3D Instability of Miscible Displacements in a Hele-Shaw Cell

摘要: We study the downward miscible displacement of a fluid by lighter and less viscous one in gap Hele-Shaw cell. For sufficiently large velocities, well-defined interface separates two fluids. As long as velocity or viscosity ratio are below critical value, has shape tongue symmetric across gap. ratios larger than estimated at 1.5, there exists velocity, above which becomes unstable, leading to new 3D pattern involving regularly spaced fingers wavelength about 5 times cell thickness. delineate stability diagram.