Pressure drop of gas–liquid Taylor flow in round 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 Qu,r, (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 mu m. The capillary number Ca (gl) varied between 2.3 x 10(-3) and 8.8 x 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 values.

Liquid-Liquid Flow in a Capillary Microreactor: Hydrodynamic Flow Patterns and Extraction Performance

The capillary micro reactor, with four stable operating flow patterns and a throughput range from grams per hour to kilograms per hour, presents an attractive alternative to chip-based and microstructured reactors for laboratory- and pilot-scale applications. In this article, results for the extraction of 2-butanol from toluene under different flow patterns in a water/toluene flow in long capillary microreactors are presented. The effects of the capillary length (0.4-2.2 m), flow rate (0.1-12 mL/min), and aqueous-to-organic volumetric flow ratio (0.25-9) on the slug, bubbly, parallel, and annular flow hydrodynamics were investigated. Weber-number-dependent flow maps were composed for capillary lengths of 0.4 and 2 m that were used to interpret the flow pattern formation in terms of surface tension and inertia forces. When the capillary length was decreased from 2 to 0.4 m, a transition from annular to parallel flow was observed. The capillary length had little influence on slug and bubbly flows. The flow patterns were evaluated in terms of stability, surface-to-volume ratio, throughput, and extraction efficiency. Slug and bubbly flow operations yielded 100% thermodynamic extraction efficiency, and increasing the aqueous-to-organic volumetric ratio to 9 allowed for 99% 2-butanol extraction. The parallel and annular flow operating windows were limited by the capillary length, thus yielding maximum 2-butanol extractions of 30% and 47% for parallel and annular flows, respectively.