Finite-element analysis of Taylor flow

A finite-element analysis of Taylor flow in a cylindrical capillary was performed using a commercial FEM program (FIDAP) to solve the fundamental fluid dynamics equations together with the capillary forces at the gas-liquid interface. A moving-surface formulation was used to calculate the bubble shape. The thickness of the liquid film surrounding the gas bubble, the degree of mixing in the liquid phase, and the slip velocity between the two phases were calculated. These parameters influence the performance of monolith reactors operating in the Taylor flow regime. On comparison with experimental results it was found that the FEM calculation generally predicts a thinner liquid film, which can possibly be explained in terms of a peripheral variation in surface tension. Moreover the wavelength of the wiggles predicted in the liquid film near the rail end of the bubble was compared to those arising from a simplified mathematical analysis available in the literature. Good agreement was found for Ca < 0.005, while for higher Ca the FEM predicts significantly shorter wavelengths, indicating that the lubrication theory is not valid here.