2018/07/17 by Paşa, Gelu
#34B09 #34D20 #35C09 #35J20 #76S05 #FOS: Physical sciences #Fluid Dynamics (physics.flu-dyn)
paper · doi:10.48550/arxiv.1807.06591
We study the Hele-Shaw immiscible displacements when all surfaces tensions on the interfaces are zero. The Saffman-Taylor instability occurs when a less viscous fluid is displacing a more viscous one, in a rectangular Hele-Shaw cell. We prove that an intermediate liquid with a variable viscosity can almost suppress this instability. On the contrary, a large number of constant viscosity liquid-layers inserted between the initial fluids gives us boundless growth rates with respect to the wave numbers of perturbations. The same amount of intermediate liquid is used in both cases.