Phase-Field simulation of small capillary-number two-phase flow in a microtube

Accurate calculation of surface tension force is critically important for numerical simulation of gas-liquid two-phase flows at small capillary number. It is well known that the errors in the surface tension calculation would cause considerable parasitic flow with conventional continuum surface force method. In the present simulation, Phase-Field method is employed to capture local two-phase interface. The surface tension force is represented by a chemical potential gradient. The numerical results show that the chemical potential formulation of surface tension force can reduce the magnitude of parasitic flow to the level of truncation error. This is because exchange between kinetic and surface energy is appropriately calculated. The method is applied to the simulations of air-water two-phase bubbly and slug flows in a microtube of 600μm. The Reynolds numbers are 60-200, and the capillary number is O(10-3). The simulated gas bubble shape and two-phase flow patterns are in good agreement with experimental results. The pressure drop, represented by Lockhart-Martinelli correlation, is found larger than that proposed for tubes in millimeter.