Investigation of microfluidic co-flow effects on step emulsification: Interfacial tension and flow velocities

Colloids and Surfaces A 568 (2019) 381–390

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Colloids and Surfaces A journal homepage: www.elsevier.com/locate/colsurfa

Investigation of microfluidic co-flow effects on step emulsification: Interfacial tension and flow velocities Jiaoyuan Liana, Xiaoye Luob, Xing Huanga, Yuehui Wanga, Zhongbin Xua, , Xiaodong Ruanc, ⁎

T ⁎

a

Institute of Process Equipment, College of Energy Engineering, Zhejiang University, Zheda Road No. 38, Hangzhou, 310027, China College of Mechanical and Electrical Engineering, Hangzhou Polytechnic, Hangzhou 311402, China c The State Key Laboratory of Fluid Power and Mechatronic Systems, Zhejiang University, Hangzhou, 310007, China b

GRAPHICAL ABSTRACT

ARTICLE INFO

ABSTRACT

Keywords: Step emulsification Co-flow Microfluidic Interfacial tension Droplet generation

We propose a novel chip combining co-flow and step emulsification for flexible on-line control of droplet generation. Through this technique, we obtain controllable uniformly sized water in oil droplets. The droplet diameter is controlled between 101 and 1550 μm and the generation frequency ranges from 0.32 to 100 Hz when using the new chip. Compared with conventional step emulsification, droplet dimension is reduced by more than 50% and throughput is increased up to a factor of 50 by using continuous phase co-flow within a certain range in the chip. We also simulate the effects of interfacial tension and flow velocities on emulsification. As continuous phase velocity increases, co-flow gradually replaces the Laplace pressure difference as the driving mechanism in step emulsification. Compared with step-emulsification, the effects of interfacial tension on droplet size and generation frequency greatly change when continuous phase co-flow is added. Coflow causes both droplet diameter and generation frequency to increase with increasing dispersed phase velocity. Meanwhile, the driving mechanism changes from co-flow to Laplace pressure difference as the dispersed phase velocity increases, because of the increase in pinch-off distance. In addition, droplet generation changes from dripping to jetting as dispersed phase velocity increases. These effects of continuous phase coflow on step emulsification are significant, and this technique can be easily used for tunable and highthroughput droplet production.

⁎

Corresponding authors. E-mail addresses: [email protected] (Z. Xu), [email protected] (X. Ruan).

https://doi.org/10.1016/j.colsurfa.2019.02.040 Received 7 December 2018; Received in revised form 8 February 2019; Accepted 17 February 2019 Available online 18 February 2019 0927-7757/ © 2019 Published by Elsevier B.V.

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Nomenclature d D D1 f F h g H l L nˆ p1 p2 P1 P2

q0 q1 q2 s t t1 t2 vc vd

diameter of micro channel [μm] droplet diameter [μm] head diameter [μm] generation frequency [Hz] interfacial force [N] height between plateaus [μm] acceleration of gravity [m·s−2] pinch-off distance [μm] center to center distance of neighbor channels [mm] length of neck and head at breakup point [μm] unit normal [–] pressure of channel outlet without dispersed phase flow [kPa] pressure of plateau outlet without dispersed phase flow [kPa] pressure of channel outlet with co-flow [kPa] pressure of plateau outlet with co-flow [kPa]

flowing pressure without co-flow [kPa] pressure of channel outlet without co-flow [kPa] pressure of plateau outlet without co-flow [kPa] plateau length [mm] time [s] the fist droplet neck pinch-off time [s] the second droplet neck pinch-off time [s] velocity of continuous phase [m·s−1] velocity of dispersed phase [m·s−1]

Greek symbols α γ ηc ηd κ ρ

volume fraction [–] interfacial tension [N·m−1] viscosity of continuous phase [Pa·s] viscosity of dispersed phase [Pa·s] curvature of interface [m−1] density [kg·m−3]

industry [40]. Many characteristics of step emulsification remain unknown, such as the single influence of interfacial tension, contact angle, and device dimensions [41]. Furthermore, the difficulty in precisely controlling parameters causes inaccurate results, thereby hindering the understanding of the underlying mechanisms. Therefore, computational fluid dynamics (CFD) has been used to analyze step emulsification to remedy the limitations of experimental work [42,33,43]. To obtain large throughput in droplet production, methods have been explored to integrate multiple microchannels [44–46]. One such method is micro-capillary film (MCF) technology devised by Hallmark et al [47]. The MCF is a thermoplastic polymer-based film containing an array of continuous and parallel capillaries running along the length. This film is produced by mature extrusion. The MCF has been developed as a microfluidic product [48] because of its structural integrity, high flexibility, reliability and disturbance-resistance. It has also been used in step emulsification for mass production and Janus droplet generation [49]. In this work, we fabricate an easily manipulable step emulsification device using an MCF for monodisperse droplet generation. Increasing the continuous phase co-flow in this device significantly reduces droplet diameter and enhances generation rate. Using CFD, we simulate the important effects of interfacial tension and flow rates on MCF emulsification. The key factors analyzed are the droplet diameter, generation frequency and pressure difference. Continuous phase co-flow has a prominent effect on droplet generation in the step-emulsification device because it enables control of droplet size, which enhances device throughput and is easy to implement.

1. Introduction Tunable and flexible droplet generation methods have attracted increasing attention. Such techniques include T-junctions [1,2], flowfocusing [3,4], and co-flow [5,6]. In addition, there are methods to control droplet size, such as tunable wettability [7] and materials [8,9], and droplet splitting [10]. However, T-junctions and flow-focusing are high-shear methods not suitable for shear-sensitive fluids, and the droplets generated are less monodisperse. Flow-focusing and typical coflow devices are also relatively complicated and difficult to integrate. Furthermore, new manipulation means are either consuming or inflexible or both. Therefore, a better strategy is needed to control monodisperse droplet generation. Step emulsification has attracted wide interest in pharmacy, biology, chemistry, food and cosmetics, for its simplicity and robustness in monodisperse micro-droplet generation [11]. The set-up of this technique is a microchannel module on a plate covered by another plate. The two plates form a step-like terrace with a certain width and create an abrupt opening to a reservoir [12,13]. Droplet formation in step emulsification is due to the interfacial tension between two phases and the Laplace pressure difference resulting from a dimensional change at the terrace boundary [14]. With this technique, many kinds of droplets [15–23], particles [24], bubbles [25] and microcapsules [21] can be generated. Physical parameters such as the section shape, microchannel dimensions [26–30], and types of materials [31,32] have been investigated and optimized for different purposes. Many factors in this technique have also been studied comparatively. Studies on disperse phase flow [27,33], have found that droplet size is almost constant below a critical flow rate and steeply increases above this value. This critical velocity corresponds to the boundary between the dripping and blow-up regimes. Similarly, the average size and monodispersibility of droplets generated by step emulsification are not significantly affected by the flow rate of the continuous phase outside the terrace [20]. Hence, this technique is also famous for mild. Interfacial tension in the step emulsification affects the breakthrough pressure and monodispersibility of the droplets [34]. In addition, surface treatment [35], temperature [36], stability [37,38], and pressure [20] have been researched and many conclusions have been drawn. Despite the many advantages of step emulsification, this technique is still insufficient in controlling droplet size because the droplet size depends strongly on the device dimensions. The device is generally made by etching and is insensitive to flow rate [39]. Because the generation frequency is limited by a single channel, it is challenging to achieve high-throughput droplet generation in step emulsification for

2. Experimental methods 2.1. Materials The MCF used in the chip was made by polymer extrusion in the laboratory. The step emulsification plateau was composed of two glass strips. The oil reservoir was bonded by acrylic plates to guarantee transparency. The flow walls of the plateau were treated with Aquapel (PPG Industries) so they would remain hydrophobic. The dispersed phase was pure water with 0.5% sodium dodecyl sulphate (SDS) (Sinopharm Chemical Reagent) and the continuous phase was silicone oil (PMX-200, 10 cSt, Dow Corning) with 5 wt% RSN 0749 (Dow Corning). The water was injected with peristaltic pumps (SHENCHEN) into the channel, and the silicone oil was injected with a syringe pump (Longer). 382

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2.2. MCF step-emulsification chip setup

3.2. Governing equations

The schematic of the MCF used in this study is shown in Fig. 1(a), and the step emulsification chip fabricated is shown in Fig. 2(b). The MCF was placed between two parallel glass strips. When the plateau length was adjusted to the desired size, the relative position of the MCF and strips was fixed with clips. Thus, a step emulsification chip was set up, for which the plateau length could be easily adjusted. Finally, the chip was submerged into the oil reservoir and the flow direction was kept consistent with the direction of gravity, as shown in Fig. 1(c). The water was pumped into the MCF microchannel using a syringe, and droplets flowed out of the chip and gradually gathered at the bottom of the reservoir because of gravity.

The VOF model tracks the interface between insoluble fluids by solving the fluid momentum equation,

2.3. Experimental procedure

where i denotes the volume fraction of phase i. If i = 1, all the fluid in the cell is in phase i; if i = 0 , there is no phase i in the cell; and if 0 < i < 1, there is an interface between phases in the cell. Hence, the physical parameters of each grid, such as density and viscosity, can be calculated with a weighted volume fraction

t

( v)+

( vv)=

p+

[ ( v +

T

v )] + g + F

(1)

where v is velocity, p is pressure, t is time, η is dynamic viscosity, ρ is density, g is the acceleration of gravity and F is interfacial force. The model calculates the volume fraction of each phase in each grid to determine the distribution of fluid phases according to i

+ vi

t

The experiment was performed with a dispersed phase velocity between 0.03 and 0.3 m·s−1 and the velocity of the continuous phase was from 0 to 5 m·s−1. The densities were 950 kg·m−3 for the continuous phase and 998 kg·m−3 for the dispersed phase. The viscosities were 5 × 10−2 and 1.003 × 10−3 Pa·s for the continuous and dispersed phases, respectively. The interfacial tension between the two phases was 0.008 N·m−1. Drop formation was monitored with a digital microscope (AmScope) and the capture software AMCap (No Danjou). The resulting droplets were photographed under a magnifying glass with a ruler. Finally, the drop size was measured using the image analysis software Image J (National Institutes of Health).

i

i

= 1,

=0

i i

(2)

= ,

i i

=

(3)

The governing mass equation is

t

+

( v)=0

(4)

The gravitational force is generally negligible on the micro-scale. The interfacial force F is calculated via

F =

3. Simulation

i,

(5)

where γ is the interfacial tension and κ the local curvature of the interface which is calculated as

3.1. Model and methods

(6)

nˆ ,

=

To simplify the simulation, three MCF microchannels were studied as shown in Fig. 2(a), and only half of the physical device was modeled in three-dimensions (3D) using the Geometry in ANSYS workbench 17.0 to save computing resources. A hexahedral mesh was used to generate the grids in the ICEM and fine meshes were constructed along the axes of the MCF channels. A coarser mesh was used for the rest of the domain. To evaluate the grid independence, three meshes with element numbers 71691, 251364 and 887175 were constructed. Results shows that the difference between 251364 and 887175 elements is negligible (< 3%). Considering the large computing resources and time consumption, the model with 251364 elements was chosen for the simulations. Fig. 2(b) presents the boundary settings used in the simulation. The default dimensions of the device were d = 200 μm, h = 1.5d, l = 1.2 mm and s = 1.4 mm. The dispersed phase flowed into the chip through inlet 2, and the continuous phase flowed in through inlets 1 and 3. Fluent was used for CFD simulation in this study. The volume of fluid (VOF) method was used to simulate droplet generation with laminar flow (Reynolds number (Re) < 60 both for dispersed and continuous phase flows) [50,51]. The continuum surface force (CSF) model was used to simulate the interfacial tension [52,53]. An outflow boundary was set as the outlet condition for uncertainty in outlet pressure. The pressure difference was determined by a SIMPLE scheme for pressure-velocity coupling and a PRESTO scheme together with a second-order upwind to compute momentum spread [54]. A non-slip wall condition was used for all inner surfaces of the device. The time step for simulation was set to 5 × 10−5 s, to facilitate calculating the generation frequency and other information. With this time step size, the global courant number varies around 1, which indicates good computational stability and ensures a relatively accurate solution. Additionally, the effects of interfacial tension and both phase velocities were each characterized by a single variable with other parameters held constant.

and nˆ is the unit normal vector defined as

nˆ =

i

|

i|

.

(7)

3.3. Characterizing droplet generation Droplet generation can be divided into six stages as illustrated in Fig. 3: (I) disk formation, (II) disk growth, (III) arrival of the disk tip at the terrace outlet, (IV) neck formation, (V) neck pinch-off, and (VI) droplet formation in the reservoir [55,56]. As the dispersed phase flow

Fig. 1. Schematic of (a) MCF, (b) the MCF emulsification chip and (c) the experiment setup. Where, l denotes to the center to center distance of neighbor channel; d denotes to the diameter of micro channel; h denotes to the high between plateaus; and s denotes to the plateau length. 383

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Fig. 2. (a) Physical model of step-emulsification device and (b) boundary conditions for simulation. Where, l corresponds to the center to center distance of neighbor channel; d corresponds to the diameter of micro channel; h corresponds to the height between plateaus; and s corresponds to the plateau length. Inlets 1 and 3 are inlets for continuous phase flow and inlet 2 is the dispersed phase inlet.

To better represent the effect of various factors, we characterize the droplet pinch-off by the neck pinch-off distance H, the length L of the head plus neck before breakup, and the head diameter D1. The droplet diameter D out of the plateau and the generation frequency f directly reflect the effects. The droplet diameter consists of both the head and neck at the moment of breakup. Hence, the factors that affect D1 and L will influence the final droplet size D. Although H does not seem to affect the final droplet size directly, it has some effect on f. More importantly, H can directly affect the transition of the flow regime from dripping to jetting. On the basis of the above, many external factors can be categorized according to different mechanisms. The droplet generation frequency is calculated from the interval between the time of the first droplet pinch-off, t1, and that of the next pinch-off, t2, using f = 1/ (t2 – t1). Fig. 4(a) shows the pressures recorded along the central symmetry line of the chip at stage I. The pressure difference is calculated by subtracting the plateau outlet (z = 4.48 mm) pressure P2 from the MCF outlet (z = 3.01 mm) pressure P1 in Fig. 4.

Fig. 3. Illustration of the droplet generation process of step-emulsification in dripping regime. Where, H denotes to the breakup distance; L denotes to the length of neck and head at breakup point; D1 denotes to the head diameter; and D denotes to the droplet diameter flowing out of plateau. Dashed line represents the plateau boundary.

through the MCF channel continues, a disk starts to form between the two glass strips. When the disk grows and expands to the plateau outlet, a head forms outside the terrace. When the total force of the head outside grows until it equals the force in the plateau, a neck starts to appear. Then, the steady influx of the dispersed phase breaks the equilibrium, causing the head to grow rapidly, and the neck becomes thinner until pinch-off. This is due to the increased pressure difference between the dispersed phase inside and outside the terrace, which is the Laplace force. This process is quite quick and generally finished within 0.05 s in this study. After pinch-off of the neck, a droplet forms instantaneously and is driven by gravity to flow slowly down to the oil reservoir. This process repeats periodically at a frequency f.

4. Results and discussion 4.1. Comparison of experimental and simulation results Compared with literature results [49], in which the diameter of device-generated droplets is 1140 ± 60 μm and the generation frequency is approximately 0.936 Hz with an interfacial tension of 0.008 N·m–1, our simulation results with the same parameters are 1107 μm for the diameter and 0.977 Hz for the frequency. The very small divergence indicates good agreement between the simulation and experiment. In addition, the experimental and simulated droplet generations are compared in Fig. 5(a) and (b), also showing consistency Fig. 4. Pressure difference calculated of (a) step emulsification with continuous phase coflow, (b) assumed co-flowing without center dispersed phase flow and (c) traditional single dispersed phase flow without co-flow. Where, white thick lines denote to the plateau boundary. P1 and q1 is the pressures of z = 3.01 mm in the central symmetry line, and P2 and q2 are the pressures of z = 4.48 mm in the central line of channels, respectively., p1 and p2 are the center pressures of z = 3.01 and z = 4.48 mm in the central line of continuous phase flow channel. When the velocity of continuous phase co-flow equals to zero, p1= p2 = 0. k1 and k2 are coefficients related to the dimensions of the chip.

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Fig. 5. A comparison of CFD simulations with experiment of the droplet formation process. (a) Experimental results in literature [39]. (b) Simulation results in this paper. (c) Experimental results with continuous phase velocity equals to 0.2 ms−1. (d) Simulation results with continuous phase velocity of 0.2 ms−1. White lines in (b) and (d) denote to the plateau boundary. (i) Disk growth in the terrace as stage II. (ii) The tip of the disk is reaching the plateau outlet as stage III. (iii) The tip of the disk flows out of the plateau outlet. (iv) Neck pinches-off as stage V.

between the simulation and experimental results. In this study, comparison experiments were performed for the step emulsification with a continuous phase velocity of 0.2 m·s−1 using the device shown in Fig. 1. The simulation and experimental results in Fig. 5(c) and (d) are very close. The average simulated droplet diameter of 625 μm is slightly smaller than the mean experimental diameter of 680 μm. The discrepancy may be due to several reasons including (among others):

c) The pump flow oscillates, which may yield inaccurate flow rates for both phases in experiment. The consistency between results validates this method of simulating step emulsification within a permissible error range under certain conditions. In addition, the experimental results have a coefficient of variation of 1.4% (for 50 droplets measured), which shows that droplets generated in this device are highly monodisperse.

a) The mesh size of the simulation model is not fine enough to accurately capture the interface. b) The interfacial tension in the simulation is constant although it is dynamic in experiment.

4.2. Effect of interfacial tension Fig. 6 shows the effect that varying the interfacial tension between the two phases has on droplet generation. As the interfacial tension 385

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Fig. 6. The influence of interfacial tension on droplet generation. (a) Influence on droplet diameter; (b) influence on droplet generation frequency; (c) influence on pressure difference between channel outlet and plateau outlet in center symmetric line; and (d) influence on neck pinch-off, bold line a denotes to the plateau boundary, b and c are reference lines.

increases from 0.001 to 0.005 N·m−1, the droplet diameter decreases rapidly. Then the decrease rate declines as the interfacial tension increases from 0.005 to 0.055 N·m−1. For a higher continuous phase velocity of 2 m·s−1, this tendency reverses as shown in Fig. 6(a). The droplet diameter increases at a higher rate as the interfacial tension increases from 0.001 to 0.008 N·m−1, while the increase rate declines as the interfacial tension increases from 0.008 to 0.055 N·m−1. The value is reduced by more than 51.7% compared with step emulsification without co-flow. The droplet generation frequency increases when the interfacial tension increases at a decreasing rate as shown in Fig. 6(b), whereas the trend reverses when neighboring continuous phase co-flow is added, and the frequency decrease rate declines with increasing interfacial tension. In addition, the overall generation frequencies increase significantly with continuous phase co-flow. We see that the smaller the droplet, the higher the generation frequency, because the relationship between droplet diameter and generation frequency can be expressed by Eq. (8) [36], which is based on the law of mass conservation:

f=

3vd d 2 2D3

P1 =

P2 = q2 + k2 p2 = C0 , where P2 and q2 are the pressures at z = 4.48 mm along the central channel line with and without co-flow respectively, p2 is the pressure at z = 4.48 mm along the central line of the continuous phase flow channel, k2 is a coefficient and C0 is a constant. Therefore, the pressure difference before expansion can be expressed as

(8)

P= P1

P2 =

2 2 + h d

C1

(11)

where C1 is a constant related to the velocities of the two phases. Hence, ΔP is proportional to the interfacial tension and has different intercepts for different co-flow velocities. It follows that a greater initial pressure difference leads to smaller droplet size and higher droplet generation frequency. Fig. 6(d) shows the neck pinch-off scenes for two conditions. Compared with droplet generation without continuous phase flow,

P1 = q1 + k1 p1 ,

2 2 + + q0 , h d

(10)

where P1 and q1 are the pressures at z = 3.01 mm along the central symmetry line of the device with and without co-flow, q0 is the flow pressure, p1 is the pressure at z = 3.01 mm along the central line of the continuous phase flow channel, γ is the interfacial tension, k1 is a coefficient, h is the plateau height and d is the diameter of the flow tip at stage I, which is equal to the channel diameter, as shown in Fig. 3. The dimensions h and d are the same for different conditions because the pressure difference is calculated at stage I with nearly the same head diameter. The quantities k1, p1 and q1 are also constants for certain velocities. The pressure out of the plateau, P2, relates to both the dispersed phase and co-flow velocities. For the coincident velocities, P2 is theoretically constant according to

Fig. 6(c) shows the pressure difference between the MCF outlet (z = 3 mm) and plateau outlet (z = 4.48 mm) at stage I. The pressure differences increase with increasing interfacial tension with nearly the same slope in both cases. Hence, continuous phase co-flow mainly affects the intercept of the pressure difference line. Assuming that the pressure follows the flow field superposition principle, the internal pressure of the flow tip in quasi-equilibrium can be estimated via

q1 =

2 2 + + q0 + k1 p1 , h d

(9) 386

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droplet generation with continuous phase flow no longer follows the sequence in Fig. 3 (The phase distributions upstream the channel outlet as co-flow rate of 2.0 ms−1 are caused by the hydrophobic and oil-wet wall of MCF. Since it is used to initialize the device, the oil phase adheres to the wall before dispersed phase flowing in. It is found out that this phase distribution is easier to occur in lower interfacial tension cases for the dispersed phase is easier to deform under external force). The neck pinch-off occurs even before the disk tip reaches the terrace outlet, which means that the droplet generation is no longer mainly depends on the pressure difference because of the change from 2D to 3D. Here the neighboring continuous phase flow field creates the pressure difference, limits the head growth and drags the dispersed phase to form the droplet. In addition, the neck pinch-off distance H, the total length L before pinch-off and the head diameter D1 decrease with increasing interfacial tension without continuous phase flow, whereas H decreases and L and D1 increase with increasing interfacial tension when the continuous phase velocity is 2 m·s−1, as Fig. 6(d) shows. This indicates that the greater the interfacial tension, the closer the pinch-off position is to the channel outlet, regardless of the continuous phase flow. The reason is that the increase of interfacial tension reduces the capillary number Ca (Ca d = d vd/ ). The viscosity ratio of the two phases is constant, therefore, the capillary instability decreases accordingly. Meanwhile, the continuous phase co-flow does not significantly affect the capillary number of the dispersed phase. The total length L before pinch-off and the head diameter D1 are both affected by the balance time of interfacial tension, Laplace force, viscous force, gravitational force as well as drag force exerted by the co-flow. Because the Laplace pressure, as the dominant force, increases with the interfacial tension according to Eq. (9), the time to attain equilibrium decreases with increasing interfacial tension. Accordingly, L and D1 decrease when there is no continuous phase flow. The co-flow drag

becomes the dominant force when a continuous-phase co-flow of 2.0 m·s–1 is introduced into the device. In a double-phase co-flowing system, the drag force is independent of the interfacial tension. Hence, higher interfacial tension leads to longer time for the drag force to reach the magnitude of the interfacial force. Therefore, L and D1 increase with increasing interfacial tension. 4.3. Effect of continuous phase velocity in co-flowing step emulsification Different continuous phase co-flow velocities were simulated, and the results are shown in Fig. 7. Droplet diameter decreases with increasing continuous phase velocity as shown in Fig. 7(a). If the continuous phase velocity reaches 5 m·s−1, the droplet size decreases by 79% for an interfacial tension of 0.008 N·m−1 and 61% for an interfacial tension of 0.055 N·m−1. This is significant for step emulsification. At the same time, the droplet diameter decrease rate also decreases with increasing continuous phase velocity in the range of 0–5 m·s−1, which reveals a limit to the effect of continuous phase co-flow on droplet diameter under certain conditions. Although the shear stress increases with the co-flow velocity, the area over which it acts decreases with decreasing head diameter and total dispersed phase length as shown in Fig. 7(d). Hence, the total drag force increases at a decreasing rate. Furthermore, higher co-flow velocity induces more satellite droplets, thereby reducing the monodispersity of droplet generation. Fig. 7(b) shows that the droplet generation frequency increases with increasing continuous phase velocity, and the lower the interfacial tension, the greater the frequency increase. The maximum frequency increase is a factor of 50 from emulsification without co-flow. This is caused by the restricting and dragging of continuous phase flow so that the neck of the dispersed phase forms and breaks up rapidly. Meanwhile, the dispersed phase is more easily affected by continuous phase

Fig. 7. The influence of continuous phase co-flow velocity on droplet generation. (a) Influence on droplet diameter; (b) influence on droplet generation frequency; (c) influence on pressure difference between channel outlet and plateau outlet in center symmetric line; and (d) influence on neck pinch-off, bold line a denotes to the plateau boundary, b and c are reference lines. 387

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co-flow with lower interfacial tension. Increased droplet generation frequency dramatically enhances the throughput of droplet production. Fig. 7(c) shows the pressure difference between the MCF outlet (z = 3 mm) and plateau outlet (z = 4.48 mm) at stage I. Pressure differences increase with the continuous phase velocity, and the increase rates are nearly the same for different interfacial tensions. Here, P1 is still expressed as Eq. (10), while P2 is related to the neighboring co-flow pressure p2. Assuming a Newtonian fluid flowing between the plates, p2 can be expressed as

p2 = p1

12 c svc h2

,

detachment. This leads to smaller droplets and shorter time spent. This indicates that the pressure difference is the key factor determining the droplet size and generation frequency. The pressure difference here is mainly due to the continuous phase co-flow rather than to the abrupt change of physical structure in the chip. Fig. 7(d) shows the neck pinch-offs for the representative interfacial tensions of 0.008 −1 and 0.035 N·m−1. As the continuous phase velocity increases, D1 decreases apparently owing to the increasing drag and squeeze forces of the neighboring channel co-flow. The greater interfacial tension leads to larger D1 and shorter H because of its enhanced resistance to deformation. In addition, H basically remains unchanged with different continuous phase velocities, which shows that co-flow alone cannot change the droplet generation regime from dripping to jetting. Hence, L mainly depends on the head dimension, which shows that continuous phase co-flow makes the neck become shorter or indistinct. Furthermore, the droplet formation gradually changes from being outside to inside the terrace, which also implies a change in the driving mechanism.

(12)

where ηc is the viscosity of the continuous phase, s is the plateau length as shown in Figs. 1 and 2(a), vc is the continuous phase velocity and h is the plateau height as shown in Figs. 1 and 2(a). Therefore,

P2 = k2 p2 + q2 , P=

2 2 + + (k1 h d

k2 ) p1 +

12k2 c svc h2

+ (q0

q2 ) ,

(14)

4.4. Effect of dispersed phase velocity on co-flowing step emulsification

where k1 and k2 are coefficients related to the channel distance l and plateau length s. Since l and s are small , k1 k2 . For a certain dispersed phase velocity, (q0–q2) is an invariant C2. Therefore, Eq. (14) is reduced to

P=

12k2 c s h2

vc +

2 2 + + C2 . h d

Fig. 8 shows the effect of dispersed phase velocity on step emulsification under a continuous phase velocity of 2 m·s–1. Droplet diameter generally increases with increasing dispersed phase velocity as shown in Fig. 8(a), because the relative velocity gradient decreases with increasing dispersed phase velocity, so the drag force becomes lower and the head grows. The increase of droplet diameter is less than 30% when the dispersed phase velocity increases from 0.03 to 0.3 m·s−1. The lines in Fig. 8(a) can be divided into two sections with different slopes. The turning point indicates a change of droplet generation mechanism. Before the turning point, the main mechanism of droplet formation is

(15)

Hence, as Fig. 7(c) shows, ΔP is proportional to the co-flow velocity for a given interfacial tension and has different intercepts for different interfacial tensions. The greater the pressure difference, the lower the amount of dispersed phase flowing into the droplet prior to

Fig. 8. The influence of dispersed phase velocity on droplet generation. (a) Influence on droplet diameter; (b) influence on droplet generation frequency; (c) influence on pressure difference between channel outlet and plateau outlet in center symmetric line; and (d) influence on neck pinch-off, bold line a denotes to the plateau boundary, b and c are reference lines. 388

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continuous phase squeezing and dragging by the co-flow. After the turning point, there is an increased Laplace pressure difference in addition to the drag and squeeze forces of the continuous phase, because the disk tip reaches the terrace outlet before the neck pinch-off. Meanwhile, the effect of the continuous phase weakens outside the plateau because of the abrupt dimensional change of the terrace boundary. Hence, the Laplace pressure difference becomes the dominant mechanism for generating droplets after the turning point. As the interfacial tension increases, the Laplace effect becomes stronger, and it becomes more difficult to affect continuous phase co-flow. Therefore, the droplet diameter fluctuations under the interfacial tension of 0.035 and 0.055 N·m−1. There are limits on the dispersed phase flow rate, because the dispersed phase becomes a liquid column flowing out of the plateau relatively quickly and forms millimeter droplets outside the chip, which then has a long neck pinch-off distance. Therefore, the situation falls into the jetting regime (with interfacial tensions of 0.008−1 and 0.015 N·m−1 at a flow rate of 0.5 m·s−1). The droplet generation frequency increases almost proportionally with increasing dispersed phase velocity. The lower the interfacial tension, the greater the frequency increase rate. The maximum frequency simulated is 7.7 times the frequency for a dispersed phase velocity of 0.03 m·s−1 and interfacial tension of 0.55 N·m−1, as shown in Fig. 8(b). The reason is that the rapid dispersed phase flow counteracts the tip retraction after the neck pinch-off and shortens the time of each stage of droplet generation in Fig. 3. The pressure difference shown in Fig. 8(c) fluctuates within a certain range with varying dispersed phase velocity. According to Eq. (14), the pressure difference is mainly affected by (q0−q2) when the dispersed phase velocity changes. As the velocity of the dispersed phase increases, q0 increases, while q2 nearly remains unchanged at relatively low dispersed phase velocity and increases after a certain critical velocity. The pressure difference becomes more complicated because of the interaction between the continuous phase and dispersed phase flows, as well as the initial breakup and discontinuity of the dispersed phase in the channel (the relatively large Re of the dispersed phase makes mixing occurred when the two phases meet in the microchannel). These factors and their interactions make the pressure difference fluctuate at stage I. The change of droplet generation mechanism can be observed in Fig. 8(d). As the dispersed phase velocity increases, the tip of dispersed phase starts to reach or leave the plateau boundary, then the pressure difference caused by the dimensional change is activated in the droplet generation. In Fig. 8(a), the droplet diameter curves are mostly crease lines with two slopes, thus, the turning point between slopes indicates the change of generation mechanism. The critical velocity of the dispersed phase increases with the interfacial tension. As the dispersed phase velocity increases, H increases dramatically, which accelerates the frequency of droplet generation on one hand and weakens the effect of the adjacent continuous phase co-flow on the other. Increasing H induces the change of droplet generation regime from dripping to jetting. At the same time, D1 increases with the dispersed phase velocity and with interfacial tension. Greater interfacial tension also yields shorter H, because of enhanced resistance to deformation. The change in L mainly depends on the head dimension because the neck is insignificant for continuous-phase co-flow.

in step emulsification with and without co-flow. Without co-flow, the Laplace pressure difference dominates droplet generation. Hence, the droplet size decreases and generation frequency increases with increasing interfacial tension, because the driving force is increasing. In co-flowing step emulsification, the driving mechanism gradually changes from the Laplace force to the co-flowing drag force as the coflow velocity increases. The droplet size decreases and generation frequency increases because the drag force increases with the continuous phase velocity. Accompanying phenomena are neck shortening before droplet pinch-off and droplet formation in the terrace. With increasing interfacial tension, the droplet size increases and generation frequency decreases because the drag force is independent of interfacial tension. Overall, continuous phase co-flow makes the droplet size and generation frequency increase with dispersed-phase velocity because the decreased velocity gradient decreases the co-flow drag force. Meanwhile, the increasing dispersed phase velocity changes the droplet generation mechanism and regime. Within the scope of this study, the calculated tunable range of droplet size is 101–1550 μm and the generation frequency range researched is 0.32–100 Hz. Therefore, the droplet size can be controlled by roughly adjusting the continuous phase co-flow and carefully regulating the dispersed phase flow rate, besides varying the interfacial tension. The throughput we investigated for a single MCF channel was 3.4–56.6 mL·h–1. Assuming an MCF has 25 microchannels and excluding the channels occupied by the continuous phase, 12 microchannels are available to produce droplets. Then, the device throughput can theoretically be as high as 319.2 mL·h–1 even for a device width of less than 34 mm and height of less than 500 μm. Hence, co-flowing step-emulsification can significantly increase droplet production throughput besides controlling droplet size. Conflict ofinterest The authors declare that they have no conflict of interest. Acknowledgements This work was supported by the National Natural Science Foundation of China (No. 21676244) and the National Basic Research Program of China (Grant No. 2015CB057301). References [1] P. Garstecki, M.J. Fuerstman, H.A. Stone, G.M. Whitesides, Formation of droplets and bubbles in a microfluidic T-junction—scaling and mechanism of break-up, Lab Chip 6 (3) (2006) 437–446, https://doi.org/10.1039/B510841A. [2] Y. Chen, Z. Deng, Hydrodynamics of a droplet passing through a microfluidic Tjunction, J. Fluid Mech. 819 (2017) 401–434, https://doi.org/10.1017/jfm.2017. 181. [3] T. Fu, Y. Ma, H.Z. Li, Breakup dynamics of slender droplet formation in shearthinning fluids in flow-focusing devices, Chem. Eng. Sci. 144 (2016) 75–86, https:// doi.org/10.1016/j.ces.2015.12.031. [4] R. Hood, D. DeVoe, High-throughput continuous flow production of nanoscale liposomes by microfluidic vertical flow focusing, Small 11 (43) (2015) 5790–5799, https://doi.org/10.1002/smll.201501345. [5] C. Cramer, P. Fischer, E.J. Windhab, Drop formation in a co-flowing ambient fluid, Chem. Eng. Sci. 59 (15) (2004) 3045–3058, https://doi.org/10.1016/j.ces.2004.04. 006. [6] R. Xiong, M. Bai, N. Chung, Formation of bubbles in a simple co-flowing microchannel, J. Micromech. Microeng. 17 (5) (2007) 1002–1011, https://doi.org/10. 1088/0960-1317/17/5/021. [7] B. He, X. Huang, H. Xu, Z. Xu, P. Wang, X. Ruan, Creating monodispersed droplets with electrowetting-on-dielectric step emulsification, AIP Adv. 8 (2018) 075113, https://doi.org/10.1063/1.5035374. [8] J. Wang, L. Sun, M. Zou, W. Gao, C. Liu, L. Shang, Z. Gu, Y. Zhao, Bioinspired shapememory graphene film with tunable wettability, Sci. Adv. 3 (6) (2017), https://doi. org/10.1126/sciadv.1700004 e1700004. [9] J. Wang, W. Gao, H. Zhang, M. Zou, Y. Chen, Y. Zhao, Programmable wettability on photocontrolled graphene film, Sci. Adv. 4 (9) (2018), https://doi.org/10.1126/ sciadv.aat7392 eaat7392. [10] Y. Chen, W. Gao, C. Zhang, Y. Zhao, Three-dimensional splitting microfluidics, Lab Chip 16 (8) (2016) 1332–1339, https://doi.org/10.1039/C6LC00186F.

5. Conclusions We have investigated a new step-emulsification technique that combines continuous phase co-flow from adjacent MCF channels. Monodispersed W/O droplets have been obtained using a co-flowing step emulsification chip, and we have used CFD to compensate for experimental limits. Tests have found very good agreement between the experimental and CFD results. Some interesting properties have been revealed and the following conclusions have been drawn. Droplet formation is dominated by different mechanisms and forces 389

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