3.1 FCOMD system for generation of monodispersed droplet
To develop a simple method for preparation of monodispersed droplet in the nanoliter to picolitre, a floating capillary based open microfluidic device (FCOMD) is constructed by inserting a capillary with an oblique angle (α) into the continuous phase (CP) (Fig. 1a). The CP is kept static in a small silicon container. While, the dispersed phase (DP) flowed through the capillary into the CP with the assistance of a syringe pump, and then broke at the tip of the capillary (inset in Fig. 1a). Differ from the capillary with a flat outlet end(Hu et al. 2017), there is no external driving force other than fluid driving force and gravity to assist the segmentation of DP into droplets in the FCOMD. The capillary with an oblique angel could also be integrated for an array to improve the droplet generating frequency. Figure 1b is an optical image of droplet generated by FCOMD based on a capillary with α = 60º when the flow rate of DP (Q) is 0.5 µL/min. The obtained emulsion droplets are in the size of 105 µm with coefficient of variation (CV) of 1.27% (Fig. 1c and 1d), showing excellent monodispersity. In this work, oblique angle (α) was regarded as a critical parameter for generating droplets. Moreover, we also analyzed the mechanism of generating droplets in FCOMD, which would help us predict the diameter of the droplet.
3.2 Controlling Parameters for the Monodispersed Droplet Generation
Comprehensive experiments reveal that the size of the generated droplet generated by microfluidic is affected by the device size, fluid properties and flow rate (Aliabouzar et al. 2023; Pan et al. 2022; Thao Minh et al. 2022; Tianyi Zhang et al. 2023). In this FCMOD system, the device size mainly contains oblique angle (α) and the inner diameter (I.D.). The influence of α on the diameter of droplet (D) was firstly investigated (Fig. 2a). A series of capillaries (I.D.=50 µm, O.D.=365 µm) with α (15°, 30°, 45°, 60° and 75°) were respectively used to construct FCMOD. The flow rate of DP (Q) was change from 0.005 to 5.0 µL/min in all experiments. As shown in Fig. 2a, when Q is in the range of 0.005-0.5 µL/min, the order of capillaries with different α for generating droplets with certain diameter under the same Q is 45°>30°>60°>15°>75°: as the angle varies from 15° to 45°, with the flow rate of 0.5 µL/min, the diameter of droplet increased gradually from 122.0, 142.9, to 243.7 µm. When the angle of 45° to 75°, with the flow rate of 0.5 µL/min, the diameter of droplet decreased gradually (Fig. S1a). It should be noted that the tip of the capillary was in contact with the bottom of the glass poll. And when the tip is far away from the bottom, D decreases with the increasing of α (Fig. S1b). The comparison between the effect of α on D of the tip contact the container’s bottom or not indicates that the bottom surface squeezes the droplets, making it easier for the droplet to leave the capillary. While, the effect of Q on D is divided into two situations: in regard to a capillary with certain α, the influence of Q on D is almost negligible when Q is in the range of 0.005-0.5 µL/min; then D increases with the increasing of Q.
We then investigated the influence of the other parameter of device size, I.D., on D, whose result is shown in Fig. 2b. The capillaries with different I.D.s have identical angles of 60º. Similar to the effect of oblique angle, D increases with the increasing of I.D. when Q is in the range of 0.005-0.1 µL/min; as Q continuous increasing, the effect of I.D. on D is no longer so regular attributed to the transition of generating mode from dripping to jetting. The minimum Q for the droplet generated mode change for capillary with different I.D. (25/50/75/100 µm) is respectively 0.5, 1, 1.2, 1.5 µL/min. The droplet generating transition leads to the formation of droplets with multi-diameters (Fig. S2).
A capillary (I.D.=50 µm, α = 60º) was used to investigate the influence of fluid viscosity of CP (ηCP) on the D of droplet. The ηCP was adjusted in the range of 0.89–17.96 mPa·s (at 25°C) by adding different amounts of glycerol to hexadecane dissolved with 3.0% Span 80. As shown in Fig. 2c, when Q is remained at 0.5 µL/min, D increases from 117.6 to 168.7 µm with the increasing of ηCP. As is well known that ηCP is an important part of dimensionless number of capillary (Zhou et al. 2022). Ca is regarded as the most useful dimensionless number to describe the multiphase microfluidic flow phenomena including flow formation and sizing (J. Wang et al. 2015). Ca increases with the increasing of ηCP, leading to the formation of monodispersed droplet. Therefore, it is more difficult to pinch-off the DP with high viscosity for droplet generation than that with low viscosity.
In addition, the influence of the flow rate (Q) on D was investigated when the tip of capillary was far away from the bottom of the container (Fig. 2d). A capillary (I.D.=50 µm) with α = 60º was used for FCMOD system. When Q was ≤ 0.5 µL/min, D was almost remained 105 µm, indicating that D is insensitive to Q. When Q changed from 0.5 to 5 µL/min, D increased from 120 to 190 µm as expected. When Q was exceeded the threshold of passive emulsification, D was sensitive to Q, and increased rapidly with Q which is also attributed to Ca related to ν.
3.3 The Mechanism of the Droplet Formation
Droplet formation is the result of interfaces deform and then pinch off due to a dynamic response to the integration of the different phase and their interactions. From an energetic perspective, the breakup of the DP for generation of droplets is an energy input process because excess energy is provided and converted into the interfacial energy in the emulsions finally produced (Taoxian Zhang et al. 2023). To understand the breakup of DP into droplets in the FCOMD device, microfluidic experiments and theoretical modeling was combined. Droplets are created by injecting the DP through a circular capillary with an oblique angle (α) into a reservoir containing an immiscible CP (Fig. 1a). Figure 3a shows OM images of the experiment together with corresponding schematic illustration of the cross-sections. At the beginning of this process, the head of the DP flowed in capillary is convex due to the hydrophilic property of capillary (Fig. 3ai). Once the convex reaches the end of the FCOMD device, it expands into the reservoir forming a bulb (Fig. 3aii). This bulb gradually becomes bigger and still remains connected to the thread in the end of the capillary through a neck (Fig. 3aiii). The width of the neck continuously decrease until the thread finally ruptures, leading to the formation of a droplet (Figs. 3aiv-v, Movie S1).
The driving force of the monodispersed droplet formed from the neck rupturing in FCOMD is the combination of difference in Laplace pressure (ΔP) between the neck (Pn) and the droplet precursor (Pd) and the supporting force of the inner bottom of the container to the droplet precursor (Fig. 3b). According to André R. Studart(Eggersdorfer et al. 2018), Pn and Pd is respectively given by:
P n= P0+\(\frac{\text{γ}}{{\text{R}}_{\text{n}}}\) (1)
P d= P0+\(\frac{\text{γ}}{{\text{R}}_{\text{d}}}\) (2)
Therefore, ΔP is expressed by:
ΔP = Pn - Pd = γ( \(\frac{\text{1}}{{\text{R}}_{\text{n}}}\text{-}\frac{\text{1}}{{\text{R}}_{\text{d}}}\text{)}\) (3)
When the flow rate is relatively low (Q < 1.0 µL/min), the formation mode of monodispersed droplet formation is dripping. At this time, ΔP is the dominant triggers due to that the droplet precursor would not touch the inner bottom of the glass vial (the left schematic drawing in Fig. 3b). After the neck appearing, Rn decreases and Rd increase, leading to that Pn > Pd, which would lead to the droplet pinch off the neck. If the flow rate is too high (Q ≥ 1.0 µL/min), the neck would not rupture before the droplet percussor touching the inner bottom of the glass vial. Instead of, the combinate effect of ΔP and Fb makes the droplet pinch off. And the formation mode is jetting, results in bigger droplets with varying sizes. And Fb is influence by α, exhibiting the rule of Fb decreases with α, because that the spacing squeezing (I.D.•tanα) increases with α.
And we conclude the phase diagram for transition from dripping to jetting as a function of oblique angle (α) and capillary number (Ca). Ca is calculated according to
Ca=\(\frac{{}_{CP}v}{\sigma }\) (4)
where ν and σ are respectively the fluidic speed and interfacial tension between CP and DP. The calculation of ν is followed by the law of conservation of mass between input and output of the capillary, ignored the fluid resistance in the FCOMD device (Fig. S3). As shown in Fig. 3c, dripping region is identified when Ca was in the range of from 10− 2-1; and jetting occurs when Ca is greater than 1. This is consistent with the previous reported droplet generation in capillary-based device (P. Zhu and Wang 2017). The transition between dripping and jetting can be achieved by change the DP capillary number and oblique angle.
3.3 Integrated FCOMD Device for High Throughput Droplet Generation
Throughput is an important evaluated parameters for droplet-based applications, especially industrial application. To obviously improve the throughput, FCOMD shows potential for high-throughput droplet generation. ten capillaries (I.D.=50 µm) with α = 60° were fixed in a flat needle with equip-distance for forming integrated FCOMD (Fig. 4a1). Then the integrated FCOMD is connected with syringe, and the fluids of DP and CP are respectively the same with a capillary which is shown in Fig. 1. From the evidence of OM images exhibited in Fig. 4a2 and Movie S2, the integrated FCOMD can be applied for generating droplets with good monodispersity. When Q is 0.5 µL/min, the generated droplets are with D of 105 ± 5µm, whose CV is 1.35% (Fig. 4a3 and 4a4). The frequency of droplet (CV = 1.35%) generation for the integrated FCOMD is 120 Hz, which is 10 times more than that of a capillary FCOMD. We applied the same strategy to integrate 16 PDMS microchannels for forming a PDMS-based FCOMD array schematic shown in Fig. 4b1. The oblique angle (α = 60°) of the PDMS microchannels were obtained by cutting the outlet of the channel using a precision manual press. The width and depth of the microchannels are respectively 75 µm and 64 µm (Fig. 4b2). When Q is 1.05 µL/min, the generated water in fluorocarbon oil (W/O) droplets are with D of 142 ± 2µm, whose CV is 1.45% (Fig. 4b3 and 4b4). And, the production yield is 242 Hz (Movie S3). It is proven that higher throughput could be realized by integrating more capillaries in one FCOMD. According to the results shown in Fig. 2, monodispersed droplets can be formed by capillaries contact the surface of container or not. Therefore, although the capillaries are bend and shake by CP due to the diversity between the hydraulic pressure and gravity, this integrated device exhibits good stability for generating monodispersed emulsion droplets. In a word, the FCOMD have great potential for high-throughput droplet-based applications by on-demand integrating different numbers of capillary.
3.4 FCOMD for Creation of Droplets for Assembly
Droplet microfluidic also has been widely applied in soft-material assembly by three-dimensional confinement of droplet (J. Wang et al. 2019; Xie et al. 2023). To verify the versatility and reliability of the FCOMD, DP of colloidal dispersion or liquid crystal is respectively used (Fig. 5). The geometrical parameters of the capillary of the used FCOMD are I.D.= 50 µm and α = 60º. Firstly, DP of 20 wt% SiO2 spherical nanoparticles (the radius is 50 nm) dispersed in water was injected in the capillary for generating W/O emulsions (Fig. 5a-b).
The CP is 25 wt% Span 80 in hexadecane. After collected, the W/O emulsions were kept static for 2–4 hours following a procedure of washing and evaporation. During this duration, the dispersed nanoparticles were concentrated and eventually formed an ordered assembly under the combined effect of surface tension and capillary forces (J. Wang et al. 2017; Y. Wang et al. 2021). The obtained assembled microspheres were characterized by scanning electronic microscope (SEM). The results shown in Fig. 5c-d, the diameter of assembled microspheres is approximately 72 µm, which is much smaller than that of the corresponding emulsion droplets (103 µm). From the enlarged SEM image inset in Fig. 5d, hexagonal condensed packing (hcp) structure was obtained. These results are also the evidence of the FCOMD is suitable for generating W/O droplets without any surface modification. Moreover, FCOMD was used to form liquid crystal droplets (Fig. 5e-f) when the CP and DP are respectively 2.8% SDS aqueous solution and nematic liquid crystal 5CB. D of the 5CB droplet is 114 µm with CV ≤ 2% when Q = 0.05 µL/min. When observed under polarized optical microscope (Fig. 5f), the 5CB droplets show clear typical four-leaf-clover patterns according to the vertical anchoring by surfactant of SDS in the confined spherical droplets (Xie et al. 2022). The above results illustrate that the FCOMD could be widely applied for different fluidic materials, including oil, water, liquid crystal, colloidal dispersion, etc, expanding the related application in material science, foods, pharmaceuticals and cosmetics.
3.5 FCOMD for Double Emulsion Generation
Double emulsion is a complex hierarchical system containing smaller droplets inside, which can be generated on demand for encapsulation and release-based application. The FCOMD could be used for generating double emulsions, showing good flexibility. Be different the former device, FCOMD for double emulsion is composed of two capillary tubes with different I.D. and O.D. but the same α. The geometrical parameters of the inner and outer capillaries are respectively I.D.=100 µm and 0.9 mm, O.D.=365 µm and 1.2 mm. And the end of oblique angle is aligned each other. Cholesteric liquid crystal is the inner phase. Middle phase is consisted of water and poly (ethylene glycol) diacrylate (PEGDA), and the outer phase is mineral oil containing 3.0 wt% ABIL EM90 (Pan et al. 2022). Because the combined effect of viscosity and interfacial tension of phasic material, a mechanical vibrator was added to the FCOMD for formation of LC/W/O double emulsions (Fig. 6a). It should be pointed that the inner capillary is longer than the outer capillary which is evidenced by Fig. 6b. Uniform LC/W/O double emulsions could be obtained when the inner capillary is longer that the outer capillary (Fig. 6bi); whereas Janus droplets with separated LC and oil were obtained (Fig. 6bii). In theoretical, the generating frequency was controlled by both the flow rate of inner phase and middle phase (Qi+m), and vibration frequency. In our experiments, the vibration frequency was maintained at 1 Hz. The effect of Q on the formation of the double emulsion droplets was investigated in detail. As shown in Fig. 6c, double emulsion could be formed when Qi and Qm is in the decent range. D increases with the increasing of Qi+m (Fig. 6d). The successfully generating double emulsion demonstrates excellent flexibility of the FCOMD devices, indicating technological improvement of the droplet-based microfluidic device without sophisticated microfabrication.