Method for calculating the void fraction and relative length of bubbles under slug flow conditions in capillaries

A method for calculating the void fraction and relative size of bubbles at the known flow rates of phases is constructed using the mathematical model of a gas—liquid slug flow in capillaries that was developed earlier. The results of the calculations are in good agreement with the experimental data of other authors. The boundedness of linear approximations such as the Armand formula by the small values of the capillary numbers is revealed. It is shown that the void fraction depends not only on the dynamic gas holdup, but also on the capillary number and the Weber number, as well as on the direction of the flow. It is found that the ratio of the dynamic gas holdup to the void fraction varies from 1 to 2.5 as the capillary number increases. A tenfold error in the experimental determination of the length of liquid slugs by a simplified procedure is revealed. A simple calculation relationship that relates the dynamic gas holdup to the void fraction is derived from the Liu—Vandu—Krishna approximation. The theoretical explanation of the causes of the abnormal dependence of the void fraction on the dynamic gas holdup in microchannels with sizes of less than 100 fum is given. The specific features of a slug flow in microchannels that are caused by the disintegration of a film into drops are explained. The developed calculation method can also be applied to liquid—liquid systems.