Numerical simulations of wall contact angle effects on droplet size during step emulsification

Abstract

Terrace-based microfluidic devices are currently used to prepare highly monodisperse micro-droplets. Droplets are generated due to the spontaneous pressure drop induced by the Laplace pressure, and so the flow rate of a dispersed phase has little effect on droplet size. As a result, control over the droplet is limited once a step emulsification device has been fabricated. In this work, a terrace model was established to study the effect of the wall contact angle on droplet size based on computational fluid dynamics simulations. The results for contact angles from 140° to 180° show that a lower contact angle induces wall-wetting, increasing the droplet size. The Laplace pressure equations for droplet generation were determined based on combining pressure change curves with theoretical analyses, to provide a theoretical basis for controlling and handling droplets generated through step emulsification.

Fig. 1. A three-dimensional schematic diagram of the step model used in the current simulation.

Fig. 2. The grid partition and boundary settings in the model. (I) Inlet, the entrance for the dispersed phase. (II) Wall, the interface between the fluid and the terrace device. (III) Symmetry. (IV) Outlet, the reservoir filled with continuous phase.

Fig. 3. A comparison of CFD simulations with experimental results. (I) Beginning of the disk expansion in the terrace. (II) The tip of the dispersed phase reaches the terrace outlet. (III) Necking occurs. (IV) Droplet detachment.

Fig. 4. Effects of the static contact angle on droplet diameter and diagrams showing terrace wetting: (I) initialization conditions for the simulation, (II) θ ≤ 135, (III) θ = 140°, (IV) θ = 145°, (V) θ = 150°, (VI) θ = 160°, (VII) θ = 180°.

Fig. 5. Several groups of variation in droplet diameter with terrace widths at different contact angles.

Fig. 6. The pressure along the symmetric axis indicated by the dashed line. (a) Pressure at a contact angle of 140° at (I) 0.08 ms, (II) 2.16 ms, (III) 3.28 ms, and (IV) 4.0 ms. (b) Pressure at a contact angle of 180° at (I) 0.1 ms, (II) 1.25 ms, (III) 1.85 ms, and (IV) 2.4 ms.

Fig. 7. Parameters used in CFD droplet simulation for step emulsification. (I) and (II) are the view from the x–z plane, and (III) is the view from the y–z plane.

Fig. 8. Variations in pressure at one point. (a) Pressure at a contact angle of 140° at T₁ = 3.38 ms. (b) Pressure at a contact angle of 180° at T₂ = 1.86 ms. The point (1,0,117) was chosen to obtain a consistent droplet fracture position.