Density-driven instabilities in capillary tubes: Influence of a variable diffusion coefficient

The influence of a variable diffusion coefficient on the gravitational instability at the interface between two variable viscosity fluids in a vertical capillary tube is investigated, based on the three-dimensional Stokes equations. As the viscosity contrast between the fluids grows, the maximum density gradient of the self-similar base concentration profile increases while its location is shifted into the more viscous fluid. Thus the perturbations are forced to grow in a more viscous environment, which can reduce their growth rate by up to 30%. For large viscosity contrasts, intermediate interface thicknesses are seen to give rise to the highest growth rates. For most parameter combinations, the first azimuthal mode is found to be most unstable. However, for large viscosity ratios and small interface thicknesses the axisymmetric mode dominates. © 2006 American Institute of Physics. DOI: 10.1063/1.2192447