Specific features of the loss of stability during radial displacement of fluid in the Hele–Shaw cell

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.