Computational model of the microfluidic device
Prior to experiments, the performance of the dual-nozzle droplet-generating microfluidic device was simulated using CFD model. For this purpose, the two phase flow with level set function of COMSOL (5.1, COMSOL Inc., USA) was used as previously suggested [29]. The governing equations for the simulation are the Navier–Stokes equation and the continuity equation for the conservation of momentum and mass:
$$\uprho\frac{{\partial {\mathbf{v}}}}{\partial t} +\uprho\left( {{\mathbf{v}} \cdot \nabla } \right){\mathbf{v}} = \nabla \cdot \left[ { - p{\mathbf{I}} + \mu \left( {\nabla {\mathbf{v}} + \left( {\nabla {\mathbf{v}}} \right)^{T} } \right)} \right] + {\mathbf{F}}_{{{\mathbf{st}}}}$$
$$\nabla \cdot {\mathbf{v}} = 0$$
where v, p, and F
st
are the velocity vector, pressure, and the surface tension, respectively. The density and dynamic viscosity is denoted by ρ and μ, respectively. The position of the phase interface can be tracked using the level set function as a transportation equation:
$$\frac{\partial \phi }{\partial t} + {\mathbf{v}} \cdot \nabla \phi = \gamma \nabla \cdot \left( { - \phi \left( {1 - \phi } \right)\frac{\nabla \phi }{{\left| {\nabla \phi } \right|}} + \varepsilon \nabla \phi } \right)$$
where ϕ is the level set function, and γ and ɛ are numerical stabilization parameters. The following equations were used for the Multiphysics coupling of density and viscosity:
$$\uprho =\uprho_{1} + \left( {\uprho_{2} -\uprho_{1} } \right)\phi$$
$$\upmu =\upmu_{1} + \left( {\upmu_{2} -\upmu_{1} } \right)\phi$$
For the simulations, a value of ρ1 = 800 kg/m3 and dynamic viscosity of μ1 = 0.01 Pa s was used. For water, the values were ρ2 = 1000 kg/m3 and μ2 = 0.001 Pa s, respectively. Furthermore, all fluids were assumed to be incompressible, homogenous Newtonian fluids. A model of the microfluidic droplet dispensing device was constructed based on the AutoCAD drawing used for device fabrication. The walls were defined as wetted boundaries with a contact angle of 120° for the water phase and no pressure was set at the outlet of the microfluidic device.
Fabrication of the dual-nozzle microfluidic device
A microfluidic dual-nozzle device consisting of two inlets for each nozzle was designed using AutoCAD (Autodesk, USA) and printed onto photomasks. All inlet channels were designed with a width of 70 µm with the exception of the water inlet in the first nozzle which had a width of 100 µm. The design from the masks was transferred to silicon wafers (Wangxing Silicon-Peak Electronics, China) using a standard soft-lithography process as shown previously [30]. Briefly, silicon wafers are cleaned using a wafer washing system and afterwards dried for 5 min at 200 °C on a hotplate. 5 mL of SU-8 50 photoresist (Microchem Corp., USA) was spin-coated onto the silicon wafers at 3000 rpm for 60 s, resulting in a 40 µm photoresist layer. The spin-coated wafer was soft-baked at 65 °C for 5 min and afterwards further heat treated at 95 °C for 15 min on a hotplate to evaporate the solvent. After UV-exposure for 10 s at an intensity of 20 mW/cm2, the wafers were baked at 65 °C for 1 min, followed by heat treatment at 95 °C for 4 min on a hotplate. The silicon masters were developed using SU-8 developer (Microchem Corp., USA) and dried with air. Poly(dimethylsiloxane) (PDMS, Dow Corning, USA) was poured onto the silicon wafers. After curing in an oven at 80 °C, the PDMS was peeled off from the silicon wafer and was subsequently bonded into glass slides using oxygen plasma.
Droplet dispensing experiments
Syringe pumps (PHD 2000, Harvard Apparatus, USA) were connected to the four inlets of the microfluidic device using tygon tubing (Sigma Aldrich, USA) to conduct droplet dispensing experiments. For experiments, de-ionized water (DI water) was used as the continuous phase and mineral oil (M5904, Sigma Aldrich, USA) as the dispersed phase. For experiments, all flow rates were systematically varied between 10 and 50 µL/min in increments of 10 µL/min, in accordance with the values previously used for numerical simulations. Images of the resulting droplets were captured using an inverted microscope (Olympus IX73, Japan) and were also analyzed using Image J (National Institute of Health, USA) regarding their droplet diameter and the distance between droplets.
