Hydrodynamics of Gas–Liquid Slug Flows in a Long In-Plane Spiral Shaped Milli-Reactor


An experimental investigation of gas–liquid Taylor flows in a millimetric in-plane spiral shaped reactor with various tube curvature ratios (52 < λ < 166) is reported. Thanks to the compactness of the reactor and the use of an ad hoc imaging system and processing, the axial evolution of bubble lengths and velocities could be recorded and extracted along the whole reactor length (~3 m). The experimental results showed a significant linear increase of bubble length and velocity with axial position. Very long, stable Taylor bubbles (LB/dit up to 40) and liquid slugs were generated, in particular due to the poor wettability of the surface and the important role it played in bubble formation. At identical inertial force (i.e., identical Reynolds number), a higher centrifugal force (i.e., lower tube curvature ratio) likely led to shorter Taylor bubble lengths while only slightly affecting the liquid slug lengths. The axial pressure drop could be estimated from the axial increase in bubble volume, and compared with the measured pressure drop and that predicted by the correlations from literatures. By considering both the friction and capillary pressure drops, it was observed that the predicted two-phase pressure drop was slightly dependent on the centrifugal force and that the capillary pressure drop, determined from the unit cell number, capillary number and static contact angle, was dominant.

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We thank Prof. Alain Line and Alexandre Boucher, who kindly provided valuable support and discussions for pressure drop and liquid film calculation.


The first author would like to acknowledge the financial assistance provided by the China Scholarship Council. We also acknowledge the support for this work from the CNRS research federation FERMaT (FR 3059).

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Corresponding author

Correspondence to Karine Loubière.

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Special issue: “Two-phase flows in microchannels: hydrodynamics, heat and mass transfer, chemical reactions”. Edited by R.Sh. Abiev



(1) Calculation of the bubble and liquid slug lengths

The bubble and liquid slug lengths are calculated based on the hypothesis that the nose and tail of the curved bubble and liquid slug are flat and that the liquid film thickness is negligible. Under these assumptions, as shown in Fig. A.1, the bubble area, AB, can be deduced from the difference between the outer sector OM1M2, Aouter, and the inner sector OM3M4, Ainner, such as

$${{A}_{{{\text{inner}},{\text{B}}}}} = \frac{{\theta }}{2}{{\left( {R - \frac{{{{d}_{{{\text{it}}}}}}}{2}} \right)}^{2}},$$
$${{A}_{{{\text{outer}},{\text{B}}}}} = \frac{{\theta }}{2}{{\left( {R + \frac{{{{d}_{{{\text{it}}}}}}}{2}} \right)}^{2}}$$
$${{A}_{{\text{B}}}} = {{A}_{{{\text{outer}},{\text{B}}}}} - {{A}_{{{\text{inner}},{\text{B}}}}} = R{{d}_{{{\text{it}}}}}{\theta }$$

The bubble length, LB, is defined according to

$${{L}_{B}} = R{\theta }$$

By combining Eqs. (A.3) and (A.4), one obtains

$${{L}_{{\text{B}}}} = \frac{{{{A}_{B}}}}{{{{d}_{{{\text{it}}}}}}}$$

Similarly, the liquid slug length can also be deduced from the liquid slug area, AS, and dit as

$${{L}_{S}} = {\theta }R = \frac{{{{A}_{{{\text{outer}},{\text{S}}}}} - {{A}_{{{\text{inner}},{\text{S}}}}}}}{{{{d}_{{{\text{it}}}}}}} = \frac{{{{A}_{{\text{S}}}}}}{{{{d}_{{{\text{it}}}}}}}$$

(2) Variation of the constant F2 related to the bubble velocity (Eq. (6))


Fig. A.1. The schematic diagram of the bubble length calculation.


Fig. A.2. Constant F2 versus gas–liquid flow ratio for configuration ET: (1) jL = 1.80 cm s–1; (2) jL = 3.61 cm s–1; (3) jL = 7.22 cm s–1; configuration MT: (4) jL = 1.80 cm s–1; (5) jL = 3.61 cm s–1; (6) jL = 7.22 cm s–1.

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Mei Mei, Felis, F., Hébrard, G. et al. Hydrodynamics of Gas–Liquid Slug Flows in a Long In-Plane Spiral Shaped Milli-Reactor. Theor Found Chem Eng 54, 25–47 (2020). https://doi.org/10.1134/S0040579520010169

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  • Taylor gas–liquid flow
  • millimetric channel
  • centrifugal force
  • bubble expansion
  • pressure drop