The study deals with linear analysis of the stability of the interface of a radially displaced fluid (at a constant flow rate or pressure) in the Hele-Shaw cell. As distinct from other studies, the calculations have been performed considering finite size of the system and nonzero viscosity of the displacing fluid. Consequently, earlier results have been considerably refined. An interesting feature-varying sensitivity of the system to perturbations with changing control parameters-has been detected and analyzed. Therefore, this system can be viewed as a specific filter which picks harmonics of certain frequencies out of random mechanical effects and amplifies them.

The entropy production in the problem of the radial displacement of a fluid in the Hele-Shaw cell is determined. The morphological stability of the interface between the displaced and displacing fluids is studied using the linear analysis for stability and the maximum entropy production principle. Regions, in which different forms of the interface can coexist, are predicted. These regions are analyzed depending on the cell size, the injected flow rate, and the ratio of the fluid viscosities.

The initial stage of interface instability upon radial displacement of a fluid in a Hele-Shaw cell is investigated. An air-silicone oil system is analyzed. The critical radii of stability relative to long-wave perturbations are determined. It is found that, in the investigated range of parameters, instability most often begins by a translational mechanism. It is ascertained that in the overwhelming majority of cases the critical radii of instability are smaller than the values predicted by the linear stability theory and external effects make this difference even greater. The obtained results are discussed and compared with the existing theories.

The problem of the morphological stability of an interface in the case of the displacement of one non-Newtonian fluid by another non-Newtonian fluid in a radial Hele-Shaw cell has been considered. Both fluids have been described by the two-parameter Ostwald-de Waele power-law model. The nonzero viscosity of the displacing fluid has been taken into account. A generalized Darcy's law for the system under consideration, as well as an equation for the determination of the critical size of morphological stability with respect to harmonic perturbations (linear analysis), has been derived. Morphological phase diagrams have been constructed, and the region of the parameters in which nonequilibrium reentrant morphological transitions are possible has been revealed.