Pressure drop of gas-liquid Taylor flow in micro-capillaries for low to intermediate Reynolds numbers

In this paper, a model is presented that describes the pressure drop of gas–liquid Taylor flow in round capillaries with a channel diameter typically less than 1 mm. The analysis of Bretherton (J Fluid Mech 10:166–188, 1961) for the pressure drop over a single gas bubble for vanishing liquid film thickness is extended to include a non-negligible liquid film thickness using the analysis of Aussillous and Quéré (Phys Fluids 12(10):2367–2371, 2000). This result is combined with the Hagen–Poiseuille equation for liquid flow using a mass balance-based Taylor flow model previously developed by the authors (Warnier et al. in Chem Eng J 135S:S153–S158, 2007). The model presented in this paper includes the effect of the liquid slug length on the pressure drop similar to the model of Kreutzer et al. (AIChE J 51(9):2428–2440, 2005). Additionally, the gas bubble velocity is taken into account, thereby increasing the accuracy of the pressure drop predictions compared to those of the model of Kreutzer et al. Experimental data were obtained for nitrogen–water Taylor flow in a round glass channel with an inner diameter of 250 µm. The capillary number Ca gl varied between 2.3 × 10-3 and 8.8 × 10-3 and the Reynolds number Re gl varied between 41 and 159. The presented model describes the experimental results with an accuracy of ±4% of the measured value