic fluid. Also, increasing permeability of media in longitudinal direction to the transverse leads to more stable flow. On the other hand, when the ratio of transverse to longitudinal dispersion is increased, the intensity of instability decreases.
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