The pipeline flow of capsules: Part 2: Theoretical analysis of the concentric flow of cylindrical forms

Abstract Predictions of capsule velocity and pressure gradient accompanying capsule flow are made for an idealised system in which a long cylindrical capsule moves concentrically with respect to the pipe. The capsule velocity always exceeds the average velocity, for example, by 22% for laminar conditions and 3% for turbulent conditions, when the ratio of the capsule diameter to the pipe diameter is 0.8. The pressure gradient accompanying capsule flow is related to the pressure gradient which would exist if the fluid alone flowed in the pipe at the same average velocity as the combined flows for different combinations of laminar and turbulent conditions. For each combination only a moderate increase in pressure gradient is predicted provided the diameter ratio does not exceed about 0.9. In the particular case of turbulent flow in the capsule‐free system and laminar flow in the annulus between the capsule and the pipe a decrease in pressure gradient of as much as 20% is predicted. A regime of instability is predicted in which neither laminar nor turbulent flow is stable in the annulus.