Buoyancy-dominated displacement flows in near-horizontal channels: the viscous limit

@article{Taghavi2009BuoyancydominatedDF,
  title={Buoyancy-dominated displacement flows in near-horizontal channels: the viscous limit},
  author={S. Taghavi and T. S{\'e}on and D. Martinez and I. Frigaard},
  journal={Journal of Fluid Mechanics},
  year={2009},
  volume={639},
  pages={1 - 35}
}
We consider the viscous limit of a plane channel miscible displacement flow of two generalized Newtonian fluids when buoyancy is significant. The channel is inclined close to horizontal. A lubrication/thin-film approximation is used to simplify the governing equations and a semi-analytical solution is found for the flux functions. We show that there are no steady travelling wave solutions to the interface propagation equation. At short times the diffusive effects of the interface slope are… Expand
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