Development of transport equations for multiphase systems—II: Application to one-dimensional axi-symmetric flows of two phases

Abstract In the previous paper, we considered the problem of transport of a solute between two moving fluid phases, and developed a formalism that would allow a priori estimates of the transport parameters in the equations for the average solute concentration in each phase. In this work, the formalism is applied to the case of one-dimensional axi-symmetric flow of the two phases. The predictions of the model are compared to the exact solution of the governing differential equations for pulsed systems. The agreement between the computed average concentrations from the model and the point equations is excellent for all values of the physical parameters. An analysis of the model equations using the method of moments leads to equations for the mean pulse positions, velocities and rates of spread for long times.