Linear stability analysis of the Hele-Shaw cell with lifting plates

The first stages of finger formation in a Hele–Shaw cell with lifting plates are investigated by means of linear stability analysis. At the beginning of lifting the square of the wavenumber of the dominant mode results to be proportional to the lifting rate (in qualitative agreement with the available experimental data), to the square of the length of the cell occupied by the more viscous fluid, and inversely proportional to the cube of the cell gap. This dependence on the cell parameters is significantly different of that found in the standard cell. On the other hand, our results show that the wavelength of the dominant mode decreases with lifting time, also in agreement with several experimental observations