Interfacial instabilities of immiscible radial displacements in homogeneous porous media are analysed in the case of sinusoidal injection flows. The analysis is carried out through numerical simulations based on the immersed interface and level set methods. Investigations of the effects of the period of the sinusoidal injection flows revealed a novel resonance effect where, for a critical period, the number of fingers as well as their structures are considerably changed. The resonance in the flow development is clearly identified through the abrupt changes in the Fourier spectrum of the interface as well as quantitative characteristics of the flow in the form of the minimum and maximum radii of the interface. For the range of parameters examined in this study that correspond to instabilities dominated by viscous forces, the resonance period was found to correlate with a characteristic time of the flow and the fluids mobility ratio. This new physical phenomenon offers new perspectives for using the flow instability to determine important physical properties such as the viscosity and the surface tension of fluids.
Discussion: “A Continuum Theory of Fluid Saturated Porous Media” (Bedford, A., and Ingram, J. D., 1971, ASME J. Appl. Mech., 38, pp. 1–7)
