Effects of wall velocity slip on droplet generation in microfluidic T-junctions

Abstract

The effect of the slip lengths of both continuous and dispersed phases on droplet formation in microfluidic T-junctions is investigated by a volume of fluid method. Results reveal that, in a dripping regime, the droplet size is mainly influenced by the slip length of the continuous phase and increases with it. In a squeezing regime, the droplet size decreases with the slip lengths of both phases. The effects of the slip lengths of both phases on droplet generation are systematically discussed and summarized. The elongation rate of the thread can be decreased with an increase of slip lengths in both dripping and squeezing regimes, which is beneficial to improve droplet monodispersity. The monodispersity of droplets can deteriorate when the slip length of either phase is small and can be improved by increasing the slip length of the other phase.

Fig. 1. Dispersed phase and continuous phase in contact with the solid wall for different contact angles and a local enlarged view of the contact area of the liquid and solid wall.

Fig. 2. T-junction microchannel geometry for simulation and a sketch of wall velocity slip.

Fig. 3. Grid independence study for Q_d = 0.2 mL h⁻¹ and Q_c = 2 mL h⁻¹ with moderate slip lengths of 2 μm. U_x1 and U_x2 represent the x-velocity along the y-direction at x = 100 μm and x = 150 μm on the symmetry plane, respectively.

Fig. 4. (a) Geometry of the microchannel for slip model validation. (b) Velocity profiles from experiment and simulation along the line of x = 300 μm and z = 15 μm; the x-axis is the velocity normalized by the free stream velocity and the y-axis is the distance from the wall.

Fig. 5. Validation with the experiments of (a) van der Graaf et al. and (b) Garstecki et al. (c) Snapshots of (I) experiments and (II) our simulations with Q_c = 2 mL h⁻¹, L_sc = 0.5 μm, L_sd = 2 μm. (d) Snapshots of experiments (left) and our simulations (right) with L_sc = 1 μm and L_sd = 0.1 μm for (I) Q_d = 0.004 μL s⁻¹, Q_c = 0.028 μL s⁻¹; (II) Q_d = 0.14 μL s⁻¹, Q_c = 0.139 μL s⁻¹; (III) Q_d = 0.05 μL s⁻¹, Q_c = 0.028 μL s⁻¹.

Fig. 6. Velocity distribution at (a) line x = 150 μm along y-direction and (b) line y = 200 μm along the x-direction on the symmetry plane for different L_sc and L_sd with Q_d = 0.2 mL h⁻¹ and Q_c = 2 mL h⁻¹; (c) and (d) represent resistant shear stresses exerted by the slow object (adjacent fluid or wall) corresponding to (a) and (b).

Fig. 7. Generating a droplet in a dripping regime and squeezing regime.

Fig. 8. Dripping regime with Q_d = 0.2 mL h⁻¹ and Q_c = 2 mL h⁻¹. (a) Droplet generation process and (b) pressure drop through the thread with time under different L_sc with L_sd = 0.5 μm. (c) Droplet generation process and (d) pressure drop through the thread with time under different L_sd with L_sc = 0.5 μm.

Fig. 9. Squeezing regime with Q_d = 0.09 mL h⁻¹ and Q_c = 0.18 mL h⁻¹. (a) Droplet generation process and (b) pressure drop through the thread with time under different L_sc with L_sd = 0.5 μm. (c) Droplet generation process and (d) pressure drop through the thread with time under different L_sd with L_sc = 0.5 μm.

Fig. 10. Velocity contours with streamlines and pressure contours of (a) different L_sc with L_sd = 0.5 μm and (b) different L_sd with L_sc = 0.5 μm. (c) Maximum pressure at continuous and dispersed phase inlets and (d) maximum pressure drop across the thread as functions of L_sc and L_sd in a dripping regime with Q_d = 0.2 mL h⁻¹ and Q_c = 2 mL h⁻¹.

Fig. 11. Velocity contours with streamlines and pressure contours of (a) different L_sc when L_sd = 0.5 μm and (b) different L_sd when L_sc = 0.5 μm. (c) Maximum pressure on continuous and dispersed phase inlets and (d) maximum pressure drop across the thread as functions of L_sc and L_sd in dripping regime with Q_d = 0.09 mL h⁻¹ and Q_c = 0.18 mL h⁻¹.

Fig. 12. Droplet surface colored by shear stress magnitude with (a) different L_sc when L_sd = 0.5 μm and (b) different L_sd when L_sc = 0.5 μm for Q_d = 0.2 mL h⁻¹ and Q_c = 2 mL h⁻¹ in a dripping regime.

Fig. 13. Droplet surface colored by shear stress magnitude with (a) different L_sc when L_sd = 0.5 μm and (b) different L_sd when L_sc = 0.5 μm for Q_d = 0.09 mL h⁻¹ and Q_c = 0.18 mL h⁻¹ in a squeezing regime.

Fig. 14. (a) Droplet diameter and (b) thread elongation rate as functions of L_sc and L_sd in a dripping regime with Q_d = 0.2 mL h⁻¹ and Q_c = 2 mL h⁻¹.

Fig. 15. (a) Droplet length and (b) thread elongation rate as functions of L_sc and L_sd in a squeezing regime with Q_d = 0.09 mL h⁻¹ and Q_c = 0.18 mL h⁻¹.

Fig. 16. (a) Three different droplet generation states and (b) phase diagram of droplet generation state as a function of L_sc and L_sd in a dripping regime with Q_d = 0.2 mL h⁻¹and Q_c = 2 mL h⁻¹.