Analytical solution for Newtonian–Bingham plastic two-phase pressure driven stratified flow through the circular ducts

For steady state, stratified, laminar, fully developed two-phase flow which one of them is Newtonian and the other one is Bingham plastic, the motion equations in horizontal pipe with appropriate boundary conditions have been solved analytically. Pressure drop, velocity distribution and location of plug region related to Bingham plastic fluid have been reported. The results show that the non-Newtonian rheological properties have negligible effects on two-phase velocity profile and consequently on pressure gradient in small viscosity ratio of two fluids. With promotion of viscosity ratio, the influence of yield stress on two-phase velocity profile is more considerable.