2019/03/04 by Gelu Paşa, Paşa, Gelu
Physics and Astronomy · Engineering · Materials Science · #Theoretical and Computational Physics #Lattice Boltzmann Simulation Studies #Material Dynamics and Properties
paper · pdf · doi:10.48550/arxiv.1903.01455
The Saffman-Taylor instability occurs when a less viscous fluid is displacing a more viscous one in a rectangular Hele-Shaw cell. A surface tension on the interface between the two fluids is improving the stability. The multi-layer Hele - Shaw model, consisting of N intermediate fluids with constant viscosities, was studied in some previous papers and very low growth constants were obtained for large N. We prove that this model leads us to a significant instability, even if N is very large. The maximum value of growth constants can not decrease under a certain value, not depending on the surface tensions on the interfaces. This contradiction with the Saffman-Taylor result makes us have some doubts concerning the correctness of multi-layer model.