Model for drop entrainment in equilibrium gas-liquid churn flow

To investigate physical behavior and quantitative prediction for the drop entrainment in churn flow, an analytical model is established based on both the Kelvin-Helmholtz instability theory and a force balance on the wave crest. The proposed model is verified qualitatively and quantitatively and the impact of the gas and liquid flow rate, pipe diameter and pressure on the drop entrainment rate is analyzed in detail. The interfacial wave in churn flow is forced by the gas drag, gravity and interfacial tension. The maximum drop entrainment appears if the resultant force acting on the wave crest balances to zero. The drop entrainment rate increases with the increase of pipe diameter and liquid mass flow rate, but decreases with the increase of gas velocity and pressure. A more accurate formula for the drop entrainment rate in churn flow is proposed by inducing a factor to consider the integrated effect of the gas velocity, liquid velocity and pressure, which can predict well in agreement with the real entrainment process.