Mechanistic modeling of critical sand deposition velocity in gas-liquid stratified flow

Two models with similar approaches are developed based on the forces acting on a particle, such as the drag, turbulent, apparent gravity, van der Waals and lift forces for prediction of the transitions between moving/stationary dunes and moving/stationary bed. Dune pilling up and collapsing mechanism considering a torque balance on a rolling particle located at the top of the dune is adopted for stationary dunes. Torque balance applied to a rolling particle located on the lowest stratum of the moving bed layer is used to predict the minimum liquid film velocity for particle to grow a stationary bed. Comparison between the predictions of the two mechanistic models and the experimental data show good agreement, with critical sand deposition velocity absolute relative errors at 16.4% for stationary dunes and 12.6% for stationary bed.