Abstract
An approximate analysis is given for miscible displacement in vertical tubes when density differences between the displaced and displacing fluids give rise to buoyancy forces which affect the velocity distribution significantly. The results of this analysis agree with the available experimental data fairly uniformly over the range of parameters studied experimentally.
By analogy with studies of heat transfer in vertcal tubes it is concluded that both cases studied, when a lighter fluid displaces a heavier fluid in upflow, or when the heavier fluid is below the lighter fluid, are potentially unstable flows because buoyancy forces can create points of inflection in the velocity profile; stagnation at the wall also is predicted for upflow when the lighter fluid is on the bottom initially, and this has been observed to induce a sudden transition to turbulence in heat transfer systems.
Buoyancy forces reduce the extent of dispersion by flattening the velocity profile when the heavier fluid is on the bottom in upflow. The velocity profile is elongated and the dispersion coefficient is increased when the bottom fluid is lighter than the one it displaces in upflow.