Characteristics of stratified laminar flows in inclined pipes

Exact solutions for laminar stratified flows in inclined pipes are presented. These include all possible configurations of stratified flows with concave and convex interfaces. The exact solution is used to study the effect of the flow geometry and pipe inclination on the holdup and pressure gradient. In particular, the possibility of reducing the pressure gradient of a viscous fluid in upward inclined flows by adding a lubricating phase is investigated. It is shown that independently of the density of the lubricant, namely, whether it is lighter or heavier than the viscous fluid, the effect of hydrostatic pressure gradient always adversely affects the possibility to reduce the pumping requirement for the flow of the viscous phase. In addition, the countercurrent flow limits and the boundaries of the multiple solution regions in concurrent inclined flow are identified and discussed. The susceptibility of the system to the Ledinegg instability when using separate pumps for each of the fluids is also examined.