Dynamics of isolated confined air bubbles in liquid flows through circular microchannels: an experimental and numerical study

Abstract

Experimental and numerical studies are performed to characterise the dynamics of isolated confined air bubbles in laminar fully developed liquid flows within channels of diameters d = 0.5 mm and d = 1 mm. Water and glycerol are used as the continuous liquid phase, and therefore, a large range of flow capillary numbers 10⁻⁴ < Ca < 10⁻¹ and Reynolds numbers 10⁻³ < Re < 10³ are covered. An extensive investigation is performed on the effect of bubble size and flow capillary number on different flow parameters, such as the shape and velocity of bubbles, thickness of the liquid film formed between the bubbles and the channel wall, and the development lengths in front and at the back of the bubbles. The micro-particle shadow velocimetry technique (μPSV) is employed in the experimental measurements allowing simultaneous quantification of important flow parameters using a single sequence of high-speed greyscale images recorded at each test condition. Bubble volume and flow rate of the continuous liquid phase are precisely determined in the post-processing stage using the μPSV images. These parameters are then used as initial and boundary conditions to set up CFD simulations reproducing the corresponding two-phase flow. Simulations based on the volume of fluid technique with the aim of capturing the interface dynamics are performed with both ANSYS Fluent v. 14.5, here augmented by implementing self-defined functions to improve the accuracy of the surface tension force estimation, and ESI OpenFOAM v. 2.1.1. The present approach not only results in valuable findings on the underlying physics involved in the problem of interest but also allows us to directly compare and validate results that are currently obtained by the experimental and computational methods. It is believed that similar methodology can be employed to rigorously investigate more complex two-phase flow regimes in micro-geometries.

Appendix 1: Selected experimental data

This appendix reports, in a tabular form, the flow parameters characterising the flow conditions (fluids, channel diameter d, dispersed phase volume $V_d$, and mean liquid flow velocity $\overline{U}_{c}$) and results (dispersed phase velocity ${U}_{d}$, dimensionless liquid film thickness δ*, dimensionless diameter of the fitted sphere to the bubble nose ${d_{\rm nose}}^{*}$ and tail ${d_{\rm tail}}^{*}$) for 22 selected experimental runs, whose corresponding bubbles shape are displayed in Figs. 5a, b, 9 and 10 of the present paper. These data are useful for benchmarking computational codes aimed to simulate the confined small and elongated bubbles in liquid flows within narrow channels.

The experimental test conditions are the following:

• Temperature: 25 °C.

• Density: water 997 kg/m³, glycerol solution 1250 kg/m³, air 1.204 kg/m³.

• Viscosity: water 0.88 mPa·s, glycerol solution 550 mPa·s, air 0.019 mPa·s.

• Surface tension: air–water 72.8 mN/m, air–glycerol 63.4 mN/m.

Case	Fluids	d (μm)	$V_d$ [μl]	$\overline{U}_{c}$ [m/s]	${U}_{d}$ [m/s]	δ* [–]	${d_{\rm nose}}^{*}$ [–]	${d_{\rm tail}}^{*}$ [–]
1. Figure 5a, ${{d}_{eq}}^{*}=0.354$	Air–glycerol	494	0.0028	0.00553	0.01033	–	0.35	0.36
2. Figure 5a, ${{d}_{eq}}^{*}=0.513$	Air–glycerol	494	0.0085	0.00454	0.00777	–	0.50	0.54
3. Figure 5a, ${{d}_{eq}}^{*}=0.677$	Air–glycerol	494	0.0196	0.00360	0.00599	–	0.62	0.74
4. Figure 5a, ${{d}_{eq}}^{*}=0.747$	Air–glycerol	494	0.0263	0.00451	0.00713	–	0.67	0.81
5. Figure 5a, ${{d}_{eq}}^{*}=0.813$	Air–glycerol	494	0.0339	0.00463	0.00708	–	0.69	0.92
6. Figure 5a, ${{d}_{eq}}^{*}=1.047$	Air–glycerol	494	0.0724	0.00435	0.00568	–	0.72	1.06
7. Figure 5a, ${{d}_{eq}}^{*}=1.189$	Air–glycerol	494	0.1061	0.00454	0.00599	0.065	0.68	1.07
8. Figure 5b, ${{d}_{eq}}^{*}=0.789$	Air–water	514	0.0349	0.0454	0.0533	–	0.79	0.79
9. Figure 5b, ${{d}_{eq}}^{*}=0.852$	Air–water	514	0.0439	0.0593	0.0697	–	0.85	0.85
10. Figure 5b, ${{d}_{eq}}^{*}=0.946$	Air–water	514	0.0602	0.0557	0.0607	–	0.95	0.97
11. Figure 5b, ${{d}_{eq}}^{*}=1.016$	Air–water	514	0.0745	0.0534	0.0550	–	0.94	0.99
12. Figure 5b, ${{d}_{eq}}^{*}=1.386$	Air–water	514	0.1893	0.0543	0.0554	0.006	0.94	0.99
13. Figure 9a, Ca = 0.008	Air–glycerol	494	0.1970	0.00084	0.00095	0.026	0.85	1.00
14. Figure 9b, Ca = 0.052	Air–glycerol	494	0.1061	0.00450	0.00600	0.062	0.69	1.05
15. Figure 9c, Ca = 0.075	Air–glycerol	494	0.1086	0.00618	0.00871	0.075	0.64	1.11
16. Figure 9d, Ca = 0.098	Air–glycerol	494	0.1231	0.00777	0.01137	0.083	0.61	1.14
17. Figure 9e, Ca = 0.163	Air–glycerol	494	0.0780	0.01145	0.01888	0.099	0.60	1.05
18. Figure 10a, Ca = 0.003	Air–water	514	0.1751	0.242	0.261	0.013	0.89	0.96
19. Figure 10b, Ca = 0.008	Air–water	514	0.1715	0.666	0.704	0.023	0.82	1.03
20. Figure 10c, Ca = 0.0098	Air–water	514	0.2208	0.757	0.815	0.025	0.78	1.05
21. Figure 10d, Ca = 0.015	Air–water	514	0.1882	1.118	1.293	0.039	0.72	1.23
22. Figure 10e, Ca = 0.023	Air–water	514	0.2179	1.580	1.944	0.054	0.64	–