A correlation for the characteristic velocity ratio to predict hydrodynamics of capillary gas-liquid Taylor flow

The ratio between bubble velocity and mean velocity of the two-phase flow is a key parameter in Taylor flow. Correlations for this characteristic velocity ratio that are valid over the entire range of attainable capillary numbers are missing so far. Here, we develop such a correlation for laminar gas-liquid Taylor flow in circular capillary channels. The proposed model is a two-parameter logistic function, which approaches the theoretical asymptotic limit of Bretherton at low capillary number. The correlation relies on prior known parameters such as channel diameter, fluid properties and gas/liquid volumetric flow rates only. In comparison with numerical and experimental data, it is accurate within 5% and 18%, respectively. The correlation should be useful to estimate various prior unknown hydrodynamics features of Taylor flow such as bubble velocity, mean liquid velocity, gas holdup, uniform liquid film thickness, bubble diameter, and streamline patterns in the liquid slug. The derived two-parameter logistic function may be useful to develop similar correlations for non-circular channels and liquid-liquid Taylor flow.